Bayesian Decision Theory

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2 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

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Latest papers 21

Oct 7, 2026cs.LG

When Should an In-Context Learner Expand Its Hypothesis Space?

Learning systems adapt quickly inside a familiar family of models. The harder step comes earlier: deciding, from observations that could be noise, an exception, a change within the family or structure outside it, whether opening a richer family is worth its cost. We treat this as a costly sequential decision: prediction failure must be turned into structural evidence, evidence into a value of expansion, and value into action. The Structural Revision Environment produces matched failures from each source, varies the price of expansion and the remaining horizon independently of the evidence, and admits exact Bayesian calculations and an exact normative solution of the one-shot decision. Its solution shows that revision is a value boundary and not an evidence threshold: one history has different optimal actions under different prices, horizons and announced queries, the boundary between local repair and expansion is set by the inputs a rule predicts and a repair cannot cover, and belief in the richer family crosses long before the decision does. Transformers trained in the environment reproduce this boundary from utility alone. Language models of three post-training lineages carry a failure-sensitive signal in their predictions that is not reflected in their revision decisions, and given the gain of expanding they read it without weighing it against price and horizon. Three models allowed to reason weigh the stated gain in the reference's proportions and still do not turn the history into an estimate of what expansion would buy. Controlled post-training of the meta-trained learners moves the prior and the sharpness of predictions, and neither moves the criterion.

Weihan Li, Xinlei Chen, Junhao Wu +1

Department of Mechanical Engineering, The University of Tokyo, Tokyo, Japan · School of Mechanical Engineering and Automation, Harbin Institute of Technology, Shenzhen, China · Faculty of Mechanical Engineering, RWTH Aachen University, Aachen, Germany +1

In-Context Learning Metacognition in Language Models Bayesian Decision Theory

Sep 28, 2026cs.CV

Mixed-Prior Decision Risk for Open-Set Recognition

In open-set recognition (OSR), a probe must either be identified as one of the known gallery classes or rejected as unknown, so three error types coexist: false acceptance, false rejection, and misidentification. An uncertainty score for selective recognition should rank probes by the risk of the decision the system has made. Bayesian gallery-aware models such as Holistic Uncertainty Estimation (HolUE) summarize the posterior over known and unknown classes by Kullback--Leibler (KL) divergence components and map them to an uncertainty score with a supervised nonlinear calibrator. We show that the KL summary is not generally monotone in decision risk: linear fusion of the KL components tuned on validation data yields negative filtering quality on several benchmarks. We propose MPRisk, a mixed-prior posterior decision-risk score that keeps the same Bayesian posterior but directly scores the error events associated with the selected decision: false-acceptance, misidentification, and false-rejection risks, plus a non-specificity penalty for rejections, enabled by modeling unknown identities as a continuous component. Four nonnegative weights tuned on a validation set suffice for ranking; no nonlinear supervised model is required. Across nine image, audio, and text benchmarks, MPRisk achieves the best or tied-best Prediction Rejection Ratio at every operating point on the image and audio benchmarks and on most text operating points, with bootstrap-confirmed gains over HolUE on five benchmarks (up to

+0.19

PRR) at comparable or lower runtime.

L. A. Erlygin, P. D. Proskura, A. A. Zaytsev

Skolkovo Institute of Science and Technology (Skoltech), Moscow, Russia · Risk Management, Sber, Moscow, Russia · The Institute for Information Transmission Problems (IITP RAS), Moscow, Russia

Selective Prediction Open-Set Recognition Classification Bayesian Decision Theory

Sep 23, 2026stat.ML

Exact Bayes Regret and Asymptotic Optimality in High-Dimensional Gaussian Bandits

We study Bayesian linear bandits with an isotropic Gaussian parameter, independent Gaussian candidate arms, and Gaussian reward noise when the horizon is proportional to the dimension. The normalized posterior uncertainty has an explicit limit that is uniform over all causal policies. Gaussian posterior identities then determine the limiting parameter overlaps without an assumed closure of the adaptive recursion. These results yield exact regret curves for Thompson sampling, posterior-mean greedy selection, and a family of policies that scale the posterior sampling covariance. The normalized realized cumulative regret converges in L1, uniformly on compact proportional-time intervals. A policy-uniform lower bound identifies the limiting optimal Bayes regret and proves that posterior-mean greedy selection attains it. Thompson sampling incurs a strictly larger leading regret; its instantaneous regret ratio relative to greedy selection lies between one and two and approaches two at long proportional horizons. Closed-form cumulative curves also identify a different comparison in the vanishing-noise limit. Finally, the instantaneous regret converges to a nondegenerate Gaussian decision-loss distribution, rather than to its mean. The analysis separates the amount of information acquired by a bandit policy from the quality of the decisions made using that information.

Prakhar Singhvi, Yi Zou, Abhishek Bhattacharjee

Abstract Math Institute

Thompson Sampling Multi-Armed Bandits Bayesian Decision Theory

Aug 6, 2026cs.AI

Bayesian Expected Uncertainty Reduction (B-EUR) Model: A Computational Account of What Makes Design Options Worth Trying

This paper proposes the Bayesian Expected Uncertainty Reduction (B-EUR) model, which formalizes the value of trying a candidate design action as its expected reduction of epistemic uncertainty about action--outcome relations. The model addresses one part of the Uncertainty Driven Action (UDA) model's open question concerning how changes in uncertainty perception determine action selection. We examine two environmental properties: generalizability, or how far knowledge from one trial extends to neighboring candidates, and outcome discriminability, or how clearly differences among outcomes can be distinguished. We tested the model through simulations and human experiments using a graph-shape guessing task that isolates learning about action--outcome relations under a limited trial budget. Epistemic value followed an inverted-U-shaped relationship with generalizability and increased with outcome discriminability in the simulations. In the human experiments, the subjective value of trying and enjoyment followed inverted-U-shaped relationships with generalizability, while choice behavior reflected both properties. The B-EUR model provides a computational account of candidate-action evaluation within uncertainty-driven design activity and offers implications for constructing prototype sets, framing design problems, and organizing feedback to support informative exploration.

Shimon Honda, Takuma Miyaguchi, Koji Koizumi +3

Department of Mechanical Engineering, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan · Laboratoire Conception de Produits et Innovation (LCPI), Arts et M´etiers ParisTech, 151 Boulevard de l’Hˆopital, 75013 Paris, France

Computational Cognitive Modeling Value of Information Bayesian Decision Theory Bayesian Experimental Design Decision-Making under Uncertainty Epistemic Uncertainty

Jul 31, 2026cs.AI

A Generalized-Bayes Perspective on Counterfactual Explanations: Posterior-Based Decision-Making and Evaluation

Counterfactual explanations (CEs) enhance the interpretability of machine learning models by identifying the smallest change to an input required to obtain a desired output. Although CEs are conventionally formulated as a distance-minimization problem, the theoretical basis of this formulation has received limited attention. We show that a distance-minimization-based CE is mathematically equivalent to the maximum a posteriori (MAP) estimate of a Gibbs posterior within the generalized Bayes framework, specifically when a distance-based prior is used. We call this formulation the Distance-Prior Generalized Bayes CE (DP-GBCE). Building on this posterior perspective, we introduce two decision rules beyond MAP within a unified framework: a Bayes decision that minimizes expected decision loss and CVaR-CE, a risk-averse decision rule. We also propose an extension that uses Bayesian model weights to mix the posterior distributions of multiple models, thereby accounting for model multiplicity, where several models have comparable predictive performance. Finally, we define metrics for evaluating both individual CEs and the posterior distribution as a whole, and use experiments on simulated data and Google Trends data to quantify the trade-offs among the decision rules.

Keita Kinjo

Faculty of Business, Kyoritsu Women’s University

Counterfactual Evaluation Counterfactual Explanations Bayesian Inference Bayesian Decision Theory Decision-Making under Uncertainty

Jul 9, 2026cs.LG

Robust Bayesian Decision Making under Adversarial Uncertainty

Scientific experiments are often designed to maximize information gain, yet in many applications the primary objective is to support reliable downstream decision-making. Existing decision-aware experimental design and active learning methods typically assume well-specified outcome models and implicitly rely on the stability of the optimal decision under real-world perturbations. In practice, however, experimental outcomes are frequently influenced by hidden or weakly modeled effects, which can substantially alter decision optimality and lead to misleading conclusions. We study sequential adversarially robust decision-aware experimental design, where data acquisition has to take into account information gain against plausible worst-case unexpected effects, modeled here as variation in adversarial variables. Building on Bayesian decision theory, we formalize an adversarially robust optimal decision under this setting and derive a principled Bayesian experimental design criterion. The criterion explicitly targets decision stability rather than nominal optimality. Experiments on synthetic and real-world scientific datasets show that conventional decision-aware design can converge rapidly to high confidence yet fragile decisions, while our robustness-aware approach yields decisions that are significantly more stable and reliable under adversarial variation.

Haripriya Harikumar, Sammie Katt, Yasir Zubayr Barlas +1

Department of Computer Science, The University of Manchester, UK · ELLIS Institute Finland · Department of Computer Science, Aalto University, Espoo, Finland

Adversarial Robustness Bayesian Decision Theory Bayesian Experimental Design Decision-Making under Uncertainty

Jul 6, 2026econ.TH

Strategic Buying Agents

Agentic AI is shifting online shopping from search toward delegated purchasing, where autonomous buying agents monitor markets and decide when to buy on a consumer's behalf. We study the design of such strategic buying agents, which must decide when to purchase within a finite shopping window, translating price observations, the remaining time horizon, and beliefs about future price changes into a purchase policy. We formulate this problem across three information regimes: stationary, Bayesian, and robust, and treat the resulting optimal policies as a policy menu for implementation. In the stationary regime, price adjustments follow a Poisson arrival process with a known post-adjustment price distribution; the optimal policy is a dynamic purchase-threshold rule, with the threshold governed by an ordinary differential equation. In the Bayesian regime, the adjustment intensity is known, but the price-adjustment distribution is uncertain; the optimal rule remains threshold-based, now depending on posterior beliefs, and we bound the value of knowing the true distribution. In the robust regime, the agent has only price bounds and seeks worst-case protection; randomized threshold policies achieve optimal competitive-ratio and minimax-regret guarantees. We evaluate the proposed policies on Amazon price histories from Keepa (367 items, 48,933 timestamped observations) and examine their integration into language-model buying agents. The stationary and Bayesian policies perform competitively on mean normalized consumer surplus despite their stylized assumptions, while the robust policy performs best at the distribution's 10th percentile. Results suggest language models are better suited to selecting among regimes and calibration samples than to making buy-or-wait decisions directly.

Mingyang Fu, Ming Hu

Rotman School of Management, University of Toronto

Sequential Decision Making Optimal Stopping Bayesian Decision Theory Agentic Commerce Decision-Making under Uncertainty

Jun 29, 2026cs.CL

Uncertainty-Aware Generation and Decision-Making Under Ambiguity

With rapidly improving capabilities, Large Language Models (LLMs) are increasingly used in many complex real-world tasks. Beyond requiring in-depth knowledge and reasoning skills, many of these tasks exhibit a high degree of subjectivity and require that the outputs of the model can be trusted. While a lot of progress has been made to train better models, decision-making algorithms have received less attention. In this work, we present and evaluate various uncertainty-aware decision-making algorithms based on Bayesian decision theory and risk-averse decision making on the tasks of tutoring and automatic peer reviewing. Concretely, we take uncertainty over tutoring strategies and review scores into account when generating a tutor response or review and use conformal prediction to provide guarantees over strategy and score. We find empirically that these algorithms can improve the utility of the generations but need to be carefully implemented when ambiguity is high. For example, risk-averse rules can degrade performance by optimizing for generic outputs, while Bayesian methods tend to perform better. Our work uses techniques from decision theory to improve LLM-based decision-making and outlines open challenges for the community.

Nico Daheim, Iryna Gurevych

Ubiquitous Knowledge Processing Lab (UKP Lab), Department of Computer Science, Technical University of Darmstadt · National Research Center for Applied Cybersecurity ATHENE, Germany

Intelligent Tutoring Systems LLM Decision-Making Bayesian Decision Theory LLM Uncertainty Estimation Automated Peer Review Decision-Making under Uncertainty

Jun 28, 2026cs.LG

Bayesian Best-Arm Identification with Abstention: A Polynomial-to-Exponential Phase Transition

We study the Bayesian fixed-budget best-arm identification problem in which a learner can abstain from making a terminal recommendation. Subject to an abstention budget

α

, we analyze the probability of undetected error--the risk of recommending a suboptimal arm without abstaining. Our central finding is that abstention induces a phase transition: without abstention, the error probability decays polynomially in the sampling budget

T

; in contrast, introducing any small positive abstention budget shifts this to an exponential decay. For Gaussian priors and rewards, in the regime

T\to\infty

followed by

α\downarrow0

, we establish exact matching information-theoretic lower bounds and algorithmic upper bounds on the optimal error exponent, which takes the form

\exp(-\frac{α^{2}T}{8κ_ν^{2}})

. The hardness parameter

κ_ν

represents the prior density of the top-two gap at zero, highlighting that nearly tied instances drive the fundamental error. We introduce an adaptive algorithm, PGWS, that successfully achieves this optimal exponent by expending its abstention budget on statistically ambiguous instances. We further demonstrate that this polynomial-to-exponential improvement is exclusively a Bayesian phenomenon--in the frequentist setting, abstention only affects lower-order exponent terms. We also extend our results beyond the Gaussian model.

Yuqi Huang, Yunlong Hou, Vincent Y. F. Tan

Department of Mathematics, National University of Singapore · Department of Electrical and Computer Engineering, National University of Singapore

Multi-Armed Bandits Best-Arm Identification Bayesian Decision Theory

Jun 23, 2026cs.AI

Bayesian control for coding agents

Modern coding agents pair LLM generators with various tools, including cheap diagnostics and expensive verifiers. The tool-use decisions are typically governed by orchestrators that often use fixed rules and ignore uncertainty. We formulate orchestration as cost-sensitive sequential hypothesis testing: a Bayesian controller maintains a belief over candidate correctness and dynamically decides whether to gather more evidence, refine the candidate, verify it, or stop. Across six generators and nine coding benchmarks, Bayesian control proves to be most valuable when verification is costly and critics are informative but imperfect. Beyond control, the belief state yields an interpretable correctness score that outperforms token-probability and raw tool-success baselines for uncertainty quantification.

Theodore Papamarkou, Vladislav Smirnov, Viktor Mazanov +4

1PolyShape · 3MBZUAI

Language Model-Based Control Coding Agents Bayesian Decision Theory LLM Uncertainty Estimation Sequential Hypothesis Testing

Jun 22, 2026stat.ML

Action-BED: Task-Driven Bayesian Experimental Design with Singly Intractable Objectives

Bayesian experimental design (BED) has traditionally been based on maximising expected uncertainty reductions from prior to posterior. A major shortfall of this approach is that it leads to doubly intractable objectives that are difficult to optimise, while customising them to particular downstream tasks of interest can also be difficult. Following first principles decision theory, we demonstrate that BED can alternatively be formulated in terms of an expected future loss (EFL) on downstream actions, providing a simple and naturally task-driven framework. Critically, we then show that all such EFLs can be rearranged into singly intractable objectives that can be jointly optimised with respect to both the design policy and a downstream action policy using stochastic gradients, an approach we refer to as ACTION-BED. This formulation further sidesteps the need for any explicit posterior or marginal likelihood estimation and is naturally implicit, requiring only the ability to sample from the joint model over model parameters and data, and evaluate the downstream loss function. It thus allows design policies to be learned more effectively, efficiently, and simply than existing methods, while providing easy customisation to different downstream tasks and losses.

Tom Rossa, Angus Phillips, Tom Rainforth

Department of Statistics University of Oxford

Bayesian Decision Theory Bayesian Experimental Design Decision-Making under Uncertainty

Jun 3, 2026stat.ML

Bayesian learning for the stochastic shortest path problem

Sequential decision-making problems are often modelled as a Markov decision process (MDP). We focus on the stochastic shortest path (SSP) problem, which is an infinite-horizon undiscounted MDP with absorbing terminal states. We develop a Bayesian framework to learn the optimal decision strategy through interactions with the decision-making task. Specifically, we learn the optimal action-value function

Q^*

, but unlike many existing Bayesian approaches, we do not rely on unrealistic modelling assumptions and ad-hoc approximations. Our approach is to directly construct the posterior beliefs for

Q^*

through Bellman's optimality equations. For deterministic rewards, we characterise the posterior as a distribution with a manifold density. To facilitate simpler inference, we relax the likelihood so that a Lebesgue density exists. The flip side is to create unidentifiability issues. Specifically, the relaxed posterior can have significant mass on improper decision rules, while the exact posterior will not. We also calculate the exact posterior probabilities for optimal action selections for the tabular parametrisation of

Q^*

, a Gaussian likelihood relaxation and a Gaussian prior, which is useful in benchmarking studies. Numerical studies on variants of the Deep Sea benchmark verify our findings. We demonstrate that our framework faithfully quantifies uncertainty and, compared to other temporal-difference-based Bayesian methodologies, is more data efficient. We conclude with recommendations for future work.

Chon Wai Ho, Sumeetpal S. Singh, Jiaqi Guo

Department of Engineering, University of Cambridge, UK · School of Mathematics and Physics, University of Wollongong, Wollongong, Australia

Markov Decision Processes Reinforcement Learning Bayesian RL Markov Models Bayesian Inference Bayesian Decision Theory

Jun 2, 2026cs.LG

Bayes-Sufficient Representations in Supervised Learning

Representation learning is often described as preserving the information in an input that is relevant for prediction. This work asks what relevance means for a fixed supervised decision problem. A representation is defined to be Bayes-sufficient for a joint distribution and loss if some prediction head can use it to implement a Bayes-optimal action rule. This makes the target information loss-dependent. In the almost-surely unique Bayes-action case, the relevant object is a Bayes quotient, which identifies inputs that require the same Bayes-optimal action. A representation is sufficient when it refines this quotient, and Bayes-minimal when it is informationally equivalent to it. The framework connects naturally to property elicitation: zero-one loss requires the Bayes class, squared loss the conditional mean, Brier loss the conditional probability in binary prediction, and log loss or strictly proper scoring rules the predictive distribution. Controlled finite experiments, learned neural bottleneck experiments, and a real-data iNaturalist taxonomic refinement experiment illustrate the distinction between sufficiency, minimality, and retained non-required information. For a fixed supervised problem, the distribution and the loss determine the Bayes action, the Bayes action determines the quotient, and the quotient determines the minimal information required for Bayes-optimal prediction.

Vasileios Sevetlidis

Athena Research Center, Kimmeria Campus, Xanthi, Greece · Democritus University of Thrace, Vas. Sofias Campus, Xanthi, Greece · International Hellenic University, Serres, Greece

Representation Learning Bayesian Decision Theory

Jun 1, 2026math.OC

MINTS: Minimalist Thompson Sampling

The Bayesian paradigm offers principled tools for sequential decision-making under uncertainty, but its reliance on a probabilistic model for all parameters can hinder the incorporation of complex structural constraints. We introduce a minimalist Bayesian framework that places a prior only on the location of the optimum, while eliminating nuisance parameters through profile likelihood. This yields a generalized posterior that naturally accommodates structural constraints. As a direct instantiation, we develop MINimalist Thompson Sampling (MINTS). For multi-armed bandits with mean constraints, we establish near-optimal non-asymptotic regret guarantees and sharp almost-sure asymptotic regret characterizations. In particular, MINTS attains the classical Lai--Robbins constant in the unstructured setting and automatically adapts to unimodal structure, achieving the sharp constant determined only by the immediate neighbors of the optimal arm.

Kaizheng Wang

Department of IEOR and Data Science Institute, Columbia University.

Thompson Sampling Multi-Armed Bandits Bayesian Inference Bayesian Decision Theory

May 31, 2026cs.LG

Sample Complexity and Decision-Theoretic Guarantees for Bayesian Model Averaging over Decision Trees with Catalan-Exponential Priors

We ask: when do Bayesian model averaging (BMA) weights over decision trees carry sufficient epistemic information to justify committed exploitation of the averaging distribution? We answer this question in closed form for Bayesian decision trees (BDTs) with Dirichlet-Multinomial leaf models and a Catalan-exponential tree-size prior (Schetinin&Jakaite, 2025), establishing a complete non-asymptotic theory of rational commitment thresholds.

Livija Jakaite, Vitaly Schetinin

School of Computing and Engineering University of Bedfordshire, Luton, UK

Sample Complexity Bayesian Inference Decision Tree Learning Bayesian Decision Theory Decision-Making under Uncertainty

May 22, 2026cs.LG

Neural Bayesian Sequential Routing

Human decision-making is sequential and uncertainty-aware, yet standard neural networks often rely on static, dense forward computation with limited visibility into evidence acquisition, uncertainty evolution, or when computation should stop. We introduce \textbf{Neural Bayesian Sequential Routing (NBSR)}, a framework that models neural inference as active evidence accumulation over a hierarchical Directed Acyclic Graph (DAG). Within a Dirichlet--Categorical conjugate framework, neural experts query a persistent global knowledge oracle to extract positive evidence vectors, which act as pseudo-counts and update a Dirichlet belief state by exact conjugate addition. Coupled with a Gumbel-Softmax Straight-Through estimator, this update enables hard, path-dependent routing while preserving surrogate gradients for end-to-end training. The resulting Dirichlet precision and entropy provide mechanisms for uncertainty quantification, entropy-based early exiting, OOD abstention, and cost-aware evidence acquisition. We prove that, under strictly positive evidence extraction, total Dirichlet precision increases monotonically along any valid trajectory and marginal predictive variance is bounded, formalizing sequential ``hypothesis sharpening''; under idealized capacity and optimization assumptions, the terminal Dirichlet expectation recovers the Bayes-optimal conditional distribution. Empirical evaluations across visual categorization, structured medical diagnosis, language modeling, partially observable control, and cost-aware Bayesian experimental design show that NBSR achieves competitive predictive performance while providing transparent routing traces, path-dependent evidence attribution, uncertainty-aware decision control, and resource-rational inference. Overall, NBSR offers a mathematically grounded framework for interpretable, modular, and resource-rational agentic AI.

Yongchao Huang

Uncertainty Quantification Adaptive Model Routing Cost-Aware Inference Bayesian Decision Theory

May 19, 2026cs.LG

Training Neural Networks with Optimal Double-Bayesian Learning

Backpropagation with gradient descent is a common optimization strategy employed by most neural network architectures in machine learning. However, finding optimal hyperparameters to guide training has proven challenging. While it is widely acknowledged that selecting appropriate parameters is crucial for avoiding overfitting and achieving unbiased outcomes, this choice remains largely based on empirical experiments and experience. This paper presents a new probabilistic framework for the learning rate, a key parameter in stochastic gradient descent. The framework develops classic Bayesian statistics into a double-Bayesian decision mechanism involving two antagonistic Bayesian processes. A theoretically optimal learning rate can be derived from these two processes and used for stochastic gradient descent. Experiments across various classification, segmentation, and detection tasks corroborate the practical significance of the theoretically derived learning rate. The paper also discusses the ramifications of the proposed double-Bayesian framework for network training and model performance.

Vy Bui, Hang Yu, Karthik Kantipudi +2

Lister Hill National Center for Biomedical Communications, National Library of Medicine National Institutes of Health, Bethesda, MD 20894, USA · Office of Cyber Infrastructure and Computational Biology, National Institute of Allergy and Infectious Diseases National Institutes of Health, Bethesda, MD 20892, USA

Neural Network Optimization Bayesian Decision Theory Hyperparameter Optimization Stochastic Gradient Descent Layer-Wise Learning Rate Adaptation

May 15, 2026cs.LG

Boundedly Rational Meta-Learning in Sequential Consumer Choice

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.

Mehrzad Khosravi, Max Kleiman-Weiner, Hema Yoganarasimhan

University of Washington

Meta-Learning Sequential Decision Making Discrete Choice Modeling Bayesian Decision Theory Bounded Rationality Decision-Making under Uncertainty

May 6, 2026cs.GR

A Bayesian Approach for Task-Specific Next-Best-View Selection with Uncertain Geometry

We develop a framework for task-specific active next-best-view selection in 3D reconstruction from point clouds, by casting the problem in the language of Bayesian decision theory. Our framework works by (a) placing a prior distribution over the space of implicit surfaces, (b) using recently-developed stochastic surface reconstruction methods to calculate the resulting posterior distribution, then (c) using the posterior distribution to carefully reason about which view to scan next. This enables us to perform camera selection in a manner that is directly optimized for the intended use of the reconstructed data - meaning, we reduce uncertainty only in those regions that make a difference in the task at hand, as opposed to prior approaches that reduce it uniformly across space. We evaluate our method across three distinct downstream tasks: semantic classification, segmentation, and PDE-guided physics simulation. Experimental results demonstrate that our framework achieves superior task performance with fewer views compared to commonly used baselines and prior general uncertainty-reduction techniques.

Jingsen Zhu, Silvia Sellán, Alexander Terenin

Cornell University, USA · Columbia University, USA

Next-Best-View Planning 3D Reconstruction Bayesian Decision Theory Active View Selection Decision-Making under Uncertainty

May 1, 2026cs.AI

Position: agentic AI orchestration should be Bayes-consistent

LLMs excel at predictive tasks and complex reasoning tasks, but many high-value deployments rely on decisions under uncertainty, for example, which tool to call, which expert to consult, or how many resources to invest. While the usefulness and feasibility of Bayesian approaches remain unclear for LLM inference, this position paper argues that the control layer of an agentic AI system (that orchestrates LLMs and tools) is a clear case where Bayesian principles should shine. Bayesian decision theory provides a framework for agentic systems that can help to maintain beliefs over task-relevant latent quantities, to update these beliefs from observed agentic and human-AI interactions, and to choose actions. Making LLMs themselves explicitly Bayesian belief-updating engines remains computationally intensive and conceptually nontrivial as a general modeling target. In contrast, this paper argues that coherent decision-making requires Bayesian principles at the orchestration level of the agentic system, not necessarily the LLM agent parameters. This paper articulates practical properties for Bayesian control that fit modern agentic AI systems and human-AI collaboration, and provides concrete examples and design patterns to illustrate how calibrated beliefs and utility-aware policies can improve agentic AI orchestration.

Theodore Papamarkou, Pierre Alquier, Matthias Bauer +27

PolyShape, Greece. · NTUA, Greece. · ESSEC Business School, Singapore. +19

LLM Agent Orchestration AI Control Bayesian Decision Theory Human-AI Decision Making Decision-Making under Uncertainty

Mar 4, 2026math.ST

Bayesian Adversarial Privacy

Theoretical and applied research into privacy encompasses an incredibly broad swathe of differing approaches, emphases and aims. This work introduces a novel quantitative notion of privacy that is both contextual and specific. Building on and extending ideas from statistical disclosure control and differential privacy, our aim is to model the implications of a disclosure decision in an adversarial setting. Our definition relies on concepts inherent to standard Bayesian decision theory, while departing from them in several important respects. In particular, (i) inference about the data itself becomes meaningful and (ii) the party controlling the release of sensitive information should make disclosure decisions from the prior viewpoint, rather than conditional on the data, which is a feature shared with Bayesian design. Illuminating toy examples are exploited towards highlighting the specificities of the method.

Cameron Bell, Timothy Johnston, Antoine Luciano +1

CEREMADE, Université Paris Dauphine–PSL, France · Department of Statistics, University of Warwick, UK

Bayesian Decision Theory