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Credit assignment in heterogeneous multi-agent reinforcement learning for fully cooperative tasks

• Published: 26 October 2023
• Volume 53 , pages 29205–29222, ( 2023 )

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• Kun Jiang 1 , 2 ,
• Wenzhang Liu 3 ,
• Yuanda Wang 1 ,
• Lu Dong 4 &
• Changyin Sun   ORCID: orcid.org/0000-0001-9269-334X 1 , 2  

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Credit assignment poses a significant challenge in heterogeneous multi-agent reinforcement learning (MARL) when tackling fully cooperative tasks. Existing MARL methods assess the contribution of each agent through value decomposition or agent-wise critic networks. However, value decomposition techniques are not directly applicable to control problems with continuous action spaces. Additionally, agent-wise critic networks struggle to differentiate the distinct contributions from the shared team reward. Moreover, most of these methods assume agent homogeneity, which limits their utility in more diverse scenarios. To address these limitations, we present a novel algorithm that factorizes and reshapes the team reward into agent-wise rewards, enabling the evaluation of the diverse contributions of heterogeneous agents. Specifically, we devise agent-wise local critics that leverage both the team reward and the factorized reward, alongside a global critic for assessing the joint policy. By accounting for the contribution differences resulting from agent heterogeneity, we introduce a power balance constraint that ensures a fairer measurement of each heterogeneous agent’s contribution, ultimately promoting energy efficiency. Finally, we optimize the policies of all agents using deterministic policy gradients. The effectiveness of our proposed algorithm has been validated through simulation experiments conducted in fully cooperative and heterogeneous multi-agent tasks.

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School of Automation, Southeast University, Nanjing, 210096, Jiangsu, China

Kun Jiang, Yuanda Wang & Changyin Sun

Peng Cheng Laboratory, Shenzhen, 518955, Guangdong, China

Kun Jiang & Changyin Sun

School of Artificial Intelligence, Anhui University, Hefei, 230039, Anhui, China

Wenzhang Liu

School of Cyber Science and Engineering, Southeast University, Nanjing, 211189, Jiangsu, China

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Jiang, K., Liu, W., Wang, Y. et al. Credit assignment in heterogeneous multi-agent reinforcement learning for fully cooperative tasks. Appl Intell 53 , 29205–29222 (2023). https://doi.org/10.1007/s10489-023-04866-0

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MINI REVIEW article

Solving the credit assignment problem with the prefrontal cortex.

• Department of Psychology, University of California, Los Angeles, Los Angeles, CA, United States

In naturalistic multi-cue and multi-step learning tasks, where outcomes of behavior are delayed in time, discovering which choices are responsible for rewards can present a challenge, known as the credit assignment problem . In this review, I summarize recent work that highlighted a critical role for the prefrontal cortex (PFC) in assigning credit where it is due in tasks where only a few of the multitude of cues or choices are relevant to the final outcome of behavior. Collectively, these investigations have provided compelling support for specialized roles of the orbitofrontal (OFC), anterior cingulate (ACC), and dorsolateral prefrontal (dlPFC) cortices in contingent learning. However, recent work has similarly revealed shared contributions and emphasized rich and heterogeneous response properties of neurons in these brain regions. Such functional overlap is not surprising given the complexity of reciprocal projections spanning the PFC. In the concluding section, I overview the evidence suggesting that the OFC, ACC and dlPFC communicate extensively, sharing the information about presented options, executed decisions and received rewards, which enables them to assign credit for outcomes to choices on which they are contingent. This account suggests that lesion or inactivation/inhibition experiments targeting a localized PFC subregion will be insufficient to gain a fine-grained understanding of credit assignment during learning and instead poses refined questions for future research, shifting the focus from focal manipulations to experimental techniques targeting cortico-cortical projections.

Introduction

When an animal is introduced to an unfamiliar environment, it will explore the surroundings randomly until an unexpected reward is encountered. Reinforced by this experience, the animal will gradually learn to repeat those actions that produced the desired outcome. The work conducted in the past several decades has contributed a detailed understanding of the psychological and neural mechanisms that support such reinforcement-driven learning ( Schultz and Dickinson, 2000 ; Schultz, 2004 ; Niv, 2009 ). It is now broadly accepted that dopamine (DA) signaling conveys prediction errors, or the degree of surprise brought about by unexpected rewards, and interacts with cortical and basal ganglia circuits to selectively reinforce the advantageous choices ( Schultz, 1998a , b ; Schultz and Dickinson, 2000 ; Niv, 2009 ). Yet, in naturalistic settings, where rewards are delayed in time, and where multiple cues are encountered, or where several decisions are made before the outcomes of behavior are revealed, discovering which choices are responsible for rewards can present a challenge, known as the credit assignment problem ( Mackintosh, 1975 ; Rothkopf and Ballard, 2010 ).

In most everyday situations, the rewards are not immediate consequences of behavior, but instead appear after substantial delays. To influence future choices, the teaching signal conveyed by DA release needs to reinforce synaptic events occurring on a millisecond timescale, frequently seconds before the outcomes of decisions are revealed ( Izhikevich, 2007 ; Fisher et al., 2017 ). This apparent difficulty in linking preceding behaviors caused by transient neuronal activity to a delayed feedback has been termed the distal reward or temporal credit assignment problem ( Hull, 1943 ; Barto et al., 1983 ; Sutton and Barto, 1998 ; Dayan and Abbott, 2001 ; Wörgötter and Porr, 2005 ). Credit for the reward delayed by several seconds can frequently be assigned by establishing an eligibility trace, a molecular memory of the recent neuronal activity, allowing modification of synaptic connections that participated in the behavior ( Pan et al., 2005 ; Fisher et al., 2017 ). On longer timescales, or when multiple actions need to be performed sequentially to reach a final goal, intermediate steps themselves can acquire motivational significance and subsequently reinforce preceding decisions, such as in temporal-difference (TD) learning models ( Sutton and Barto, 1998 ).

Several excellent reviews have summarized the accumulated knowledge on mechanisms that link choices and their outcomes through time, highlighting the advantages of eligibility traces and TD models ( Wörgötter and Porr, 2005 ; Barto, 2007 ; Niv, 2009 ; Walsh and Anderson, 2014 ). Yet these solutions to the distal reward problem can impede learning in multi-choice tasks, or when an animal is presented with many irrelevant stimuli prior to or during the delay. Here, I only briefly overview the work on the distal reward problem to highlight potential complications that can arise in credit assignment based on eligibility traces when learning in multi-cue environments. Instead, I focus on the structural (or spatial ) credit assignment problem, requiring animals to select and learn about the most meaningful features in the environment and ignore irrelevant distractors. Collectively, the reviewed evidence highlights a critical role for the prefrontal cortex (PFC) in such contingent learning.

Recent studies have provided compelling support for specialized functions of the orbitofrontal (OFC) and dorsolateral prefrontal (dlPFC) cortices in credit assignment in multi-cue tasks, with fewer experiments targeting the anterior cingulate cortex (ACC). For example, it has seen suggested that the dlPFC aids reinforcement-driven learning by directing attention to task-relevant cues ( Niv et al., 2015 ), the OFC assigns credit for rewards based on the causal relationship between trial outcomes and choices ( Jocham et al., 2016 ; Noonan et al., 2017 ), whereas the ACC contributes to unlearning of action-outcome associations when the rewards are available for free ( Jackson et al., 2016 ). However, this work has similarly revealed shared contributions and emphasized rich and heterogeneous response properties of neurons in the PFC, with different subregions monitoring and integrating the information about the task (i.e., current context, available options, anticipated rewards, as well as delay and effort costs) at variable times within a trial (upon stimulus presentation, action selection, outcome anticipation, and feedback monitoring; ex., Hunt et al., 2015 ; Khamassi et al., 2015 ). In the concluding section, I overview the evidence suggesting that contingent learning in multi-cue environments relies on dynamic cortico-cortical interactions during decision making and outcome valuation.

Solving the Temporal Credit Assignment Problem

When outcomes follow choices after short delays (Figure 1A ), the credit for distal rewards can frequently be assigned by establishing an eligibility trace, a sustained memory of the recent activity that renders synaptic connections malleable to modification over several seconds. Eligibility traces can persist as elevated levels of calcium in dendritic spines of post-synaptic neurons ( Kötter and Wickens, 1995 ) or as a sustained neuronal activity throughout the delay period ( Curtis and Lee, 2010 ) to allow for synaptic changes in response to reward signals. Furthermore, spike-timing dependent plasticity can be influenced by neuromodulator input ( Izhikevich, 2007 ; Abraham, 2008 ; Fisher et al., 2017 ). For example, the magnitude of short-term plasticity can be modulated by DA, acetylcholine and noradrenaline, which may even revert the sign of the synaptic change ( Matsuda et al., 2006 ; Izhikevich, 2007 ; Seol et al., 2007 ; Abraham, 2008 ; Zhang et al., 2009 ). Sustained neural activity has been observed in the PFC and striatum ( Jog et al., 1999 ; Pasupathy and Miller, 2005 ; Histed et al., 2009 ; Kim et al., 2009 , 2013 ; Seo et al., 2012 ; Her et al., 2016 ), as well as the sensory cortices after experience with consistent pairings between the stimuli and outcomes separated by predictable delays ( Shuler and Bear, 2006 ).

Figure 1 . Example tasks highlighting the challenge of credit assignment and learning strategies enabling animals to solve this problem. (A) An example of a distal reward task that can be successfully learned with eligibility traces and TD rules, where intermediate choices can acquire motivational significance and subsequently reinforce preceding decisions (ex., Pasupathy and Miller, 2005 ; Histed et al., 2009 ). (B) In this version of the task, multiple cues are present at the time of choice, only one of which is meaningful for obtaining rewards. After a brief presentation, the stimuli disappear, requiring an animal to solve a complex structural and temporal credit assignment problem (ex., Noonan et al., 2010 , 2017 ; Niv et al., 2015 ; Asaad et al., 2017 ; while the schematic of the task captures the challenge of credit assignment, note that in some experimental variants of the behavioral paradigm stimuli disappeared before an animal revealed its choice, whereas in others the cues remained on the screen until the trial outcome was revealed). Under such conditions, learning based on eligibility traces is suboptimal, as non-specific reward signals can reinforce visual cues that did not meaningfully contribute, but occurred close, to beneficial outcomes of behavior. (C) On reward tasks, similar to the one shown in (B) , the impact of previous decisions and associated rewards on current behavior can be assessed by performing regression analyses ( Jocham et al., 2016 ; Noonan et al., 2017 ). Here, the color of each cell in a matrix represents the magnitude of the effect of short-term choice and outcome histories, up to 4 trials into the past (red-strong influence; blue-weak influence on the current decision). Top: an animal learning based on the causal relationship between outcomes and choices (i.e., contingent learning). Middle: each choice is reinforced by a combined history of rewards (i.e., decisions are repeated if beneficial outcomes occur frequently). Bottom: the influence of recent rewards spreads to unrelated choices.

On extended timescales, when multiple actions need to be performed sequentially to reach a final goal, the distal reward problem can be solved by assigning motivational significance to intermediate choices that can subsequently reinforce preceding decisions, such as in TD learning models ( Montague et al., 1996 ; Sutton and Barto, 1998 ; Barto, 2007 ). Assigning values to these intervening steps according to expected future rewards allows to break complex temporal credit assignment problems into smaller and easier tasks. There is ample evidence for TD learning in humans and other animals that on the neural level is supported by transfer of DA responses from the time of reward delivery to preceding cues and actions ( Montague et al., 1996 ; Schultz, 1998a , b ; Walsh and Anderson, 2014 ).

Both TD learning and eligibility traces offer elegant solutions to the distal reward problem, and models based on cooperation between these two mechanisms can predict animal behavior as well as neuronal responses to rewards and predictive stimuli ( Pan et al., 2005 ; Bogacz et al., 2007 ). Yet assigning credit based on eligibility traces can be suboptimal when an animal interacts with many irrelevant stimuli prior to or during the delay (Figure 1B ). Under such conditions sensory areas remain responsive to distracting stimuli and the arrival of non-specific reward signals can reinforce intervening cues that did not meaningfully contribute, but occurred close, to the outcome of behavior ( FitzGerald et al., 2013 ; Xu, 2017 ).

The Role of the PFC in Structural Credit Assignment

Several recent studies have investigated the neural mechanisms of appropriate credit assignment in challenging tasks where only a few of the multitude of cues predict rewards reliably. Collectively, this work has provided compelling support for causal contributions of the PFC to structural credit assignment. For example, Asaad et al. (2017) examined the activity of neurons in monkey dlPFC while subjects were performing a delayed learning task. The arrangement of the stimuli varied randomly between trials and within each block either the spatial location or stimulus identity was relevant for solving the task. The monkeys' goal was to learn by trial-and-error to select one of the four options that led to rewards according to current rules. When stimulus identity was relevant for solving the task, neural activity in the dlPFC at the time of feedback reflected both the relevant cue (regardless of its spatial location) and the trial outcome, thus integrating the information necessary for credit assignment. Such responses were strategy-selective: these neurons did not encode cue identity at the time of feedback when it was not necessary for learning in the spatial location task, in which making a saccade to the same position on the screen was reinforced within a block of trials. Previous research has similarly indicated that neurons in the dlPFC respond selectively to behaviorally-relevant and attended stimuli ( Lebedev et al., 2004 ; Markowitz et al., 2015 ) and integrate information about prediction errors, choice values as well as outcome uncertainty prior to trial feedback ( Khamassi et al., 2015 ).

The activity within the dlPFC has been linked to structural credit assignment through selective attention and representational learning ( Niv et al., 2015 ). Under conditions of reward uncertainty and unknown relevant task features, human participants opt for computational efficiency and engage in a serial-hypothesis-testing strategy ( Wilson and Niv, 2011 ), selecting one cue and its anticipated outcome as the main focus of their behavior, and updating the expectations associated exclusively with that choice upon feedback receipt ( Akaishi et al., 2016 ). Niv and colleagues tested participant on a three-armed bandit task, where relevant stimulus dimensions (i.e., shape, color or texture) predicting outcome probabilities changed between block of trials ( Niv et al., 2015 ). In such multidimensional environment, reinforcement-driven learning was aided by attentional control mechanisms that engaged the dlPFC, intraparietal cortex, and precuneus.

In many tasks, the credit for outcomes can be assigned according to different rules: based on the causal relationship between rewards and choices (i.e., contingent learning), their temporal proximity (i.e., when the reward is received shortly after a response), or their statistical relationship (when an action has been executed frequently before beneficial outcomes; Jocham et al., 2016 ; Figure 1C ). The analyses presented in papers discussed above did not allow for the dissociation between these alternative strategies of credit assignment. By testing human participants on a task with continuous stimulus presentation, instead of a typical trial-by-trial structure, Jocham et al. (2016) demonstrated that the tendency to repeat choices that were immediately followed by rewards and causal learning operate in parallel. In this experiment, activity within another subregion of the PFC, the OFC, was associated with contingent learning. Complementary work in monkeys revealed that the OFC contributes causally to credit assignment ( Noonan et al., 2010 ): animals with OFC lesions were unable to associate a reward with the choice on which it was contingent and instead relied on temporal and statistical learning rules. In another recent paper, Noonan and colleagues (2017) extended these observations to humans, demonstrating causal contributions of the OFC to credit assignment across species. The participants were tested on a three-choice probabilistic learning task. The three options were presented simultaneously and maintained on the screen until the outcome of a decision was revealed, thus requiring participants to ignore irrelevant distractors. Notably, only patients with lateral OFC lesions displayed any difficulty in learning the task, whereas damage to the medial OFC or dorsomedial PFC preserved contingent learning mechanisms. However, it is presently unknown whether lesions to the dlPFC or ACC affect such causal learning.

In another test of credit assignment in learning, contingency degradation, the subjects are required to track causal relationships between the stimuli or actions and rewards. During contingency degradation sessions, the animals are still reinforced for responses, but rewards are also available for free. After experiencing non-contingent rewards, control subjects reliably decrease their choices of the stimuli. However, lesions to both the ACC and OFC inhibit contingency degradation ( Jackson et al., 2016 ). Taken together, these observations demonstrate causal contributions of the PFC to appropriate credit assignment in multi-cue environments.

Cooperation Between PFC Subregions Supports Contingent Learning in Multi-Cue Tasks

Despite the segregation of temporal and structural aspects of credit assignment in earlier sections of this review, in naturalistic settings the brains frequently need to tackle both problems simultaneously. Here, I overview the evidence favoring a network perspective, suggesting that dynamic cortico-cortical interactions during decision making and outcome valuation enable adaptive solutions to complex spatio-temporal credit assignment problems. It has been previously suggested that feedback projections from cortical areas occupying higher levels of processing hierarchy, including the PFC, can aid in attribution of outcomes to individual decisions by implementing attention-gated reinforcement learning ( Roelfsema and van Ooyen, 2005 ). Similarly, recent theoretical work has shown that even complex multi-cue and multi-step problems can be solved by an extended cascade model of synaptic memory traces, in which the plasticity is modulated not only by the activity within a population of neurons, but also by feedback about executed decisions and resulting rewards ( Urbanczik and Senn, 2009 ; Friedrich et al., 2010 , 2011 ). Contingent learning, according to these models, can be supported by the communication between neurons encoding available options, committed choices and outcomes of behavior during decision making and feedback monitoring. For example, at the time of outcome valuation, information about recent choices can be maintained as a memory trace in the neuronal population involved in action selection or conveyed by an efference copy from an interconnected brain region ( Curtis and Lee, 2010 ; Khamassi et al., 2011 , 2015 ). Similarly, reinforcement feedback is likely communicated as a global reward signal (ex., DA release) as well as projections from neural populations engaged in performance monitoring, such as those within the ACC ( Friedrich et al., 2010 ; Khamassi et al., 2011 ). The complexity of reciprocal and recurrent projections spanning the PFC ( Barbas and Pandya, 1989 ; Felleman and Van Essen, 1991 ; Elston, 2000 ) may enable this network to implement such learning rules, integrating the information about the task, executed decisions and performance feedback.

In many everyday decisions, the options are compared across multiple features simultaneously (ex., by considering current context, needs, available reward types, as well as delay and effort costs). Neurons in different subregions of the PFC exhibit rich response properties, signaling these features of the task at various time epochs within a trial. For example, reward selectivity in response to predictive stimuli emerges earlier in the OFC and may then be passed to the dlPFC that encodes both the expected outcome and the upcoming choice ( Wallis and Miller, 2003 ). Similarly, on trials where options are compared based on delays to rewards, choices are dependent on interactions between the OFC and dlPFC ( Hunt et al., 2015 ). Conversely, when effort costs are more meaningful for decisions, it is the ACC that influences choice-related activity in the dlPFC ( Hunt et al., 2015 ). The OFC is required not only for the evaluation of stimuli, but also more complex abstract rules, based on rewards they predict ( Buckley et al., 2009 ). While both the OFC and dlPFC encode abstract strategies (ex., persisting with recent choices or shifting to a new response), such signals appear earlier in the OFC and may be subsequently conveyed to the dlPFC where they are combined with upcoming response (i.e., left vs. right saccade) encoding ( Tsujimoto et al., 2011 ). Therefore, the OFC may be the first PFC subregion to encode task rules and/or potential rewards predicted by sensory cues; via cortico-cortical projections, this information may be subsequently communicated to the dlPFC or ACC ( Kennerley et al., 2009 ; Hayden and Platt, 2010 ) to drive strategy-sensitive response planning.

The behavioral strategy that the animal follows is influenced by recent reward history ( Cohen et al., 2007 ; Pearson et al., 2009 ). If its choices are reinforced frequently, the animal will make similar decisions in the future (i.e., exploit its current knowledge). Conversely, unexpected omission of expected rewards can signal a need for novel behaviors (i.e., exploration). Neurons in the dlPFC carry representations of planned as well as previous choices, anticipate outcomes, and jointly encode the current decisions and their consequences following feedback ( Seo and Lee, 2007 ; Seo et al., 2007 ; Tsujimoto et al., 2009 ; Asaad et al., 2017 ). Similarly, the ACC tracks trial-by-trial outcomes of decisions ( Procyk et al., 2000 ; Shidara and Richmond, 2002 ; Amiez et al., 2006 ; Quilodran et al., 2008 ) as well as reward and choice history ( Seo and Lee, 2007 ; Kennerley et al., 2009 , 2011 ; Sul et al., 2010 ; Kawai et al., 2015 ) and signals errors in outcome prediction ( Kennerley et al., 2009 , 2011 ; Hayden et al., 2011 ; Monosov, 2017 ). At the time of feedback, neurons in the OFC encode committed choices, their values and contingent rewards ( Tsujimoto et al., 2009 ; Sul et al., 2010 ). Notably, while the OFC encodes the identity of expected outcomes and the value of the chosen option after the alternatives are presented to an animal, it does not appear to encode upcoming decisions ( Tremblay and Schultz, 1999 ; Wallis and Miller, 2003 ; Padoa-Schioppa and Assad, 2006 ; Sul et al., 2010 ; McDannald et al., 2014 ), therefore it might be that feedback projections from the dlPFC or ACC are required for such activity to emerge at the time of reward feedback.

To capture the interactions between PFC subregions in reinforcement-driven learning, Khamassi and colleagues have formulated a computation model in which action values are stored and updated in the ACC and then communicated to the dlPFC that decides which action to trigger ( Khamassi et al., 2011 , 2013 ). This model relies on meta-learning principles ( Doya, 2002 ), flexibly adjusting the exploration-exploitation parameter based on performance history and variability in the environment that are monitored by the ACC. The explore-exploit parameter then influences action-selection mechanisms in the dlPFC, prioritizing choice repetition once the rewarded actions are discovered and encouraging switching between different options when environmental conditions change. In addition to highlighting the dynamic interactions between the dlPFC and ACC in learning, the model similarly offers an elegant solution to the credit assignment problem by restricting value updating only to those actions that were selected on a given trial. This is implemented by requiring the prediction error signals in the ACC to coincide with a motor efference copy sent by the premotor cortex. The model is endorsed with an ability to learn meta-values of novel objects in the environment based on the changes in the average reward that follow the presentation of such stimuli. While the authors proposed that such meta-value learning is implemented by the ACC, it is plausible that the OFC also plays a role in this process based on its contributions to stimulus-outcome and state learning ( Wilson et al., 2014 ; Zsuga et al., 2016 ). Intriguingly, this model could reproduce monkey behavior and neural responses on two tasks: four-choice deterministic and two-choice probabilistic paradigms, entailing a complex spatio-temporal credit assignment problem as the stimuli disappeared from the screen prior to action execution and outcome presentation ( Khamassi et al., 2011 , 2013 , 2015 ). Model-based analyses of neuronal responses further revealed that information about prediction errors, action values and outcome uncertainty is integrated both in the dlPFC and ACC, but at different timepoints: before trial feedback in the dlPFC and after feedback in the ACC ( Khamassi et al., 2015 ).

Collectively, these findings highlight the heterogeneity of responses in each PFC subregion that differ in temporal dynamics within a single trial and suggest that the cooperation between the OFC, ACC and dlPFC may support flexible, strategy- and context-dependent choices. This network perspective further suggests that individual PFC subregions may be less specialized in their functions than previously thought. For example, in primates both the ACC and dlPFC participate in decisions based on action values ( Hunt et al., 2015 ; Khamassi et al., 2015 ). And more recently, it has been demonstrated that the OFC is involved in updating action-outcome values as well ( Fiuzat et al., 2017 ). Analogously, while it has been proposed that the OFC is specialized for stimulus-outcome and ACC for action-outcome learning ( Rudebeck et al., 2008 ), lesions to the ACC have been similarly reported to impair stimulus-based reversal learning ( Chudasama et al., 2013 ), supporting shared contributions of the PFC subregions to adaptive behavior. Indeed, these brain regions communicate extensively, sharing the information about presented options, executed decisions and received rewards (Figure 2 ), which can enable them to assign credit for outcomes to choices on which they are contingent ( Urbanczik and Senn, 2009 ; Friedrich et al., 2010 , 2011 ). Attention-gated learning likely relies on the cooperation between PFC subregions as well: for example, coordinated and synchronized activity between the ACC and dlPFC aids in goal-directed attentional shifting and prioritization of task-relevant information ( Womelsdorf et al., 2014 ; Oemisch et al., 2015 ; Voloh et al., 2015 ).

Figure 2 . Cooperation between PFC subregions in multi-cue tasks. In many everyday decisions, the options are compared across multiple features simultaneously (ex., by considering current context, needs, available reward types, as well as delay and effort costs). Neurons in different subregions of the PFC exhibit rich response properties, integrating many aspects of the task at hand. The OFC, ACC and dlPFC communicate extensively, sharing the information about presented options, executed decisions and received rewards, which can enable them to assign credit for outcomes to choices on which they are contingent.

Functional connectivity within the PFC can support contingent learning on shorter timescales (ex., across trials within the same task), when complex rules or stimulus-action-outcome mappings are switching frequently ( Duff et al., 2011 ; Johnson et al., 2016 ). Under such conditions, the same stimuli can carry different meaning depending on task context or due to changes in the environment (ex., serial discrimination-reversal problems) and the PFC neurons with heterogeneous response properties may be better targets for modification, allowing the brain to exert flexible, rapid and context-sensitive control over behavior ( Asaad et al., 1998 ; Mansouri et al., 2006 ). Indeed, it has been shown that rule and reversal learning induce plasticity in OFC synapses onto the dorsomedial PFC (encompassing the ACC) in rats ( Johnson et al., 2016 ). When motivational significance of reward-predicting cues fluctuates frequently, neuronal responses and synaptic connections within the PFC tend to update more rapidly (i.e., across block of trials) compared to subcortical structures and other cortical regions ( Padoa-Schioppa and Assad, 2008 ; Morrison et al., 2011 ; Xie and Padoa-Schioppa, 2016 ; Fernández-Lamo et al., 2017 ; Saez et al., 2017 ). Similarly, neurons in the PFC promptly adapt their responses to incoming information based on the recent history of inputs ( Freedman et al., 2001 ; Meyers et al., 2012 ; Stokes et al., 2013 ). Critically, changes in the PFC activity closely track behavioral performance ( Mulder et al., 2003 ; Durstewitz et al., 2010 ), and interfering with neural plasticity within this brain area prevents normal responses to contingency degradation ( Swanson et al., 2015 ).

When the circumstances are stable overall and the same cues or actions remain reliable predictors of rewards, long-range connections between the PFC, association and sensory areas can support contingent learning on prolonged timescales. Neurons in the lateral intraparietal area demonstrate larger post-decisional responses and enhanced learning following choices that predict final outcomes of sequential behavior in a multi-step and -cue task ( Gersch et al., 2014 ). Such changes in neuronal activity likely rely on information about task rules conveyed by the PFC directly or via interactions with neuromodulatory systems. These hypotheses could be tested in future work.

In summary, dynamic interactions between subregions of the PFC can support contingent learning in multi-cue environments. Furthermore, via feedback projections, the PFC can guide plasticity in other cortical areas associated with sensory and motor processing ( Cohen et al., 2011 ). This account suggests that lesion experiments targeting a localized PFC subregion will be insufficient to gain fine-grained understanding of credit assignment during learning and instead poses refined questions for future research, shifting the focus from focal manipulations to experimental techniques targeting cortico-cortical projections. To gain novel insights into functional connectivity between PFC subregions, it will be critical to assess neural correlates of contingent learning in the OFC, ACC, and dlPFC simultaneously in the context of the same task. In humans, functional connectivity can be assessed by utilizing coherence, phase synchronization, Granger causality and Bayes network approaches ( Bastos and Schoffelen, 2016 ; Mill et al., 2017 ). Indeed, previous studies have linked individual differences in cortico-striatal functional connectivity to reinforcement-driven learning ( Horga et al., 2015 ; Kaiser et al., 2017 ) and future work could focus on examining cortico-cortical interactions in similar paradigms. To probe causal contributions of projections spanning the PFC, future research may benefit from designing multi-cue tasks for rodents and taking advantage of recently developed techniques (i.e., chemo- and opto-genetic targeting of projection neurons followed by silencing of axonal terminals to achieve pathway-specific inhibition; Deisseroth, 2010 ; Sternson and Roth, 2014 ) that afford increasingly precise manipulations of cortico-cortical connectivity. It should be noted, however, that most experiments to date have probed the contributions of the PFC to credit assignment in primates, and functional specialization across different subregions may be even less pronounced in mice and rats. Finally, as highlighted throughout this review, the recent progress in understanding the neural mechanisms of credit assignment has relied on introduction of more complex tasks, including multi-cue and probabilistic choice paradigms. While such tasks better mimic the naturalistic problems that the brains have evolved to solve, they also produce behavioral patterns that are more difficult to analyze and interpret ( Scholl and Klein-Flügge, 2017 ). As such, computational modeling of the behavior and neuronal activity may prove especially useful in future work on credit assignment.

Author Contributions

The author confirms being the sole contributor of this work and approved it for publication.

This work was supported by UCLA's Division of Life Sciences Recruitment and Retention fund (Izquierdo), as well as the UCLA Distinguished University Fellowship (Stolyarova).

Conflict of Interest Statement

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

The author thanks her mentor Dr. Alicia Izquierdo for helpful feedback and critiques on the manuscript, and Evan E. Hart, as well as the members of the Center for Brains, Minds and Machines and Lau lab for stimulating conversations on the topic.

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Keywords: orbitofrontal, dorsolateral prefrontal, anterior cingulate, learning, reward, reinforcement, plasticity, behavioral flexibility

Citation: Stolyarova A (2018) Solving the Credit Assignment Problem With the Prefrontal Cortex. Front. Neurosci . 12:182. doi: 10.3389/fnins.2018.00182

Received: 27 September 2017; Accepted: 06 March 2018; Published: 27 March 2018.

Reviewed by:

Copyright © 2018 Stolyarova. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Alexandra Stolyarova, [email protected]

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

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• Corporate Finance
• Corporate Debt

Debt Assignment: How They Work, Considerations and Benefits

Daniel Liberto is a journalist with over 10 years of experience working with publications such as the Financial Times, The Independent, and Investors Chronicle.

Charlene Rhinehart is a CPA , CFE, chair of an Illinois CPA Society committee, and has a degree in accounting and finance from DePaul University.

Katrina Ávila Munichiello is an experienced editor, writer, fact-checker, and proofreader with more than fourteen years of experience working with print and online publications.

Investopedia / Ryan Oakley

What Is Debt Assignment?

The term debt assignment refers to a transfer of debt , and all the associated rights and obligations, from a creditor to a third party. The assignment is a legal transfer to the other party, who then becomes the owner of the debt. In most cases, a debt assignment is issued to a debt collector who then assumes responsibility to collect the debt.

Key Takeaways

• Debt assignment is a transfer of debt, and all the associated rights and obligations, from a creditor to a third party (often a debt collector).
• The company assigning the debt may do so to improve its liquidity and/or to reduce its risk exposure.
• The debtor must be notified when a debt is assigned so they know who to make payments to and where to send them.
• Third-party debt collectors are subject to the Fair Debt Collection Practices Act (FDCPA), a federal law overseen by the Federal Trade Commission (FTC).

How Debt Assignments Work

When a creditor lends an individual or business money, it does so with the confidence that the capital it lends out—as well as the interest payments charged for the privilege—is repaid in a timely fashion. The lender , or the extender of credit , will wait to recoup all the money owed according to the conditions and timeframe laid out in the contract.

In certain circumstances, the lender may decide it no longer wants to be responsible for servicing the loan and opt to sell the debt to a third party instead. Should that happen, a Notice of Assignment (NOA) is sent out to the debtor , the recipient of the loan, informing them that somebody else is now responsible for collecting any outstanding amount. This is referred to as a debt assignment.

The debtor must be notified when a debt is assigned to a third party so that they know who to make payments to and where to send them. If the debtor sends payments to the old creditor after the debt has been assigned, it is likely that the payments will not be accepted. This could cause the debtor to unintentionally default.

When a debtor receives such a notice, it's also generally a good idea for them to verify that the new creditor has recorded the correct total balance and monthly payment for the debt owed. In some cases, the new owner of the debt might even want to propose changes to the original terms of the loan. Should this path be pursued, the creditor is obligated to immediately notify the debtor and give them adequate time to respond.

The debtor still maintains the same legal rights and protections held with the original creditor after a debt assignment.

Special Considerations

Third-party debt collectors are subject to the Fair Debt Collection Practices Act (FDCPA). The FDCPA, a federal law overseen by the Federal Trade Commission (FTC), restricts the means and methods by which third-party debt collectors can contact debtors, the time of day they can make contact, and the number of times they are allowed to call debtors.

If the FDCPA is violated, a debtor may be able to file suit against the debt collection company and the individual debt collector for damages and attorney fees within one year. The terms of the FDCPA are available for review on the FTC's website .

Benefits of Debt Assignment

There are several reasons why a creditor may decide to assign its debt to someone else. This option is often exercised to improve liquidity  and/or to reduce risk exposure. A lender may be urgently in need of a quick injection of capital. Alternatively, it might have accumulated lots of high-risk loans and be wary that many of them could default . In cases like these, creditors may be willing to get rid of them swiftly for pennies on the dollar if it means improving their financial outlook and appeasing worried investors. At other times, the creditor may decide the debt is too old to waste its resources on collections, or selling or assigning it to a third party to pick up the collection activity. In these instances, a company would not assign their debt to a third party.

Criticism of Debt Assignment

The process of assigning debt has drawn a fair bit of criticism, especially over the past few decades. Debt buyers have been accused of engaging in all kinds of unethical practices to get paid, including issuing threats and regularly harassing debtors. In some cases, they have also been charged with chasing up debts that have already been settled.

Federal Trade Commission. " Fair Debt Collection Practices Act ." Accessed June 29, 2021.

Federal Trade Commission. " Debt Collection FAQs ." Accessed June 29, 2021.

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Understanding Assignments

What this handout is about.

The first step in any successful college writing venture is reading the assignment. While this sounds like a simple task, it can be a tough one. This handout will help you unravel your assignment and begin to craft an effective response. Much of the following advice will involve translating typical assignment terms and practices into meaningful clues to the type of writing your instructor expects. See our short video for more tips.

Basic beginnings

Regardless of the assignment, department, or instructor, adopting these two habits will serve you well :

• Read the assignment carefully as soon as you receive it. Do not put this task off—reading the assignment at the beginning will save you time, stress, and problems later. An assignment can look pretty straightforward at first, particularly if the instructor has provided lots of information. That does not mean it will not take time and effort to complete; you may even have to learn a new skill to complete the assignment.
• Ask the instructor about anything you do not understand. Do not hesitate to approach your instructor. Instructors would prefer to set you straight before you hand the paper in. That’s also when you will find their feedback most useful.

Assignment formats

Many assignments follow a basic format. Assignments often begin with an overview of the topic, include a central verb or verbs that describe the task, and offer some additional suggestions, questions, or prompts to get you started.

An Overview of Some Kind

The instructor might set the stage with some general discussion of the subject of the assignment, introduce the topic, or remind you of something pertinent that you have discussed in class. For example:

“Throughout history, gerbils have played a key role in politics,” or “In the last few weeks of class, we have focused on the evening wear of the housefly …”

The Task of the Assignment

Pay attention; this part tells you what to do when you write the paper. Look for the key verb or verbs in the sentence. Words like analyze, summarize, or compare direct you to think about your topic in a certain way. Also pay attention to words such as how, what, when, where, and why; these words guide your attention toward specific information. (See the section in this handout titled “Key Terms” for more information.)

“Analyze the effect that gerbils had on the Russian Revolution”, or “Suggest an interpretation of housefly undergarments that differs from Darwin’s.”

Additional Material to Think about

Here you will find some questions to use as springboards as you begin to think about the topic. Instructors usually include these questions as suggestions rather than requirements. Do not feel compelled to answer every question unless the instructor asks you to do so. Pay attention to the order of the questions. Sometimes they suggest the thinking process your instructor imagines you will need to follow to begin thinking about the topic.

“You may wish to consider the differing views held by Communist gerbils vs. Monarchist gerbils, or Can there be such a thing as ‘the housefly garment industry’ or is it just a home-based craft?”

These are the instructor’s comments about writing expectations:

“Be concise”, “Write effectively”, or “Argue furiously.”

Technical Details

These instructions usually indicate format rules or guidelines.

“Your paper must be typed in Palatino font on gray paper and must not exceed 600 pages. It is due on the anniversary of Mao Tse-tung’s death.”

The assignment’s parts may not appear in exactly this order, and each part may be very long or really short. Nonetheless, being aware of this standard pattern can help you understand what your instructor wants you to do.

Interpreting the assignment

Ask yourself a few basic questions as you read and jot down the answers on the assignment sheet:

Why did your instructor ask you to do this particular task?

Who is your audience.

• What kind of evidence do you need to support your ideas?

What kind of writing style is acceptable?

• What are the absolute rules of the paper?

Try to look at the question from the point of view of the instructor. Recognize that your instructor has a reason for giving you this assignment and for giving it to you at a particular point in the semester. In every assignment, the instructor has a challenge for you. This challenge could be anything from demonstrating an ability to think clearly to demonstrating an ability to use the library. See the assignment not as a vague suggestion of what to do but as an opportunity to show that you can handle the course material as directed. Paper assignments give you more than a topic to discuss—they ask you to do something with the topic. Keep reminding yourself of that. Be careful to avoid the other extreme as well: do not read more into the assignment than what is there.

Of course, your instructor has given you an assignment so that he or she will be able to assess your understanding of the course material and give you an appropriate grade. But there is more to it than that. Your instructor has tried to design a learning experience of some kind. Your instructor wants you to think about something in a particular way for a particular reason. If you read the course description at the beginning of your syllabus, review the assigned readings, and consider the assignment itself, you may begin to see the plan, purpose, or approach to the subject matter that your instructor has created for you. If you still aren’t sure of the assignment’s goals, try asking the instructor. For help with this, see our handout on getting feedback .

Given your instructor’s efforts, it helps to answer the question: What is my purpose in completing this assignment? Is it to gather research from a variety of outside sources and present a coherent picture? Is it to take material I have been learning in class and apply it to a new situation? Is it to prove a point one way or another? Key words from the assignment can help you figure this out. Look for key terms in the form of active verbs that tell you what to do.

Key Terms: Finding Those Active Verbs

Here are some common key words and definitions to help you think about assignment terms:

Information words Ask you to demonstrate what you know about the subject, such as who, what, when, where, how, and why.

• define —give the subject’s meaning (according to someone or something). Sometimes you have to give more than one view on the subject’s meaning
• describe —provide details about the subject by answering question words (such as who, what, when, where, how, and why); you might also give details related to the five senses (what you see, hear, feel, taste, and smell)
• explain —give reasons why or examples of how something happened
• illustrate —give descriptive examples of the subject and show how each is connected with the subject
• summarize —briefly list the important ideas you learned about the subject
• trace —outline how something has changed or developed from an earlier time to its current form
• research —gather material from outside sources about the subject, often with the implication or requirement that you will analyze what you have found

Relation words Ask you to demonstrate how things are connected.

• compare —show how two or more things are similar (and, sometimes, different)
• contrast —show how two or more things are dissimilar
• apply—use details that you’ve been given to demonstrate how an idea, theory, or concept works in a particular situation
• cause —show how one event or series of events made something else happen
• relate —show or describe the connections between things

Interpretation words Ask you to defend ideas of your own about the subject. Do not see these words as requesting opinion alone (unless the assignment specifically says so), but as requiring opinion that is supported by concrete evidence. Remember examples, principles, definitions, or concepts from class or research and use them in your interpretation.

• assess —summarize your opinion of the subject and measure it against something
• prove, justify —give reasons or examples to demonstrate how or why something is the truth
• evaluate, respond —state your opinion of the subject as good, bad, or some combination of the two, with examples and reasons
• support —give reasons or evidence for something you believe (be sure to state clearly what it is that you believe)
• synthesize —put two or more things together that have not been put together in class or in your readings before; do not just summarize one and then the other and say that they are similar or different—you must provide a reason for putting them together that runs all the way through the paper
• analyze —determine how individual parts create or relate to the whole, figure out how something works, what it might mean, or why it is important
• argue —take a side and defend it with evidence against the other side

More Clues to Your Purpose As you read the assignment, think about what the teacher does in class:

• What kinds of textbooks or coursepack did your instructor choose for the course—ones that provide background information, explain theories or perspectives, or argue a point of view?
• In lecture, does your instructor ask your opinion, try to prove her point of view, or use keywords that show up again in the assignment?
• What kinds of assignments are typical in this discipline? Social science classes often expect more research. Humanities classes thrive on interpretation and analysis.
• How do the assignments, readings, and lectures work together in the course? Instructors spend time designing courses, sometimes even arguing with their peers about the most effective course materials. Figuring out the overall design to the course will help you understand what each assignment is meant to achieve.

Now, what about your reader? Most undergraduates think of their audience as the instructor. True, your instructor is a good person to keep in mind as you write. But for the purposes of a good paper, think of your audience as someone like your roommate: smart enough to understand a clear, logical argument, but not someone who already knows exactly what is going on in your particular paper. Remember, even if the instructor knows everything there is to know about your paper topic, he or she still has to read your paper and assess your understanding. In other words, teach the material to your reader.

Aiming a paper at your audience happens in two ways: you make decisions about the tone and the level of information you want to convey.

• Tone means the “voice” of your paper. Should you be chatty, formal, or objective? Usually you will find some happy medium—you do not want to alienate your reader by sounding condescending or superior, but you do not want to, um, like, totally wig on the man, you know? Eschew ostentatious erudition: some students think the way to sound academic is to use big words. Be careful—you can sound ridiculous, especially if you use the wrong big words.
• The level of information you use depends on who you think your audience is. If you imagine your audience as your instructor and she already knows everything you have to say, you may find yourself leaving out key information that can cause your argument to be unconvincing and illogical. But you do not have to explain every single word or issue. If you are telling your roommate what happened on your favorite science fiction TV show last night, you do not say, “First a dark-haired white man of average height, wearing a suit and carrying a flashlight, walked into the room. Then a purple alien with fifteen arms and at least three eyes turned around. Then the man smiled slightly. In the background, you could hear a clock ticking. The room was fairly dark and had at least two windows that I saw.” You also do not say, “This guy found some aliens. The end.” Find some balance of useful details that support your main point.

You’ll find a much more detailed discussion of these concepts in our handout on audience .

The Grim Truth

With a few exceptions (including some lab and ethnography reports), you are probably being asked to make an argument. You must convince your audience. It is easy to forget this aim when you are researching and writing; as you become involved in your subject matter, you may become enmeshed in the details and focus on learning or simply telling the information you have found. You need to do more than just repeat what you have read. Your writing should have a point, and you should be able to say it in a sentence. Sometimes instructors call this sentence a “thesis” or a “claim.”

So, if your instructor tells you to write about some aspect of oral hygiene, you do not want to just list: “First, you brush your teeth with a soft brush and some peanut butter. Then, you floss with unwaxed, bologna-flavored string. Finally, gargle with bourbon.” Instead, you could say, “Of all the oral cleaning methods, sandblasting removes the most plaque. Therefore it should be recommended by the American Dental Association.” Or, “From an aesthetic perspective, moldy teeth can be quite charming. However, their joys are short-lived.”

Convincing the reader of your argument is the goal of academic writing. It doesn’t have to say “argument” anywhere in the assignment for you to need one. Look at the assignment and think about what kind of argument you could make about it instead of just seeing it as a checklist of information you have to present. For help with understanding the role of argument in academic writing, see our handout on argument .

What kind of evidence do you need?

There are many kinds of evidence, and what type of evidence will work for your assignment can depend on several factors–the discipline, the parameters of the assignment, and your instructor’s preference. Should you use statistics? Historical examples? Do you need to conduct your own experiment? Can you rely on personal experience? See our handout on evidence for suggestions on how to use evidence appropriately.

Make sure you are clear about this part of the assignment, because your use of evidence will be crucial in writing a successful paper. You are not just learning how to argue; you are learning how to argue with specific types of materials and ideas. Ask your instructor what counts as acceptable evidence. You can also ask a librarian for help. No matter what kind of evidence you use, be sure to cite it correctly—see the UNC Libraries citation tutorial .

You cannot always tell from the assignment just what sort of writing style your instructor expects. The instructor may be really laid back in class but still expect you to sound formal in writing. Or the instructor may be fairly formal in class and ask you to write a reflection paper where you need to use “I” and speak from your own experience.

Try to avoid false associations of a particular field with a style (“art historians like wacky creativity,” or “political scientists are boring and just give facts”) and look instead to the types of readings you have been given in class. No one expects you to write like Plato—just use the readings as a guide for what is standard or preferable to your instructor. When in doubt, ask your instructor about the level of formality she or he expects.

No matter what field you are writing for or what facts you are including, if you do not write so that your reader can understand your main idea, you have wasted your time. So make clarity your main goal. For specific help with style, see our handout on style .

Technical details about the assignment

The technical information you are given in an assignment always seems like the easy part. This section can actually give you lots of little hints about approaching the task. Find out if elements such as page length and citation format (see the UNC Libraries citation tutorial ) are negotiable. Some professors do not have strong preferences as long as you are consistent and fully answer the assignment. Some professors are very specific and will deduct big points for deviations.

Usually, the page length tells you something important: The instructor thinks the size of the paper is appropriate to the assignment’s parameters. In plain English, your instructor is telling you how many pages it should take for you to answer the question as fully as you are expected to. So if an assignment is two pages long, you cannot pad your paper with examples or reword your main idea several times. Hit your one point early, defend it with the clearest example, and finish quickly. If an assignment is ten pages long, you can be more complex in your main points and examples—and if you can only produce five pages for that assignment, you need to see someone for help—as soon as possible.

Tricks that don’t work

Your instructors are not fooled when you:

• spend more time on the cover page than the essay —graphics, cool binders, and cute titles are no replacement for a well-written paper.
• use huge fonts, wide margins, or extra spacing to pad the page length —these tricks are immediately obvious to the eye. Most instructors use the same word processor you do. They know what’s possible. Such tactics are especially damning when the instructor has a stack of 60 papers to grade and yours is the only one that low-flying airplane pilots could read.
• use a paper from another class that covered “sort of similar” material . Again, the instructor has a particular task for you to fulfill in the assignment that usually relates to course material and lectures. Your other paper may not cover this material, and turning in the same paper for more than one course may constitute an Honor Code violation . Ask the instructor—it can’t hurt.
• get all wacky and “creative” before you answer the question . Showing that you are able to think beyond the boundaries of a simple assignment can be good, but you must do what the assignment calls for first. Again, check with your instructor. A humorous tone can be refreshing for someone grading a stack of papers, but it will not get you a good grade if you have not fulfilled the task.

Critical reading of assignments leads to skills in other types of reading and writing. If you get good at figuring out what the real goals of assignments are, you are going to be better at understanding the goals of all of your classes and fields of study.

You may reproduce it for non-commercial use if you use the entire handout and attribute the source: The Writing Center, University of North Carolina at Chapel Hill

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Assignment of credits

1. ASSIGNMENT

Perfection of assignment

⦁ An assignment of credits and other incorporeal rights shall be perfected in accordance with the provisions of Article 1475. (Article 1624, Ibid.)

Cross-referenced article/sThe contract of sale is perfected at the moment there is a meeting of minds upon the thing which is the object of the contract and upon the price. (Art. 1475, Ibid.)From that moment, the parties may reciprocally demand performance, subject to the provisions of the law governing the form of contracts. (Paragraph 2, Art. 1475, Ibid.)

⦁ Accessory rights included. The assignment of a credit includes all the accessory rights, such as a guaranty, mortgage, pledge or preference. (Article 1627, Ibid.)

To bind third parties

⦁ Public instrument for non-real properties; Recorded in Registry for real properties. An assignment of a credit, right or action shall produce no effect as against third person, unless it appears in a public instrument, or the instrument is recorded in the Registry of Property in case the assignment involves real property. (Article 1625, Ibid.)

2. DEBTOR IN GOOD FAITH

⦁ The debtor who, before having knowledge of the assignment, pays his creditor shall be released from the obligation. (Article 1626, Ibid.)

In good faith

⦁ The seller in good faith shall be responsible for the existence and legality of the credit at the time of the sale, unless it should have been sold as doubtful; but not for the solvency of the d...

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Perplexing puzzles.

Solo MP This MP, as well as all other MPs in CS 225, are to be completed without a partner.

You are welcome to get help on the MP from course staff, via open lab hours, or Piazza!

Goals and Overview

In this MP, you will:

• Work with a graph that is to large too store completely in memory
• Use a graph algorithm to solve a complex problem
• Implement an algorithm from public sources documents
• See the difference in performance between a guided and unguided search algorithm

Checking Out the Code

All assignments will be distributed via our release repo on github this semester. You will need to have set up your git directory to have our release as a remote repo as described in our git set up

You can merge the assignments as they are released into your personal repo with

if you are using multiple machines you may need to use the following to allow them to work correcly.

The first git command will fetch and merge changes from the main branch on your remote repository named release into your personal. The --no-edit flag automatically generates a commit message for you, and the --no-rebase flag will merge the upstream branch into the current branch. Generally, these two flags shouldn’t be used, but are included for ease of merging assignments into your repo.

The second command will push to origin (your personal), which will allow it to track the new changes from release .

You will need to run these commands for every assignment that is released.

All the files for this mp are in the mp_puzzle directory.

Preparing Your Code

This semester for MPs we are using CMake rather than just make. This allows for us to use libraries such as Catch2 that can be installed in your system rather than providing them with each assignment. This change does mean that for each assignment you need to use CMake to build your own custom makefiles. To do this you need to run the following in the base directory of the assignment. Which in this assignment is the mp_puzzle directory.

This first makes a new directory in your assignment directory called build . This is where you will actually build the assignment and then moves to that directory. This is not included in the provided code since we are following industry standard practices and you would normally exclude the build directory from any source control system.

Now you need to actually run CMake as follows.

This runs CMake to initialize the current directory which is the build directory you just made as the location to build the assignment. The one argument to CMake here is .. which referes to the parent of the current directory which in this case is top of the assignment. This directory has the files CMake needs to setup your assignment to be build.

At this point you can in the build directory run make as described to build the various programs for the MP.

You will need to do the above once for each assignment. You will need to run make every time you change source code and want to compile it again.

Assignment Description

In this mp we will be developing a puzzle solver for 15 puzzle as a graph problem. If you have not heard of 15 puzzle before you may want to look at the wikipedia article on it here . We will then generate an animation of the solution.

Part 1: The PuzzleState data structure

In the first part of this assignment we will work on representing the puzzle as a graph. To do this we will have a node for every possible position of the puzzle and an edge between two nodes if there is a single move of a tile that will move from one position to the next. The tricky part in this is that there are 16 factorial possible positions for the puzzle. Since this is way too large to store in memory we will need to only use the portions of the graph that we need to get from the starting position until we can find a solution.

To do this we will build a class PuzzleState that stores a single vertex of the graph but can also create its neighbors when asked. This is not hard to do since the possible positions you can move to are easy to compute only knowing the current position. This will give you a system where you only need to create the nodes of the graph when you explore them. You will need to implement all the methods in the PuzzleState class.

Creating and Outputing

While the internal implementation of the PuzzleState class is entirely up to you we are defining two functions to make sure that we agree on what state we are referring to. These functions are the Constructor that takes an array of positions and creates a PuzzleState with those positions and asArray which returns the array version of that state. The format of this is to list the values in the puzzle starting for the upper left hand corner and moving to the right until the end of the line then moving to the next line until all 16 positions are provided.

Implementing operator<

To ensure that you can use std::map to store PuzzleStates we require you to implement an operator<() . While this operator does not represent any real relation between the different puzzle states it will satisfy the requirement for a total order so that you can use std::map .

Manhattan Distance

One function that might be unclear is the manhattanDistance function. This is asking you to compute a distance value between two states. This distance is the distance that each tile has to travel in the x dimension and the y dimension to reach the location of the tile in the other state.

Testing Your Code

Provided Catch test cases are available as well by running:

Extra Credit Submission

For extra credit, you can submit the code you have implemented and tested for part one of mp_puzzle. You must submit your work before the extra credit deadline as listed at the top of this page. See Handing in Your Code for instructions.

Part 2: The Solve Functions

In part 2 we are writing two different functions that will each solve the puzzle by finding the shortest path from the start state to the goal state. If the goal is not stated, the standard solved state will be used. The first version will solve this by implementing breadth first search. The second will use the A* algorithm. The doxygen of these functions can be seen here solveBFS and solveAstar .

A* search Algorithm

The A* algorithm is an algorithm for finding the shortest path from one point in a graph to another point in the graph. Documentation on the general algorithm can be found on wikipedia here . You should use the material provided there as the basis for your implementation. The key idea here is that A* uses a heuristic function to estimate how much further a state is from the goal state. In our case we will be using the manhattan distance function we wrote in part 1. This works since each move in the puzzle moves a single piece in a single direction so the minimum distance from a state to the goal state is enough moves to move each piece directly there.

Handing in your code

You must submit your work on PL for grading. We will use the following files for grading:

All other files will not be used for grading.

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Computer Science > Machine Learning

Title: a survey of temporal credit assignment in deep reinforcement learning.

Abstract: The Credit Assignment Problem (CAP) refers to the longstanding challenge of Reinforcement Learning (RL) agents to associate actions with their long-term consequences. Solving the CAP is a crucial step towards the successful deployment of RL in the real world since most decision problems provide feedback that is noisy, delayed, and with little or no information about the causes. These conditions make it hard to distinguish serendipitous outcomes from those caused by informed decision-making. However, the mathematical nature of credit and the CAP remains poorly understood and defined. In this survey, we review the state of the art of Temporal Credit Assignment (CA) in deep RL. We propose a unifying formalism for credit that enables equitable comparisons of state of the art algorithms and improves our understanding of the trade-offs between the various methods. We cast the CAP as the problem of learning the influence of an action over an outcome from a finite amount of experience. We discuss the challenges posed by delayed effects, transpositions, and a lack of action influence, and analyse how existing methods aim to address them. Finally, we survey the protocols to evaluate a credit assignment method, and suggest ways to diagnoses the sources of struggle for different credit assignment methods. Overall, this survey provides an overview of the field for new-entry practitioners and researchers, it offers a coherent perspective for scholars looking to expedite the starting stages of a new study on the CAP, and it suggests potential directions for future research

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Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .

For Earth Day, Try These Green Classroom Activities (Downloadable)

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Earth Day is April 22 in the United States and the day the spring equinox occurs in some parts of the world. It’s a day to reflect on the work being done to raise awareness of climate change and the need to protect natural resources for future generations. Protecting the earth can feel like an enormous, distant undertaking to young people. To help them understand that they can play a role by focusing on their backyards or school yards, educators can scale those feelings of enormity to manageable activities that make a difference.

We collected simple ideas for teachers and students to educate, empower, and build a connection with nature so that they may be inspired to respect it and protect it. Classrooms can be the perfect greenhouse to grow future stewards of the environment.

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Diamondbacks updates: Sewald set for rehab assignment, Alexander out of lineup

Amid a brutal spate of injuries, there is finally some positive news for the Diamondbacks. Closer Paul Sewald is set to begin a rehab assignment with Triple-A Reno on Tuesday. He will throw one inning and up to 25 pitches.

Manager Torey Lovullo said he is expecting Sewald to need multiple outings with Reno, although that could change.

“I don't think it'll be later, if anything it would be sooner,” Lovullo said. “But we're gonna let Paul determine how he feels.”

Sewald suffered a Grade 2 left oblique strain just before Opening Day and has been rehabbing at Salt River Fields. His return should provide a boost to a bullpen that has been plagued by inconsistency despite solid overall numbers.

Last year, his arrival at the trade deadline helped the bullpen improve drastically in the second half. He finished the year with a 3.12 ERA and 34 saves in 39 opportunities.

All things D'backs: Latest Arizona Diamondbacks news, schedule, roster, stats, injury updates and more.

Blaze Alexander out of lineup but hamstring feeling better

Shortstop Blaze Alexander was out of the lineup Monday night and likely only available in an emergency situation against the Cardinals. He exited Sunday’s game against the Giants with a cramp in his right hamstring, though he appears to have avoided further injury.

“Definitely a lot better than it was yesterday,” Alexander said. “I'm in a better head space with it, knowing it's not anything too serious.”

Alexander has not undergone any imaging on the hamstring. Lovullo sounded confident he will avoid a trip to the injured list, though it seemed as if the Diamondbacks will want to use him off the bench before returning him to the starting lineup.

“I feel really good about him needing some time down and not starting,” Lovullo said. “Maybe coming into games at the very back end and preserving him the best way we can and saving some gas in his tank and he's gonna heal up just fine.”

Alexander first felt something in his hamstring after running out a ground ball in the second inning Sunday. He remained in the game and tried to work out the discomfort with trainers between innings before being removed after another groundout in his second at-bat.

With shortstop Geraldo Perdomo on the injured list, Alexander has been a boon for the Diamondbacks. He’s struggled defensively, with three errors, but is slashing .321/.379/.566 in 58 plate appearances.

Merrill Kelly undergoing second MRI

The Diamondbacks have not yet placed right-hander Merrill Kelly on the injured list. An initial MRI in San Francisco revealed a right teres major strain for Kelly, which caused shoulder soreness, but he is undergoing a second MRI in Phoenix on Monday.

“We just wanted to get our hands on him with our group,” Lovullo said. “We feel more comfortable doing that before we make a decision.”

If the second MRI confirms the results of the first, it would almost certainly require an injured list stint for Kelly, though the length of that stint is uncertain.

Left-hander Tommy Henry is with the Diamondbacks in St. Louis, but he has not yet been activated. If Kelly does need to head to the injured list, Henry would likely be officially recalled and start Tuesday’s game. Because he was optioned to Triple-A less than 10 days ago, Henry cannot be recalled without a player being placed on the injured list in the corresponding move.

The Diamondbacks will have another open spot in the rotation later this week, because of the injuries to Kelly and Ryne Nelson, who has a right elbow contusion. That spot — which will come up on Saturday — is likely to be filled by Slade Cecconi, who allowed two runs in six innings in an emergency start against the Giants after Kelly’s injury surfaced.

“Slade did everything for us to strongly consider him,” Lovullo said. “(Pitching coach Brent Strom) came in here this afternoon and we talked over Plan A, Plan B and Plan C. I think a lot of it has to do with A) What happens to Merrill, B) What happens tonight in our game and who do we have to use to get through the game. And then once we get through the next 24 hours, we'll be able to lay down what the plan is and the road map is for the next couple turns.”

Injury updates on Alek Thomas, Geraldo Perdomo, Eduardo Rodriguez

Center fielder Alek Thomas ran “10-yard bursts” at Salt River Fields on Monday, Lovullo said. He is working his way back from a hamstring strain and has also been taking live at-bats without running the bases.

Perdomo, who is recovering from a torn meniscus, has begun some light activity. He is taking ground balls from a seated position and doing work in the pool as his knee heals from surgery.

Pitcher Eduardo Rodriguez appears to be the furthest Diamondback from a return. He has yet to begin baseball activities after suffering a setback in his recovery from a left lat strain during a bullpen session on April 9. Rodriguez sustained the initial injury on March 19. He remains symptomatic, Lovullo said.

Monday's game: Diamondbacks at Cardinals, 4:45 p.m., Cox, Ch. 34

Diamondbacks RHP Brandon Pfaadt (1-1, 5.32) vs. Cardinals RHP Lance Lynn (1-0, 2.18).

Pfaadt is coming off his best start of the year, in which he gave up three runs (two earned) in seven innings against the Cubs. He took a no-decision in a 5-3 loss. … He had a rough go when he faced the Cardinals in the start before that, allowing six runs in six innings. All six runs came in the first three innings, after which Pfaadt put up three scoreless innings. … Pfaadt is getting whiffs on 37 percent of the time on his slider, up from 33 percent last year. He also has given up three homers on the pitch, the same number he allowed all of last season. … Lynn, who signed with the Cardinals in the offseason, has seven walks and 19 strikeouts through 20 2/3 innings this season. … The Diamondbacks last saw him in the division series, when they homered in four consecutive at-bats off him while he was a pitching for the Los Angeles Dodgers. … Lynn mostly relies on hard stuff, a 91.9 mph fastball, 87.8 mph cutter and 90.9 mph sinker.

Diamondbacks LHP Tommy Henry (0-1, 6.87) vs. Cardinals LHP Steven Matz (1-1, 3.60), 4:45 p.m.

Henry has not officially been named the Diamondbacks starter on Tuesday, but he is with the club in St. Louis and ready to take the place of right-hander Merrill Kelly, should Kelly need a stint on the injured list. Kelly is undergoing an MRI in Phoenix on Monday to determine the extent of the damage to his right teres major. … If the Diamondbacks do not turn to Henry, left-hander Logan Allen could be an option after he pitched 4 2/3 scoreless innings in relief on Thursday. … Henry has struggled this year, never pitching more than five innings or allowing fewer than two earned runs in his four starts. … He was optioned to Triple-A last week, but is likely set to get another opportunity following injuries to Ryne Nelson and Merrill Kelly. … Matz has solid numbers in the third year of a four-year deal with the Cardinals but he only has 12 strikeouts in 20 innings. He allowed four runs (one earned) in 4 2/3 innings against the Diamondbacks in Phoenix earlier this month. … Matz’s best pitch is a sinker that he throws over half the time.

Wednesday:  At St. Louis, 10:15 a.m., Diamondbacks LHP Jordan Montgomery (1-0, 1.50) vs. Cardinals RHP Kyle Gibson (1-2, 5.04).

Thursday:  Off.

Friday:  At Seattle, 6:40 p.m., Diamondbacks RHP Zac Gallen (1-0, 1.50) vs. Mariners TBA.

Saturday: At Seattle, 6:40 p.m., Diamondbacks RHP Slade Cecconi (1-0, 3.00) vs. Mariners TBA

PRESS RELEASE: Budget 2024 Disappoints – Major Shortfalls in Canada Disability Benefit Funding & Eligibility

For Immediate Release April 17, 2024 OTTAWA, ON –  Inclusion Canada expresses profound disappointment over the inadequate funding allocated to the Canada Disability Benefit (CDB) in Budget 2024. The announced funding falls far short of what is necessary to fulfill the program’s primary objective: lifting people with disabilities out of poverty.

Budget 2024 announced funding of $6.1 billion over six years, beginning in

2024-25, and $1.4 billion annually ongoing, for a new Canada Disability Benefit. This will result in $2400/year or $200/month per person. Eligibility will be based on the Disability Tax Credit, with an estimated 600,000 people eligible. The program will only be fully implemented in 2028 at the $1.4 billion level.

Despite expectations, over 1.5 million Canadians with disabilities, including 75% of persons who have an intellectual disability living independently, continue to face deep poverty. This poverty is unchanged by the new budget. This budget leaves most of these individuals behind.  

The passage of Bill C-22 was a monumental legislative victory, underscoring widespread bipartisan support and countless disability groups rallying behind the legislation. Despite this, the announced funding in Budget 2024 leaves people with disabilities feeling abandoned, and uncertain about their future.

“Our disappointment cannot be overstated,” admitted Krista Carr, Executive Vice President of Inclusion Canada, “A maximum benefit of $200/month or $6/day is inadequate. This benefit was supposed to lift persons with disabilities out of poverty, not merely make them marginally less poor than they already are.” said Carr.

The government’s insistence on using the Disability Tax Credit (DTC) program to determine eligibility is also deeply concerning. The DTC program currently excludes many individuals who face significant barriers to qualifying, meaning many people with disabilities who are currently in poverty would not get the benefit. The government must commit to a wholesale review and reform of the DTC problem in parallel with rolling out the benefit to maximize its impact.

Budget 2024’s financial commitment also fails to uphold the legislation instructing its creation.

“The legislation states that the government must consider the official poverty line and additional costs associated with living with a disability when determining the benefit,” commented Moira Wilson, President of Inclusion Canada, “What poverty line did they consider in their determination? This benefit fails to achieve what it is designed to do and will not bring people with intellectual disabilities out of poverty. We expected more from this budget, and our hope is fading.”

The clock is ticking louder than ever for Canadians with disabilities. Every day without an adequately funded Canada Disability Benefit is a missed opportunity to support people to live with dignity. We call on the government to announce enhanced investments in the next Fiscal Economic Statement (FES) to substantially increase this benefit and broaden the eligibility.

For media inquiries, please contact: Marc Muschler Senior Communications Officer 416-661-9611 ext. 232 [email protected] About Inclusion Canada   Inclusion Canada  is a nationwide community that champions the rights and inclusion of individuals with intellectual disabilities, their families, allies, and local associations across Canada. The organization is committed to creating an inclusive Canada where everyone, regardless of intellectual capability, is valued and fully engaged in community life.

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Sports. Honestly. Since 2011

Dodgers all-star embarking on another rehab assignment.

• April 22, 2024
• cresswellmccoy

The Los Angeles Dodgers have been on a roll after a rough start to the season. The club is picking up the pace with their performance as they remain at the top of the NL West. One of the primary reasons for the team’s struggle has been their pitching. Despite adding Tyler Glasnow and Yoshinobu Yamamoto in the offseason, the pitching staff has not progressed in the right direction. On the other hand, the franchise has been missing out on top pitchers. With Clayton Kershaw still sidelined from offseason surgery , the Dodgers expected Walker Buehler to return. However, the two-time All-Star’s debut is still a ways off. Buehler will take on Oklahoma City as part of his rehab assignment.

Walker Buehler’s Rehab Assignment Continues

Buehler will need to improve to get back into the majors. Buehler’s last assignment with Oklahoma City was a struggle. The Dodgers are concerned about getting him on board since he failed to last more than three innings against a Triple-A team.

Los Angeles Dodger Walker Buehler is scheduled to take the mound against the Topes as part of a Major League Rehab Assignment! The two-time All-Star and 2020 World Series Champ is scheduled to pitch this Wednesday. ?️ https://t.co/xEE9xmTmO9 pic.twitter.com/fFi80bDRck — Albuquerque Isotopes (@ABQTopes) April 22, 2024

Dave Roberts Weighs In on Buehler’s Progress

Dodgers manager Dave Roberts has kept an eye on Buehler’s situation and feels time will help him progress. Roberts stated that Buehler has been on and off with his performance. He has seen improvement in Buehler’s performance, but his curveball has been slightly off.

While Roberts appreciated the pitcher’s improvement, he felt Buehler needed more pitching practice. Buehler will make his fifth rehab start and hope to pick up the pace. The Dodgers are keen on bringing back Buehler, as they could use some extra firepower in their starting rotation.

Buehler has also struggled with minor injuries during his rehab stint.  In his Single-A assignment against Rancho Cucamonga, Buehler was hit in the right hand and was forced to leave the field after pitching only two innings. It’s been a hard journey for the Dodgers star, but a strong comeback would certainly help the team.

Photo Credit: © Kiyoshi Mio-USA TODAY Sports

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Mets activated Reid-Foley from IL, designate Tonkin for assignment

• Field Level Media

The New York Mets designated Michael Tonkin for assignment Monday for the second time this month and activated fellow right-hander Sean Reid-Foley off the 15-day injured list.

Reid-Foley, 28, opened the season on the IL with a shoulder impingement. He appeared in eight games with the Mets in 2023 and is 7-10 with a 4.58 ERA in 48 career appearances (13 starts) for Toronto (2018-20) and the Mets.

The club also called up LHP Josh Walker after it optioned RHP Grant Hartwig to Triple-A Syracuse following Sunday's blowout loss to the Los Angeles Dodgers .

The Mets DFA'd Tonkin, 34, was April 5 before trading him to Minnesota a few days later. The Mets brought him back last week after the Twins DFA'd him on April 13. He is 1-2 with a 6.00 ERA in six relief appearances overall this season.

Hartwig, 26, appeared in two games and had a strikeout in three innings of work.

Walker, 29, appeared in 14 games with the Mets in 2023, going 0-1 with an 8.10 ERA. He's 0-1 with a 2.79 ERA in seven relief appearances at Syracuse this season.

The Mets open a three-game series at San Francisco on Monday night.