Bounded Rationality

Human cognitive constraints are generally viewed as limiting factors in problem-solving. We argue that these constraints can instead play a critical role in driving advances in mathematics and beyond. We propose a theory of mathematical abstraction as a resource-rational search for bottlenecks in problem-solving. Bottlenecks arising from cognitive constraints create pressure to restructure existing knowledge, potentially giving rise to novel formalisms with applications beyond the problems that originally motivated them. Drawing on episodes from the history of mathematics, we illustrate how such bottlenecks can drive the development of novel abstractions and examine how cognitive constraints and affective responses shape this process. Finally, we discuss the implications of this account for machine mathematical discovery and argue that incorporating human-like constraints may facilitate the discovery of useful mathematical abstractions.

This work considers adaptive shared human-robot control for nonlinear control-affine systems, where the assumption of a fully rational human is relaxed and the robot adapts its assistance to observed boundedly rational human behavior. We use a level-k bounded-rationality model of the two-player game to construct a finite bank of candidate human and robot policies through alternating best-response computations, with the associated value functions and policies approximated using adaptive dynamic programming. During the shared-control interaction, state-transition residuals compare the measured system evolution with the trajectories predicted by the candidate human policies. The residuals are accumulated using a forgetting factor and mapped to a probabilistic human-behavior model over the finite candidate bank. Rather than selecting a single candidate or averaging stored robot policies, the robot computes a distribution-aware one-step best response by minimizing an expected cooperative cost over the complete estimated human behavior distribution. For a quadratic terminal-value approximation and Euler state propagation, this response admits a closed-form solution expressed in terms of the expected human input. The proposed methods are evaluated in simulations of a benchmark nonlinear system stabilization task, and of a planar manipulator shared control setup. The reported results show decreasing Kullback-Leibler divergence between the estimated and simulated human behavior distributions, and a lower accumulated running cost for the robot agent over the shared control interaction period, than the maximum-probability and probability-weighted alternative policies baseline.

AI assistants often collaborate by proposing candidate edits, plans, or designs that users evaluate before adoption. Existing assistance methods focus on proposal quality or user-goal inference, often assuming that the user can reliably evaluate any proposal, which can fail in practice because of bounded rationality. We study evaluability-aware proposal planning, where proposals serve both as task interventions and as probes for learning latent preferences and evaluation constraints, where the resulting belief updates then guide later proposals. We formalise this setting as ProSE, a hidden-parameter sequential assistance problem, and instantiate it with a KL-regularised bounded-rational binary response model in which acceptance trades off value gain against a distance-dependent evaluability penalty. Analysing the planning consequence of this likelihood reveals that likely accepted proposals and informative probes need not coincide, which explains why planners that only pursue acceptance systematically underperform. We operationalise ProSE with \textsc{ProSE-Plan}, a depth-2 Bayes-adaptive planner that scores proposals by possible responses and response-induced posterior beliefs. In controlled graph simulations, \textsc{ProSE-Plan} improves over evaluability-unaware and myopic baselines when evaluation cost is the bottleneck, and a probe-commit ablation confirms that our approach selects informative proposals that simpler methods miss. Our results thus identify user evaluability as a planning-relevant dimension of AI assistance, complementary to generation quality and preference inference.

Collective artificial intelligence, where multiple agents work on shared tasks, holds potential to solve expansive problems in fields from medicine to collective governance. But while prescriptive engineering solutions abound, we lack descriptive scientific understanding of artificial collectives, and therefore principles for how to design resource efficient multi-agent systems. Through systematic experiments with optimizing agents, we characterize how agent interpretive abilities, rationality bounds, and task qualities interact to shape collective performance. Agents range from specialists, with narrow interpretive abilities, to generalists, with broad ones. Collectives of specialists correspond to sparse, centralized networks, while collectives of generalists correspond to dense, decentralized ones. We show that interpretive network properties have small performance effects on average (0.07 standard deviations of performance). However, for specific task qualities, these effects are 4.5 times larger (0.33 sd) and can reach much higher for certain task qualities (1.84 sd). This leads collectives of generalists to perform better on tasks that involve generating, choosing, and coordinating, while collectives of specialists with a few generalist mediators perform better on tasks that involve negotiating. Rationality bounds then moderate these relationships. At loose bounds, specialists outperform generalists through more effective sampling of high-dimensional decision spaces. At tight bounds, generalists outperform specialists through better gradient estimation. A fundamental trade-off between performance and convergence speed emerges at moderate bounds. These findings suggest that multi-agent design could benefit from matching interpretive networks to both task demands and agents' computational limits, with implications for the efficiency and energy costs of multi-agent systems.

Strategic classification(SC) studies the interaction between decision models and agents who strategically manipulate their features for favorable outcomes. Existing SC frameworks typically rely on the idealized assumption that agents are strictly rational. However, evidence from behavioral economics and psychology consistently shows that real-world decision-making is often shaped by cognitive biases, deviating from pure rationality. To formalize this limitation, we identify and define a new problem setting, termed the behaviorally realistic strategic classification problem, where agents' strategic manipulations deviate from full rationality due to psychological biases. Motivated by the identified limitation, we propose the Prospect-Guided Strategic Framework (Pro-SF) to address the problem, a principled framework grounded in prospect theory to model and learn under behaviorally realistic strategic responses. Specifically, to capture behaviorally realistic strategic manipulations, our framework reformulates the Stackelberg-style interaction between agents and the decision-maker by incorporating three key mechanisms inspired by prospect theory, including the asymmetry between benefits and costs, different subjective reference points, and non-rational probability distortion. Experiments on synthetic and real-world datasets establish Pro-SF as a behaviorally grounded approach to strategic classification, bridging machine learning and behavioral economics for more reliable deployment in the real world.

Many consumer decisions are repeated choices under uncertainty. Standard models capture these decisions using Bayesian learning and dynamic programming: consumers update beliefs from feedback and use those beliefs to guide future choices. In many markets, however, learning does not restart when consumers enter a new context: prior experience with a brand, product, or provider can shape beliefs in later, related decisions. We study this cross-context knowledge transfer, or meta-learning, in sequential choice. We design a hierarchical laboratory task in which participants repeatedly choose among airlines across routes and observe noisy binary outcomes. Reduced-form evidence shows that participants improve not only within routes, but also across routes: they choose better airlines earlier in later routes and reduce pseudo-regret. To identify the mechanism behind this transfer, we compare human choices to a no-transfer benchmark and a fully integrated Bayesian meta-learning benchmark. In particular, we introduce a class of boundedly rational meta dynamic programming policies, BRMDP(D), that approximate full integration using a limited number of hyper-posterior draws, denoted by D. Trial-by-trial likelihood comparisons show that low-D boundedly rational meta-learning, especially BRMDP(1), fits participant behavior better than both no transfer and fully integrated Bayesian transfer. Consumers, therefore, transfer brand-level regularities across contexts, but through coarse representations of prior uncertainty. The findings imply that models of consumer learning should allow for approximate cross-context transfer, and that managerial counterfactuals based on either no-transfer or fully integrated learning can be misleading.

A learner does not only fit data; it also determines how strongly the training sample may shape its output and how much distortion it can hedge. We study this relation as a bounded-rational decision problem whose primitive object is the induced channel from samples to outputs. The learner's response law determines which changes in this channel are cheap or costly, and therefore induces both a lower tradeoff curve between training loss and sample dependence and a matched upper certificate curve. When the response law is represented by an $f$-divergence regularizer, these curves live in the regularizer's native information geometry, with KL as the special case corresponding to Shannon mutual information. We show how the hedge and the two curves can be recovered from black-box behavior by observing responses to scaled losses and local loss perturbations. In learning, population loss is empirical loss plus the distortion induced by the particular training sample. The recovered hedge gives a practical certificate when it covers that distortion. Thus generalization is treated as a testable hedging property of the learner's own response law.

Hospital pharmacists make high-stakes decisions to mitigate drug shortages under uncertainty, time pressure, and patient risk. Interviews revealed that pharmacists focus attention on a small subset of drugs, limiting cognitive effort to the most urgent cases. Motivated by these findings, we formalize a bounded-rational, attention-guided decision framework that dynamically decomposes drugs into a subset for high-cost reasoning and a complementary subset for low-cost monitoring. We develop two agents: an Expert Agent that applies attention weights derived from pharmacist interviews, and a Learner Agent that adapts attention allocation over time through experience. Across simulated scenarios spanning short to long horizons, we show that attention-guided planning supports stable decision-making without complete state reasoning. These results suggest that a primary decision is not what action to take, but where to allocate cognitive effort, and that attention-guided, satisficing strategies can reduce problem complexity while maintaining stable performance.

In this (work in progress) paper, we present Bounded Pragmatic Listener (or BPL), a cognitively grounded Bayesian framework for modelling susceptibility to information disorder. BPL extends Rational Speech Act theory with three cognitively motivated bounds derived from the bounded rationality literature with a) a recursion depth bound (that emphasises working memory limits);b) a prior compression parameter (which is oriented at capturing information bottleneck); and c) an availability sample size (that operationalises importance sampling with saliency-weighted proposals). This allows us to test predictions about misinformation susceptibility, annotator disagreement, and the differential vulnerability to mis-, dis-, and mal-information as defined in the Information Disorder framework. We validate BPL on the LIAR and MultiFC benchmarks showcasing competitive veracity classification and experimental support for the depth-mismatch paradox.

Games have long been a microcosm for studying planning and reasoning in both natural and artificial intelligence (AI), often focusing on expert-level or even super-human play. But real life also pushes human intelligence along a different frontier, requiring people to flexibly navigate decision-making problems that they have never thought about before. Here, we use novice gameplay to study how people reason about new problem settings. Through a series of large-scale behavioral studies with over 1000 participants and 121 two-player strategic board games (almost all novel to our participants), we show that people are systematic and adaptively rational in how they play a game for the first time, or evaluate a game (e.g., how fair or how fun it is likely to be) before they have played it even once. We explain these capacities via a computational cognitive model that we call the 'Intuitive Gamer', a model based on mechanisms of fast and flat (depth-limited) goal-directed probabilistic simulation. Our work offers new insights into how people rapidly evaluate, act, and make suggestions when encountering novel problems, and could inform the design of more flexible and human-like AI systems that can determine not just how to solve new tasks, but whether a task is worth thinking about at all.