Bayesian Reinforcement Learning with Limited Cognitive Load

All biological and artificial agents must learn and make decisions given limits on their ability to process information. As such, a general theory of adaptive behavior should be able to account for the complex interactions between an agent's learning history, decisions, and capacity constraints. Recent work in computer science has begun to clarify the principles that shape these dynamics by bridging ideas from reinforcement learning, Bayesian decision-making, and rate-distortion theory. This body of work provides an account of capacity-limited Bayesian reinforcement learning, a unifying normative framework for modeling the effect of processing constraints on learning and action selection. Here, we provide an accessible review of recent algorithms and theoretical results in this setting, paying special attention to how these ideas can be applied to studying questions in the cognitive and behavioral sciences.

Humans decompose tasks by trading off utility and computational cost

Human behavior emerges from planning over elaborate decompositions of tasks into goals, subgoals, and low-level actions. How are these decompositions created and used? Here, we propose and evaluate a normative framework for task decomposition based on the simple idea that people decompose tasks to reduce the overall cost of planning while maintaining task performance. Analyzing 11,117 distinct graph-structured planning tasks, we find that our framework justifies several existing heuristics for task decomposition and makes predictions that can be distinguished from two alternative normative accounts. We report a behavioral study of task decomposition ($N=806$) that uses 30 randomly sampled graphs, a larger and more diverse set than that of any previous behavioral study on this topic. We find that human responses are more consistent with our framework for task decomposition than alternative normative accounts and are most consistent with a heuristic -- betweenness centrality -- that is justified by our approach. Taken together, our results provide new theoretical insight into the computational principles underlying the intelligent structuring of goal-directed behavior.

On Rate-Distortion Theory in Capacity-Limited Cognition & Reinforcement Learning

Throughout the cognitive-science literature, there is widespread agreement that decision-making agents operating in the real world do so under limited information-processing capabilities and without access to unbounded cognitive or computational resources. Prior work has drawn inspiration from this fact and leveraged an information-theoretic model of such behaviors or policies as communication channels operating under a bounded rate constraint. Meanwhile, a parallel line of work also capitalizes on the same principles from rate-distortion theory to formalize capacity-limited decision making through the notion of a learning target, which facilitates Bayesian regret bounds for provably-efficient learning algorithms. In this paper, we aim to elucidate this latter perspective by presenting a brief survey of these information-theoretic models of capacity-limited decision making in biological and artificial agents.

Linguistic communication as (inverse) reward design

Natural language is an intuitive and expressive way to communicate reward information to autonomous agents. It encompasses everything from concrete instructions to abstract descriptions of the world. Despite this, natural language is often challenging to learn from: it is difficult for machine learning methods to make appropriate inferences from such a wide range of input. This paper proposes a generalization of reward design as a unifying principle to ground linguistic communication: speakers choose utterances to maximize expected rewards from the listener's future behaviors. We first extend reward design to incorporate reasoning about unknown future states in a linear bandit setting. We then define a speaker model which chooses utterances according to this objective. Simulations show that short-horizon speakers (reasoning primarily about a single, known state) tend to use instructions, while long-horizon speakers (reasoning primarily about unknown, future states) tend to describe the reward function. We then define a pragmatic listener which performs inverse reward design by jointly inferring the speaker's latent horizon and rewards. Our findings suggest that this extension of reward design to linguistic communication, including the notion of a latent speaker horizon, is a promising direction for achieving more robust alignment outcomes from natural language supervision.

On the Expressivity of Markov Reward

Reward is the driving force for reinforcement-learning agents. This paper is dedicated to understanding the expressivity of reward as a way to capture tasks that we would want an agent to perform. We frame this study around three new abstract notions of "task" that might be desirable: (1) a set of acceptable behaviors, (2) a partial ordering over behaviors, or (3) a partial ordering over trajectories. Our main results prove that while reward can express many of these tasks, there exist instances of each task type that no Markov reward function can capture. We then provide a set of polynomial-time algorithms that construct a Markov reward function that allows an agent to optimize tasks of each of these three types, and correctly determine when no such reward function exists. We conclude with an empirical study that corroborates and illustrates our theoretical findings.

Cognitive science as a source of forward and inverse models of human decisions for robotics and control

Those designing autonomous systems that interact with humans will invariably face questions about how humans think and make decisions. Fortunately, computational cognitive science offers insight into human decision-making using tools that will be familiar to those with backgrounds in optimization and control (e.g., probability theory, statistical machine learning, and reinforcement learning). Here, we review some of this work, focusing on how cognitive science can provide forward models of human decision-making and inverse models of how humans think about others' decision-making. We highlight relevant recent developments, including approaches that synthesize blackbox and theory-driven modeling, accounts that recast heuristics and biases as forms of bounded optimality, and models that characterize human theory of mind and communication in decision-theoretic terms. In doing so, we aim to provide readers with a glimpse of the range of frameworks, methodologies, and actionable insights that lie at the intersection of cognitive science and control research.

Extending rational models of communication from beliefs to actions

Speakers communicate to influence their partner's beliefs and shape their actions. Belief- and action-based objectives have been explored independently in recent computational models, but it has been challenging to explicitly compare or integrate them. Indeed, we find that they are conflated in standard referential communication tasks. To distinguish these accounts, we introduce a new paradigm called signaling bandits, generalizing classic Lewis signaling games to a multi-armed bandit setting where all targets in the context have some relative value. We develop three speaker models: a belief-oriented speaker with a purely informative objective; an action-oriented speaker with an instrumental objective; and a combined speaker which integrates the two by inducing listener beliefs that generally lead to desirable actions. We then present a series of simulations demonstrating that grounding production choices in future listener actions results in relevance effects and flexible uses of nonliteral language. More broadly, our findings suggest that language games based on richer decision problems are a promising avenue for insight into rational communication.

Control of mental representations in human planning

One of the most striking features of human cognition is the capacity to plan. Two aspects of human planning stand out: its efficiency, even in complex environments, and its flexibility, even in changing environments. Efficiency is especially impressive because directly computing an optimal plan is intractable, even for modestly complex tasks, and yet people successfully solve myriad everyday problems despite limited cognitive resources. Standard accounts in psychology, economics, and artificial intelligence have suggested this is because people have a mental representation of a task and then use heuristics to plan in that representation. However, this approach generally assumes that mental representations are fixed. Here, we propose that mental representations can be controlled and that this provides opportunities to adaptively simplify problems so they can be more easily reasoned about -- a process we refer to as construal. We construct a formal model of this process and, in a series of large, pre-registered behavioral experiments, show both that construal is subject to online cognitive control and that people form value-guided construals that optimally balance the complexity of a representation and its utility for planning and acting. These results demonstrate how strategically perceiving and conceiving problems facilitates the effective use of limited cognitive resources.

Show or Tell? Demonstration is More Robust to Changes in Shared Perception than Explanation

Successful teaching entails a complex interaction between a teacher and a learner. The teacher must select and convey information based on what they think the learner perceives and believes. Teaching always involves misaligned beliefs, but studies of pedagogy often focus on situations where teachers and learners share perceptions. Nonetheless, a teacher and learner may not always experience or attend to the same aspects of the environment. Here, we study how misaligned perceptions influence communication. We hypothesize that the efficacy of different forms of communication depends on the shared perceptual state between teacher and learner. We develop a cooperative teaching game to test whether concrete mediums (demonstrations, or "showing") are more robust than abstract ones (language, or "telling") when the teacher and learner are not perceptually aligned. We find evidence that (1) language-based teaching is more affected by perceptual misalignment, but (2) demonstration-based teaching is less likely to convey nuanced information. We discuss implications for human pedagogy and machine learning.

Learning Rewards from Linguistic Feedback

We explore unconstrained natural language feedback as a learning signal for artificial agents. Humans use rich and varied language to teach, yet most prior work on interactive learning from language assumes a particular form of input (e.g. commands). We propose a general framework which does not make this assumption. We decompose linguistic feedback into two components: a grounding to $\textit{features}$ of a Markov decision process and $\textit{sentiment}$ about those features. We then perform an analogue of inverse reinforcement learning, regressing the teacher's sentiment on the features to infer their latent reward function. To evaluate our approach, we first collect a corpus of teaching behavior in a cooperative task where both teacher and learner are human. We use our framework to implement two artificial learners: a simple "literal" model and a "pragmatic" model with additional inductive biases. We baseline these with a neural network trained end-to-end to predict latent rewards. We then repeat our initial experiment pairing human teachers with our models. We find our "literal" and "pragmatic" models successfully learn from live human feedback and offer statistically-significant performance gains over the end-to-end baseline, with the "pragmatic" model approaching human performance on the task. Inspection reveals the end-to-end network learns representations similar to our models, suggesting they reflect emergent properties of the data. Our work thus provides insight into the information structure of naturalistic linguistic feedback as well as methods to leverage it for reinforcement learning.