Average Reward Rate Research Articles

Regulation of reinforcement learning parameters captures long-term changes in rat behaviour.

In uncertain environments in which resources fluctuate continuously, animals must permanently decide whether to stabilise learning and exploit what they currently believe to be their best option, or instead explore potential alternatives and learn fast from new observations. While such a trade-off has been extensively studied in pretrained animals facing non-stationary decision-making tasks, it is yet unknown how they progressively tune it while learning the task structure during pretraining. Here, we compared the ability of different computational models to account for long-term changes in the behaviour of 24 rats while they learned to choose a rewarded lever in a three-armed bandit task across 24 days of pretraining. We found that the day-by-day evolution of rat performance and win-shift tendency revealed a progressive stabilisation of the way they regulated reinforcement learning parameters. We successfully captured these behavioural adaptations using a meta-learning model in which either the learning rate or the inverse temperature was controlled by the average reward rate.

Striatal and Behavioral Responses to Reward Vary by Socioeconomic Status in Adolescents.

Disparities in socioeconomic status (SES) lead to unequal access to financial and social support. These disparities are believed to influence reward sensitivity, which in turn are hypothesized to shape how individuals respond to and pursue rewarding experiences. However, surprisingly little is known about how SES shapes reward sensitivity in adolescence. Here, we investigated how SES influenced adolescent responses to reward, both in behavior and the striatum-a brain region that is highly sensitive to reward. We examined responses to both immediate reward (tracked by phasic dopamine) and average reward rate fluctuations (tracked by tonic dopamine) as these distinct signals independently shape learning and motivation. Adolescents (n = 114; 12-14 years; 58 female) performed a gambling task during functional magnetic resonance imaging. We manipulated trial-by-trial reward and loss outcomes, leading to fluctuations between periods of reward scarcity and abundance. We found that a higher reward rate hastened behavioral responses, and increased guess switching, consistent with the idea that reward abundance increases response vigor and exploration. Moreover, immediate reward reinforced previously rewarding decisions (win-stay, lose-switch) and slowed responses (postreward pausing), particularly when rewards were scarce. Notably, lower-SES adolescents slowed down less after rare rewards than higher-SES adolescents. In the brain, striatal activations covaried with the average reward rate across time and showed greater activations during rewarding blocks. However, these striatal effects were diminished in lower-SES adolescents. These findings show that the striatum tracks reward rate fluctuations, which shape decisions and motivation. Moreover, lower SES appears to attenuate reward-driven behavioral and brain responses.

Average reward rates enable motivational transfer across independent reinforcement learning tasks

Outcomes and feedbacks on performance may influence behavior beyond the context in which it was received, yet it remains unclear what neurobehavioral mechanisms may account for such lingering influences on behavior. The average reward rate (ARR) has been suggested to regulate motivated behavior, and was found to interact with dopamine-sensitive cognitive processes, such as vigilance and associative memory encoding. The ARR could therefore provide a bridge between independent tasks when these are performed in temporal proximity, such that the reward rate obtained in one task could influence performance in a second subsequent task. Reinforcement learning depends on the coding of prediction error signals by dopamine neurons and their downstream targets, in particular the nucleus accumbens. Because these brain regions also respond to changes in ARR, reinforcement learning may be vulnerable to changes in ARR. To test this hypothesis, we designed a novel paradigm in which participants (n = 245) performed two probabilistic reinforcement learning tasks presented in interleaved trials. The ARR was controlled by an "induction" task which provided feedback with a low (p = 0.58), a medium (p = 0.75), or a high probability of reward (p = 0.92), while the impact of ARR on reinforcement learning was tested by a second "reference" task with a constant reward probability (p = 0.75). We find that performance was significantly lower in the reference task when the induction task provided low reward probabilities (i.e., during low levels of ARR), as compared to the medium and high ARR conditions. Behavioral modeling further revealed that the influence of ARR is best described by models which accumulates average rewards (rather than average prediction errors), and where the ARR directly modulates the prediction error signal (rather than affecting learning rates or exploration). Our results demonstrate how affective information in one domain may transfer and affect motivated behavior in other domains. These findings are particularly relevant for understanding mood disorders, but may also inform abnormal behaviors attributed to dopamine dysfunction.

The Average Reward Rate Modulates Behavioral and Neural Indices of Effortful Control Allocation.

People tend to avoid exerting cognitive effort, and findings from recent behavioral studies suggest that effort allocation is in part determined by the opportunity cost of slothful responding-operationalized as the average reward rate per unit time. When the average rate of reward is high, individuals make more errors in cognitive control tasks, presumably owing to a withdrawal of costly cognitive processing. An open question remains whether the presumed modulations of cognitively effortful control processes are observable at the neural level. Here, we measured EEG while participants completed the Simon task, a well-known response conflict task, while the experienced average reward rate fluctuated across trials. We examined neural activity associated with the opportunity cost of time by applying generalized eigendecomposition, a hypothesis-driven source separation technique, to identify a midfrontal component associated with the average reward rate. Fluctuations in average reward rate modulated not only component amplitude but also, most importantly, component theta power (4-8 Hz). Higher average reward rate was associated with reduced theta power, suggesting that the opportunity of time modulates effort allocation. These neural results provide evidence for the idea that people strategically modulate the amount of cognitive effort they exert based on the opportunity cost of time.

Dopamine and reward-related vigor in younger and older adults

Vigor reflects how motivated people are to respond to stimuli. We previously showed that, on average, humans are more vigorous when a higher rate of reward is available, and that this relationship is modulated by the dopamine precursor levodopa. Dopamine signaling and probabilistic reward learning deteriorate across the adult life span, and thus, the relationship between vigor and reward may also change in aging. We tested this assertion and assessed whether it correlates with D1 dopamine receptor availability, measured using Positron Emission Tomography. We registered response times of 30 older and 30 younger participants during an oddball discrimination task where rewards varied systematically between trials. The average reward rate had a similar impact on vigor in both age groups. There was a weak positive association between ventral striatal dopamine receptor availability and the effect of average reward rate on response time. Overall, the effect of reward on response vigor was similar in younger and older adults, and weakly correlated with dopamine D1 receptor availability.

Rat Anterior Cingulate Cortex Continuously Signals Decision Variables in a Patch Foraging Task.

In patch foraging tasks, animals must decide whether to remain with a depleting resource or to leave it in search of a potentially better source of reward. In such tasks, animals consistently follow the general predictions of optimal foraging theory (the marginal value theorem; MVT): to leave a patch when the reward rate in the current patch depletes to the average reward rate across patches. Prior studies implicate an important role for the anterior cingulate cortex (ACC) in foraging decisions based on MVT: within single trials, ACC activity increases immediately preceding foraging decisions, and across trials, these dynamics are modulated as the value of staying in the patch depletes to the average reward rate. Here, we test whether these activity patterns reflect dynamic encoding of decision-variables and whether these signals are directly involved in decision-making. We developed a leaky accumulator model based on the MVT that generates estimates of decision variables within and across trials, and tested model predictions against ACC activity recorded from male rats performing a patch foraging task. Model predicted changes in MVT decision variables closely matched rat ACC activity. Next, we pharmacologically inactivated ACC in male rats to test the contribution of these signals to decision-making. ACC inactivation had a profound effect on rats' foraging decisions and response times (RTs) yet rats still followed the MVT decision rule. These findings indicate that the ACC encodes foraging-related variables for reasons unrelated to patch-leaving decisions.SIGNIFICANCE STATEMENT The ability to make adaptive patch-foraging decisions, to remain with a depleting resource or search for better alternatives, is critical to animal well-being. Previous studies have found that anterior cingulate cortex (ACC) activity is modulated at different points in the foraging decision process, raising questions about whether the ACC guides ongoing decisions or serves a more general purpose of regulating cognitive control. To investigate the function of the ACC in foraging, the present study developed a dynamic model of behavior and neural activity, and tested model predictions using recordings and inactivation of ACC. Findings revealed that ACC continuously signals decision variables but that these signals are more likely used to monitor and regulate ongoing processes than to guide foraging decisions.

Effects of average reward rate on vigor as a function of individual variation in striatal dopamine.

We constantly need to decide not only which actions to perform, but also how vigorously to perform them. In agreement with an earlier theoretical model, it has been shown that a significant portion of the variance in our action vigor can be explained by the average rate of rewards received for that action. Moreover, this invigorating effect of average reward rate was shown to vary with within-subject changes in dopamine, both in human individuals and experimental rodents. Here, we assessed whether individual differences in the effect of average reward rate on vigor are related to individual variation in a stable measure of striatal dopamine function in healthy, unmedicated participants. Forty-four participants performed a discrimination task to test the effect of average reward rate on response times to index vigor and completed an [18F]-DOPA PET scan to index striatal dopamine synthesis capacity. We did not find an interaction between dopamine synthesis capacity and average reward rate across the entire group. However, a post hoc analysis revealed that participants with higher striatal dopamine synthesis capacity, particularly in the nucleus accumbens, exhibited a stronger invigorating effect of average reward rate among the 30 slowest participants. Our findings provide converging evidence for a role of striatal dopamine in average reward rate signaling, thereby extending the current literature on the mechanistic link between average reward rate, vigor, and dopamine.

Control over patch encounters changes foraging behavior

SummaryForaging is a common decision problem in natural environments. When new exploitable sites are always available, a simple optimal strategy is to leave a current site when its return falls below a single average reward rate. Here, we examined foraging in a more structured environment, with a limited number of sites that replenished at different rates and had to be revisited. When participants could choose sites, they visited fast-replenishing sites more often, left sites at higher levels of reward, and achieved a higher net reward rate. Decisions to exploit-or-leave a site were best explained with a computational model that included both the average reward rate for the environment and reward information about the unattended sites. This suggests that unattended sites influence leave decisions, in foraging environments where sites can be revisited.

Seizing the opportunity: Lifespan differences in the effects of the opportunity cost of time on cognitive control

Previous work suggests that lifespan developmental differences in cognitive control reflect maturational and aging-related changes in prefrontal cortex functioning. However, complementary explanations exist: It could be that children and older adults differ from younger adults in how they balance the effort of engaging in control against its potential benefits. Here we test whether the degree of cognitive effort expenditure depends on the opportunity cost of time (average reward rate per unit time): if the average reward rate is high, participants should withhold cognitive effort whereas if it is low, they should invest more. In Experiment 1, we examine this hypothesis in children, adolescents, younger, and older adults, by applying a reward rate manipulation in two cognitive control tasks: a modified Erikson Flanker and a task-switching paradigm. We found that young adults and adolescents reflexively withheld effort when the opportunity cost of time was high, whereas older adults and, to a lesser degree children, invested more resources to accumulate reward as quickly as possible. We tentatively interpret these results in terms of age- and task-specific differences in the processing of the opportunity cost of time. We qualify our findings in a second experiment in younger adults in which we address an alternative explanation of our results and show that the observed age differences in effort expenditure may not result from differences in task difficulty.To conclude, we think that our results present an interesting first step at relating opportunity costs to motivational processes across the lifespan. We frame the implications of further work in this area within a recent developmental model of resource-rationality, which points to developmental sweet spots in cognitive control.

Predictive Maintenance and Sensitivity Analysis for Equipment with Multiple Quality States

This paper discusses the predictive maintenance (PM) problem of a single equipment system. It is assumed that the equipment has deteriorating quality states as it operates, resulting in multiple yield levels represented as system observation states. We cast the equipment deterioration as discrete-state and continuous-time semi-Markov decision process (SMDP) model and solve the SMDP problem in reinforcement learning (RL) framework using the strategy-based method. In doing so, the goal is to maximize the system average reward rate (SARR) and generate the optimal maintenance strategy for given observation states. Further, the PM time is capable of being produced by a simulation method. In order to prove the advantage of our proposed method, we introduce the standard sequential preventive maintenance algorithm with unequal time interval. Our proposed method is compared with the sequential preventive maintenance algorithm in a test objective of SARR, and the results tell us that our proposed method can outperform the sequential preventive maintenance algorithm. In the end, the sensitivity analysis of some parameters on the PM time is given.

Control Over Patch Encounters Changes Foraging Behaviour

Foraging is a common decision problem in natural environments. When new exploitable sites are always available, a simple optimal strategy is to leave a current site when its return falls below a single average reward rate. Here, we examined foraging in a more structured environment, with a limited number of sites that replenished at different rates and had to be revisited. When participants could choose sites, they visited fast-replenishing sites more often, left sites at higher levels of reward, and achieved a higher net reward rate. Decisions to exploit-or-leave a site were best explained with a computational model estimating separate reward rates for each site. This suggests option-specific information can be used to construct a threshold for patch leaving in some foraging settings, rather than a single average reward rate.

Global reward state affects learning and activity in raphe nucleus and anterior insula in monkeys

People and other animals learn the values of choices by observing the contingencies between them and their outcomes. However, decisions are not guided by choice-linked reward associations alone; macaques also maintain a memory of the general, average reward rate – the global reward state – in an environment. Remarkably, global reward state affects the way that each choice outcome is valued and influences future decisions so that the impact of both choice success and failure is different in rich and poor environments. Successful choices are more likely to be repeated but this is especially the case in rich environments. Unsuccessful choices are more likely to be abandoned but this is especially likely in poor environments. Functional magnetic resonance imaging (fMRI) revealed two distinct patterns of activity, one in anterior insula and one in the dorsal raphe nucleus, that track global reward state as well as specific outcome events.

A Basal Forebrain-Cingulate Circuit in Macaques Decides It Is Time to Act

SummaryThe medial frontal cortex has been linked to voluntary action, but an explanation of why decisions to act emerge at particular points in time has been lacking. We show that, in macaques, decisions about whether and when to act are predicted by a set of features defining the animal’s current and past context; for example, respectively, cues indicating the current average rate of reward and recent previous voluntary action decisions. We show that activity in two brain areas—the anterior cingulate cortex and basal forebrain—tracks these contextual factors and mediates their effects on behavior in distinct ways. We use focused transcranial ultrasound to selectively and effectively stimulate deep in the brain, even as deep as the basal forebrain, and demonstrate that alteration of activity in the two areas changes decisions about when to act.

Ventromedial Prefrontal Cortex Tracks Multiple Environmental Variables during Search.

To make efficient foraging decisions, we must combine information about the values of available options with nonvalue information. Some accounts of ventromedial PFC (vmPFC) suggest that it has a narrow role limited to evaluating immediately available options. We examined responses of neurons in area 14 (a putative macaque homolog of human vmPFC) as 2 male macaques performed a novel foraging search task. Although many neurons encoded the values of immediately available offers, they also independently encoded several other variables that influence choice, but that are conceptually distinct from offer value. These variables include average reward rate, number of offers viewed per trial, previous offer values, previous outcome sizes, and the locations of the currently attended offer. We conclude that, rather than serving as specialized economic value center, vmPFC plays a broad role in integrating relevant environmental information to drive foraging decisions.SIGNIFICANCE STATEMENT Decision makers must often choose whether to take an immediately available option or continue to search for a better one. We hypothesized that this process, which is integral to foraging theory, leaves neural signatures in the brain region ventromedial PFC. Subjects performed a novel foraging task in which they searched through differently valued options and attempted to balance their reward threshold with various time costs. We found that neurons not only encode the values of immediately available offers, but multiplexed these with environmental variables, including reward rate, number of offers viewed, previous offer values, and spatial information. We conclude that vmPFC plays a rich role in encoding and integrating multiple foraging-related variables during economic decisions.

The opportunity cost of time modulates cognitive effort

A spate of recent work demonstrates that humans seek to avoid the expenditure of cognitive effort, much like physical effort or economic resources. Less is clear, however, about the circumstances dictating how and when people decide to expend cognitive effort. Here we adopt a popular theory of opportunity costs and response vigor and to elucidate this question. This account, grounded in Reinforcement Learning, formalizes a trade-off between two costs: the harder work assumed necessary to emit faster actions and the opportunity cost inherent in acting more slowly (i.e., the delay that results to the next reward and subsequent rewards). Recent work reveals that the opportunity cost of time—operationalized as the average reward rate per unit time, theorized to be signaled by tonic dopamine levels, modulates the speed with which a person responds in a simple discrimination tasks. We extend this framework to cognitive effort in a diverse range of cognitive tasks, for which 1) the amount of cognitive effort demanded from the task varies from trial to trial and 2) the putative expenditure of cognitive effort holds measureable consequences in terms of accuracy and response time. In the domains of cognitive control, perceptual decision-making, and task-switching, we found that subjects tuned their level of effort exertion in accordance with the experienced average reward rate: when the opportunity cost of time was high, subjects made more errors and responded more quickly, which we interpret as a withdrawal of cognitive effort. That is, expenditure of cognitive effort appeared to be modulated by the opportunity cost of time. Further, and consistent with our account, the strength of this modulation was predicted by individual differences in efficacy of cognitive control. Taken together, our results elucidate the circumstances dictating how and when people expend cognitive effort.

To Do or Not to Do: Dopamine, Affordability and the Economics of Opportunity.

Five years ago, we introduced the thrift hypothesis of dopamine (DA), suggesting that the primary role of DA in adaptive behavior is regulating behavioral energy expenditure to match the prevailing economic conditions of the environment. Here we elaborate that hypothesis with several new ideas. First, we introduce the concept of affordability, suggesting that costs must necessarily be evaluated with respect to the availability of resources to the organism, which computes a value not only for the potential reward opportunity, but also the value of resources expended. Placing both costs and benefits within the context of the larger economy in which the animal is functioning requires consideration of the different timescales against which to compute resource availability, or average reward rate. Appropriate windows of computation for tracking resources requires corresponding neural substrates that operate on these different timescales. In discussing temporal patterns of DA signaling, we focus on a neglected form of DA plasticity and adaptation, changes in the physical substrate of the DA system itself, such as up- and down-regulation of receptors or release probability. We argue that changes in the DA substrate itself fundamentally alter its computational function, which we propose mediates adaptations to longer temporal horizons and economic conditions. In developing our hypothesis, we focus on DA D2 receptors (D2R), arguing that D2R implements a form of “cost control” in response to the environmental economy, serving as the “brain’s comptroller”. We propose that the balance between the direct and indirect pathway, regulated by relative expression of D1 and D2 DA receptors, implements affordability. Finally, as we review data, we discuss limitations in current approaches that impede fully investigating the proposed hypothesis and highlight alternative, more semi-naturalistic strategies more conducive to neuroeconomic investigations on the role of DA in adaptive behavior.

Reward Rate Maximization and Optimal Transmission Policy of EH Device With Temporal Death in EH-WSNs

For the perpetual wireless sensor network (WSN), energy harvesting (EH) technology is emerging as a promising solution. However, the randomness and the instability of the harvested energy may lead to the occurrence of the temporal death, which is harmful to the functions of the WSN, and has negative impact on the quality of service of the network. With temporal death being taken into account, this paper proposes a novel and overall framework, namely, a multi-layer Markov fluid queue (MLMFQ) model, for modeling and analyzing the data transmission nature of the EH devices (EHDs). We formulate the model of the whole system in terms of MLMFQ, and obtain the stead-state probabilities of the EHD. We study the issue of how to maximize the steady-state average reward rate of the reported data packets. We then propose an optimization model, in which one can maximize the overall steady-state average reward rate with relation to transmission policy under the specific constraints. On this basis, we are able to propose an algorithm for calculating the optimal transmission policy of the EHD with temporal death. We validate our results using a numerical example and report some interesting findings from our numerical studies.

An extended geometric process repair model with delayed repair and slight failure type

ABSTRACTThis article proposes an extended geometric process repair model to generalize the geometric process repair model and studies a repair-replacement problem for a simple repairable system with delayed repair, based on the failure number N of the system under the new model. An optimal replacement policy N* is determined by maximizing the average reward rate of the system. The explicit expression of the average reward rate is derived, and the uniqueness of the optimal replacement policy N* is also proved. Finally, a numerical example is given to illustrate some theoretical results and the model applicability.

Dopamine Manipulation Affects Response Vigor Independently of Opportunity Cost.

Dopamine is known to be involved in regulating effort investment in relation to reward, and the disruption of this mechanism is thought to be central in some pathological situations such as Parkinson's disease, addiction, and depression. According to an influential model, dopamine plays this role by encoding the opportunity cost, i.e., the average value of forfeited actions, which is an important parameter to take into account when making decisions about which action to undertake and how fast to execute it. We tested this hypothesis by asking healthy human participants to perform two effort-based decision-making tasks, following either placebo or levodopa intake in a double blind within-subject protocol. In the effort-constrained task, there was a trade-off between the amount of force exerted and the time spent in executing the task, such that investing more effort decreased the opportunity cost. In the time-constrained task, the effort duration was constant, but exerting more force allowed the subject to earn more substantial reward instead of saving time. Contrary to the model predictions, we found that levodopa caused an increase in the force exerted only in the time-constrained task, in which there was no trade-off between effort and opportunity cost. In addition, a computational model showed that dopamine manipulation left the opportunity cost factor unaffected but altered the ratio between the effort cost and reinforcement value. These findings suggest that dopamine does not represent the opportunity cost but rather modulates how much effort a given reward is worth. Dopamine has been proposed in a prevalent theory to signal the average reward rate, used to estimate the cost of investing time in an action, also referred to as opportunity cost. We contrasted the effect of dopamine manipulation in healthy participants in two tasks, in which increasing response vigor (i.e., the amount of effort invested in an action) allowed either to save time or to earn more reward. We found that levodopa-a synthetic precursor of dopamine-increases response vigor only in the latter situation, demonstrating that, rather than the opportunity cost, dopamine is involved in computing the expected value of effort.

Do learning rates adapt to the distribution of rewards?

Studies of reinforcement learning have shown that humans learn differently in response to positive and negative reward prediction errors, a phenomenon that can be captured computationally by positing asymmetric learning rates. This asymmetry, motivated by neurobiological and cognitive considerations, has been invoked to explain learning differences across the lifespan as well as a range of psychiatric disorders. Recent theoretical work, motivated by normative considerations, has hypothesized that the learning rate asymmetry should be modulated by the distribution of rewards across the available options. In particular, the learning rate for negative prediction errors should be higher than the learning rate for positive prediction errors when the average reward rate is high, and this relationship should reverse when the reward rate is low. We tested this hypothesis in a series of experiments. Contrary to the theoretical predictions, we found that the asymmetry was largely insensitive to the average reward rate; instead, the dominant pattern was a higher learning rate for negative than for positive prediction errors, possibly reflecting risk aversion.