Decision-Making under Uncertainty

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18 papers in the last four weeks, up 200% on the four weeks before. 0.2% of all new papers.

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Latest papers 139

Aug 7, 2026stat.ML

Optimized Certainty Equivalent Risk Minimization Using Samples: Algorithms, Convergence Rates, and Applications

We consider the optimization of the Optimized Certainty Equivalent (OCE) risk, with applications including portfolio optimization in finance, and uncertainty quantification, classification, and regression in machine learning. Our contributions cover popular special cases of OCE, such as entropic risk, mean-variance risk, and smooth variants of Conditional Value-at-Risk. Our treatment sets out the conditions that facilitate the extension of OCE to unbounded r.v.s.. We provide a useful characterization of OCE that links OCE to utility-based shortfall risk (UBSR). Our characterization enables us to form an OCE estimator from the classic sample-average approximation (SAA) of UBSR. We derive mean-squared error (MSE) bounds for our proposed OCE estimator. For OCE optimization, we first derive an expression for the OCE gradient using the characterization linking OCE to UBSR. This expression serves as the basis for a gradient estimator for the OCE. We derive non-asymptotic bounds on the MSE for the proposed OCE gradient estimator. We incorporate the aforementioned gradient estimator into a stochastic gradient (SG) algorithm to optimize OCE and quantify its convergence rate using non-asymptotic bounds that we derive. Finally, we present three experiments that use our OCE optimization algorithm to solve portfolio optimization and uncertainty quantification problems.

Sumedh Gupte, Prashanth L. A., Sanjay P. Bhat

TCS Research, IIIT-H Research Park, Hyderabad, 500032, India · Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, 600036, India

Stochastic Optimization Convergence Portfolio Optimization Decision-Making under Uncertainty

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

Aug 5, 2026cs.LG

Risk-Aware Decision Policies for Agents Under Noisy Perception

Perception in biological systems is inherently noisy, requiring organisms to make decisions under uncertainty where misclassification can be costly or fatal. We present an Artificial Life predator-prey model of foraging under noisy perception, and compare agent performance when using various policies that take into account their noisy predictions. Through controlled experiments under both symmetric and asymmetric perceptual noise, we show that blindly trusting perceptual labels leads to catastrophic failure as noise increases, while uncertainty-aware strategies significantly improve survival and reduce fatal errors. We further observe qualitative regime shifts in behaviour, with agents transitioning from exploratory to conservative strategies as uncertainty increases. Our model links risk-sensitive foraging, ecological information use, and Artificial Life by showing that explicit information gathering can improve robustness when perception is unreliable. These results highlight the importance of uncertainty-aware decision-making and provide an interpretable artificial life analogue to robust learning with noisy labels.

David Szczecina

University of Waterloo, Canada

Artificial Life Agent-Based Modeling Noise Robustness Decision-Making under Uncertainty

Aug 5, 2026cs.AI

Posture and Sustainment Optimization Under Adversarial Uncertainty

Pre-commitment posture, the assignment of military assets to theater locations before conflict scenarios resolve, is a critical and formally unsolved problem in joint operational planning. Current practice relies on greedy heuristics that maximize value and ignore geographic coverage and are structurally vulnerable to adversaries that target high-strategic value locations. This paper presents a scenario-weighted adversarially robust posture optimization engine for the Posture and sustainability allocation (PSA) problem, modeled as a finite-horizon Markov Decision Process over assets, theater locations, and time steps. We introduce the Composite Expected Value (CEV) optimizer, which places assets by maximizing scenario-weighted expected posture efficiency over a distribution of threat scenarios, and the RobustCEV extension, which iterates against a Bayesian adversary that updates its targeting distribution in response to observed placement. Across three experiments in an Indo-Pacific basing environment with 20 assets and 5 theater locations, we demonstrate that: (1) the greedy baseline incurs a permanent 25.1% posture efficiency penalty due to geographic under-coverage and a 57.3% scenario-weighted readiness collapse under value-correlated adversarial threat; (2) the CEV optimizer recovers up to 19.8% efficiency over greedy when the threat distribution carries a geographic signal, with a curated set of 5 to 20 scenarios sufficient to capture the majority of this gain; and (3) the RobustCEV extension recovers up to 158% efficiency relative to a naive optimizer when an adaptive adversary employs a deceptive threat prior. All findings are validated using paired t-tests with Bonferroni correction and two-level variance decomposition, confirming that the performance gaps reported are structural properties of placement strategies rather than sampling artifacts.

Amelie Norris, Alyssa Lee, Natan Vidra +1

Robust Optimization Decision-Making under Uncertainty

Aug 5, 2026cs.LG

Local Violation Certification for Linear Predict-Then-Optimize Pipelines

Data-driven decision pipelines combining predictive machine learning models with downstream optimization software are increasingly used to make high-stakes operational decisions. Certifying the safety, fairness, and reliability of these decisions is essential, yet traditional scenario generation methods rely on repeated random testing, which becomes computationally prohibitive when failure events are rare and offers little insight into why failures occur. We present a framework for local violation certification designed specifically for linear decision pipelines under input uncertainty. We mathematically demonstrate that standard sampling methods fail efficiently for rare violations, motivating a direct structural approach. By analyzing the fixed decision boundary of a deployed pipeline, we show that the local risk of failure can be calculated directly in closed form using a single optimization solve. Furthermore, we introduce an exact sampling procedure and closed-form risk statistics that provide feature-level attributions (identifying which input characteristics contribute most to potential non-compliance) without requiring repetitive random trials or complex sampling algorithms. We demonstrate our approach on an economic power dispatch system subject to emissions regulations, delivering precise, auditable risk assessments at a fraction of the traditional computational cost.

Ş. İlker Birbil, Wenhao Chi

Faculty of Economics and Business, University of Amsterdam, The Netherlands · Yau Mathematical Sciences Center, Tsinghua University

Algorithmic Auditing Predict-Then-Optimize Decision-Making under Uncertainty

Aug 3, 2026cs.LG

Analytic Planning under Uncertainty with Moment Closure

Effective model-based reinforcement learning in stochastic environments requires planning that accounts for predictive uncertainty. Propagating full state distributions analytically offers a principled way to do this, but has traditionally required restrictive policy or reward structures to remain tractable. Consequently, modern deep reinforcement learning has largely retreated to either stochastic sampling, which introduces significant target variance, or deterministic point estimates that ignore predictive covariance entirely. We investigate whether distribution-aware planning is possible without these constraints. Using a quadratic action-value parameterization, we first reduce the Bellman backup to an expectation over the state-value function alone; the key idea is then a compatibility principle between the predictive transition distribution and the value function class, under which this expectation is analytic in the distribution's moments. We instantiate this principle with a Gaussian transition model paired with a radial-basis value function, yielding a closed-form backup that propagates both predictive mean and covariance. Empirically, our approach reduces target variance and yields well-calibrated predictive uncertainty under stochastic observations in continuous control, providing a principled framework for planning with learned distribution models.

Shishir Sharma, Doina Precup

1McGill University, Montreal, Canada · 2Mila – Quebec Artificial Intelligence Institute, Montreal, Canada

Decision-Making under Uncertainty Model-Based RL

Aug 3, 2026cs.AI

Optimizing Minimax Regret in Uncertain MDPs with Small Sets of Policies

Sequential decision-making in real-world applications often involves uncertainty about the environment's model. Uncertain Markov decision processes (UMDPs) represent the possible environments as a set of MDPs with shared states and actions but potentially different transition probabilities and rewards. Optimizing a single policy across all possible MDPs may sacrifice performance, while preparing an individually optimized policy for every MDP may violate operational, regulatory, or interpretability constraints on the number of policies that can be prepared and deployed. We consider settings in which model uncertainty is resolved shortly before execution, allowing the most suitable policy to be selected from a limited set prepared in advance. We introduce

k

-adaptable policy synthesis, which optimizes such a set of

k

policies under a minimax-regret objective. We prove that the problem is NP-hard and develop KAPS, an exact nested branch-and-bound algorithm with problem-specific bounds and heuristics. KAPS jointly optimizes which MDPs share a policy and the policies themselves. Experiments across various UMDP benchmarks show that the largest reduction in regret consistently occurs when increasing from one to two policies. In the single-policy setting, KAPS is competitive with existing methods in solution quality and proves optimality substantially more often.

Sterre Lutz, Daniël Vos, Matthijs T. J. Spaan +1

Delft University of Technology

Markov Decision Processes Branch and Bound Minimax Regret Policy Optimization Combinatorial Optimization Decision-Making under 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 30, 2026cs.LG

Strategies for Milestone-driven Start-ups in Multi-activity Settings

New venture start-ups need to ``survive'' through multiple stages of reaching milestone targets. We investigate the strategies for start-ups in a milestone-oriented setting. We examine a model of an entrepreneurial start-up firm, where its state is captured by a diffusion process. The entrepreneur can choose between multiple activities (or controls), which incur different cost and determine the drift and the variance of the process. Depending on whether the process reaches a fixed upper boundary or a lower one, the start-up firm succeeds or fails. Continuous-time stochastic models with multiple (

\ge 3

) controls are typically very challenging to deal with. In this work, we are able to completely solve for the optimal policy and provide an explicit characterization of its structure. In particular, the optimal policy only uses controls from a set characterized by a so-called efficient frontier curve that orders the controls by two intuitive measures: riskiness (drift-to-volatility ratio) and cost-effectiveness (drift-to-cost ratio). A unique feature of our model is that depending on the model parameters, the efficient frontier curves can be of different types, resulting in qualitatively different structures of the optimal policy. As far as we know, this is the first study that analyzes a stochastic control model which admits efficient frontier curves of different types. Our work provides start-up firms with intuitive measures to evaluate their activities and offers valuable insights on how the optimal strategies in a milestone-oriented setting change qualitatively contingent upon the specific scenario. We believe the results provide a foundational block in the study of entrepreneurial decision-making.

Zhengli Wang

Faculty of Business & Economics, the University of Hong Kong

Stochastic Optimal Control Decision-Making under Uncertainty

Jul 29, 2026cs.AI

Belief-Guided Decision Making with Uncertainty Gating in the Game of Go

Recent advancements in Computer Go, driven by AlphaZero and MuZero, rely heavily on Monte Carlo Tree Search (MCTS) to correct the errors of the neural network policy. While effective on massive computational clusters, this dependence creates a critical bottleneck on consumer-grade hardware, where the computational cost of tree management severely limits inference rates. Furthermore, without deep search, these models suffer from hallucination, proposing moves with high confidence that are strategically fatal. This paper introduces a novel Belief-Guided architecture that disentangles the Policy head from a distinct Belief head. Unlike traditional value functions, the Belief head acts as an internal simulator and independent critic, modeling epistemic uncertainty and strategic stability. By integrating memory mechanisms (Transformer/GRU) to handle long-term dependencies and the Ko rule, and utilizing a gating mechanism to filter overconfident policy errors, our model shifts the burden of intelligence from runtime search to parametric "intuition." Experimental results demonstrate that this approach significantly improves search-free win rates and reduces hallucination, enabling professional-level play on limited hardware where massive MCTS is infeasible.

Mehrad Yaghoubi, Azam Bastanfard, Abbas Jalilvand +1

Department of Computer Engineering, Ka.C, Islamic Azad University, Karaj, Iran

Game-Playing Agents Decision-Making under Uncertainty Epistemic Uncertainty

Jul 28, 2026stat.ML

More Data, Worse Decisions? Preference Reversals in Neural Networks under Gram Incompatibility

Neural networks increasingly combine data across populations, time periods, and operating conditions to improve generalization. This raises a reliability question: whether a model refitted on pooled data preserves an action ordering supported by both sources. Case-Based Decision Theory (CBDT) formalizes this requirement through its composition axiom, which requires source-supported preferences to survive their union. We study when this property holds for fixed-representation neural networks with ordinary least squares (OLS) output heads. First, we show that pooled refitting recomputes the inverse-Gram geometry used to weight source evidence, which can reverse shared preferences, and derive exact and approximate preservation conditions. Next, we introduce a scale-invariant Gram mismatch measure for prioritizing candidate pools and geometry-oriented regularization for shaping source geometry during training. Finally, we develop a three-stage audit that traces strict pairwise reversals through decision changes to task-defined utility loss. Experiments spanning a load-based bidding proxy and medical and financial decision proxies reveal stable and reversal-prone pooling regimes: the load audit identifies a measurable nonzero class of source-consensus-relative harmful decisions under the proxy utility, while cross-domain audits show that comparable mismatch can correspond to sharply different preservation rates. Geometry-oriented objectives occupy distinct descriptive accuracy-consistency-geometry-harm operating points. Together, the framework makes compositional reliability measurable and operational through screening, analytic certification, geometry-oriented training, and decision-consequence auditing.

Yanli Yan, Yuanzheng Li, Yong Zhao +2

Huazhong University of Science and Technology Wuhan, China

Neural Network Generalization Neural Representation Geometry Decision-Making under Uncertainty

Jul 26, 2026cs.CY

AI Strategy: How to Choose What AI Product to Implement

Firms struggle to choose AI projects that pay off: two projects can look equally promising to smart, motivated stakeholders and yet deserve opposite decisions. At the residential real-estate brokerage Compass, one AI product (Likely-to-Sell recommendations) flagged sales outreach opportunities and went on to account for nine figures in annual gross commission revenue. Another championed AI product (a Time-on-Market pricing tool) was rightly shelved. A simple ROI estimate could not distinguish the two. We present expected ROI (eROI), a framework that decomposes each bet into three components and rates them separately: Value if Successful, Likelihood of Success, and Investment Required. Each maps to a question executives can answer before building: How valuable would it be if it worked? How likely is it to work? And what would it cost to implement? Separating the three breaks a common catch-22: teams cannot estimate ROI until they know whether a project will work, yet cannot know whether it will work without building it. Judging Value if Successful on its own dissolves the loop, letting a team argue that a product would be valuable if it worked while it weighs how likely that is. The framework also asks, before ranking anything, whether there are enough good ideas on the table. After ranking, it guides assembling a portfolio of bets rather than funding only the single top-ranked project. We illustrate eROI on Compass's candidate AI products. Precise ROI estimates are hard to make given the inherent uncertainty of AI projects. Coarse business-level ratings of the three components are enough to tell strong bets from weak ones.

Foster Provost, Panos Ipeirotis

Stern School of Business, New York University

AI-Assisted Decision Making Decision-Making under Uncertainty

Jul 22, 2026cs.AI

TRUST-ESD: A Risk-Calibrated and Governance-Aware AI Framework for Enterprise Strategic Decision Support Under Uncertainty

Enterprise strategic decision support requires AI systems that are not only accurate, but also uncertainty-aware, risk-calibrated, explainable, and governance-compliant. This paper proposes TRUST-ESD, a risk-calibrated and governance-aware framework for enterprise decision support under uncertainty. TRUST-ESD evaluates feasible counterfactual strategies through predictive utility estimation, conformal uncertainty calibration, CVaR-based downside-risk scoring, risk-memory retrieval, policy-as-code governance, explainability, and human oversight. Unlike prediction-only methods that select actions by maximum expected utility, TRUST-ESD recommends strategies that balance value, reliability, risk exposure, and compliance. Experimental results show that TRUST-ESD improves risk-adjusted utility by 7.95%, reduces risk exposure by 23.22%, reduces CVaR by 23.78%, lowers calibration error by 13.89%, improves explanation fidelity by 10.90%, and increases governance compliance by 9.76% compared with strong uncertainty-aware baselines, while maintaining competitive predictive accuracy. Ablation and case-study analyses further confirm that uncertainty calibration, downside-risk scoring, risk memory, explainability, and governance validation jointly improve trustworthy enterprise decision-making.

Tian Qiu, Li Yan, Mahabubur Rahman Miraj +3

School of Economics and Management, Xinyu University, Xinyu, China · College of Computer Science, Chongqing University, Chongqing, China · School of Economics and Business Administration, Chongqing University +2

AI-Assisted Decision Making Explainable Artificial Intelligence AI Governance Decision-Making under Uncertainty

Jul 22, 2026cs.AI

Long-Term Sequential Decision Making under Risk

We study finite-horizon MDP planning under \emph{root-based} (resolute) risk objectives that apply a rank-dependent functional to the distribution of total returns. Such objectives are non-linear in the return distribution and generally break Bellman optimality, so direct optimization by scenario-tree enumeration is intractable. We propose \textbf{ERQDP}, an enumeration-free and sampling-free method that solves a rank--quantile surrogate via exact DP (Dynamic Programming), evaluates candidate policies exactly by DP over return Probability Mass Functions (PMFs) on a discretized return grid (with an explicit rounding bound), and refines the surrogate in an anytime loop that reports an explicit upper--lower gap (certificate) for the target objective up to discretization budgets. Across tested benchmarks, ERQDP returns certified solutions or explicit residual gaps, enables fast risk-parameter sweeps with substantial runtime gains, and supports both risk-averse and risk-seeking behaviors.

Irmaan, Mirzanejad, Nadjet Bourdache +1

Mohammad · Université de Caen Normandie, ENSICAEN, CNRS, Normandie Univ, GREYC UMR 6072, France

Markov Decision Processes Dynamic Programming Risk-Sensitive RL Decision-Making under Uncertainty

Jul 21, 2026econ.EM

Optimizing Regret

Building on the identity that expected regret equals the covariance between costs and decisions, this paper develops a derivative theory of the covariance regret functional. We derive the Gâteaux derivative, showing that the universal steepest-descent direction is the contrarian policy

-(c-\bar c)

, while ascent yields momentum. For linear policies

\hatπ(c)=Ac+b

, the gradient is the cost covariance matrix

Σ_c

, with a zero Hessian implying boundary-optimal solutions such as the minimum-variance portfolio. We extend to constrained optimization, sign-gradient duality between regret minimization and alpha maximization, finite-sample convergence bounds paralleling Thompson Sampling, and gradient-descent algorithms requiring only input observations.

Irene Aldridge

Risk AI Center

Gradient Descent Regret Minimization Decision-Making under Uncertainty

Jul 20, 2026cs.LG

Weak-to-Strong Learning in Decision Making

Many operational decisions rely on predictive models that estimate uncertain outcomes conditional on observable contexts. Training such models, however, often faces a fundamental data asymmetry: labeled outcomes are scarce or costly to obtain, while contextual covariates are abundant. Motivated by this data asymmetry, we develop a decision-aware weak-to-strong (W2S) framework that leverages both labeled and unlabeled data to improve contextual stochastic optimization. Specifically, we first train a weak model using limited labeled data and then use it to generate predicted outcome distributions on unlabeled contexts. These distributions provide soft supervision for training a strong model. We establish a non-asymptotic upper bound on the excess decision risk of W2S and a complementary lower bound for a strong-only benchmark. Their comparison yields explicit sufficient conditions under which W2S improves downstream decision performance. The key quantity is the correlation dimension between the weak and strong feature representations: when it is small, abundant unlabeled data reduce the effect of teacher errors along non-overlapping directions. A synthetic newsvendor experiment and a comment moderation experiment based on real-world data provide empirical evidence consistent with the theory.

Jingwei Ji, Renyuan Xu

Management Science and Engineering, Stanford University

Stochastic Optimization Decision-Focused Learning Weak-to-Strong Generalization Semi-Supervised Learning Decision-Making under Uncertainty

Jul 19, 2026cs.LG

Rationalizing Boltzmann Rationality: An Axiomatic Characterization of Entropy-Regularized Policies

The softmax policy

π(a \mid s) \propto \exp(βQ(s,a))

is the default model of stochastic choice in reinforcement learning (RL). Various justifications based on robustness, exploration, and optimization have been offered in the RL literature, but none uniquely derives the softmax form from first principles. This leaves a basic tension unresolved: the entropy bonus in the soft Bellman equation violates the Independence axiom that underwrites the Markov decision process (MDP) reward structure. We dissolve this tension by distinguishing two kinds of randomness: chance and choice. By restricting von Neumann-Morgenstern (VNM) Independence to environmental lotteries over base prospects, we show that imposing independence of irrelevant alternatives (IIA) and monotonicity on the policy and value functions at choice nodes uniquely determines the Boltzmann policy, the entropy-regularized representation, and the soft Bellman equation. The choice between the soft and hard Bellman equations thus reduces to a design decision: whether the agent values its own ability to choose. We develop RL-specific consequences, including return monotonicity and convergence under generalized discounting, and synthesize the independent lines from economics and information theory that arrive at the same structure, offering a normative assessment of when IIA is appropriate for agent design.

Silviu Pitis

University of Michigan

Markov Decision Processes Maximum Entropy RL Decision-Making under Uncertainty

Jul 18, 2026cs.AI

Expected Free Energy as Belief-Dependent Utility for rho-POMDPs

An agent acting under partial observability must decide when to gather information and which observations are worth their cost. Standard POMDPs value information only through its eventual effect on reward. The

ρ

-POMDP framework instead rewards uncertainty reduction directly, through a belief-dependent utility

ρ

, but in practice both the choice of

ρ

and the weight placed on it are tuned by hand for every task. We show that active inference removes this tuning entirely. Minimizing Expected Free Energy (EFE) is exactly equivalent to solving a

ρ

-POMDP whose utility is expected information gain, and the exploration weight is fixed at

w=1

because the variational bound expresses pragmatic and epistemic value in the same units (nats). We prove this equivalence for observe-then-commit POMDPs and extend it to factored observation POMDPs, a broader class that covers interleaved observe-act problems such as non-destructive testing and mobile sensing, where gathering information leaves the hidden state unchanged. Experiments support the theory. Across environments ranging from the classic Tiger problem to RockSample and a new Structural Inspection benchmark with over 65,000 states, the untuned weight matches or outperforms reward-only planning at the same horizon, avoids the over-exploration of bonuses tuned per task, and sits near the reward-maximizing knee of the success-reward Pareto frontier. The practical payoff is an exploration objective that works out of the box. In applications such as fault detection and medical screening, where every test has a price and every missed fault has a cost, EFE supplies a belief-dependent utility that is derived rather than tuned.

Patrick Cooper, Alvaro Velasquez

Department of Computer Science, University of Colorado Boulder, Boulder, CO, USA

Free Energy Calculation Active Inference Value of Information Free Energy Principle Partially Observable Markov Decision Processes Decision-Making under Uncertainty

Jul 18, 2026stat.ML

A Causal Markov Condition for Value

This paper proposes a causal independence principle for value -- the value Causal Markov Condition (v-CMC) -- and develops the conceptual and mathematical foundations of a "causal value theory" linking causality and utility. After motivating a local formulation of the v-CMC, we introduce a probability-value duality that translates standard causal-inference results into the value setting. In particular, we formulate local, global, and decomposition versions of the v-CMC and prove their equivalence. We also define v-separation and show that it is sound and complete for conditional value independence. Furthermore, we derive a Bellman-type recursion as a special case of the v-CMC, thereby generalizing standard Bellman recursion from linear chains to causal DAGs. Finally, we show how the v-CMC supports modular transfer and updating of utility information across causal contexts and develop algorithms for causally structured utility elicitation and canonical influence-diagram construction.

Olav Benjamin Vassend

University of Inland Norway

Decision-Making under Uncertainty

Jul 16, 2026cs.LG

Evaluating Epistemic Uncertainty: Beyond OOD Detection and Active Learning

Current evaluation of epistemic uncertainty relies on tasks such as out-ofdistribution detection and active learning. However, the Bayes-optimal decision strategies for these tasks do not coincide with the scores commonly used to quantify epistemic uncertainty. Building on the epistemic reject-option framework, we evaluate epistemic uncertainty using its ability to identify regret, the reducible error. Formulating selective prediction as a constrained optimization over coverage, expected risk, and regret, we prove the optimal selector is a thresholded convex combination of the ground-truth aleatoric and epistemic uncertainties. This theoretical unification exposes a weakness in recent uncertainty disentanglement literature: we demonstrate that standard correlation metrics between learned components do not necessarily predict their actual operational utility. We instead propose to evaluate the achievable risk, regret, coverage surface of the decomposition as a diagnostic for joint disentanglement and utility. Benchmarking standard methods on datasets with dense human annotations reveals that decision-theoretic rankings can disagree substantially with proxy-task rankings, including pairwise rank inversions between methods that are top-ranked on one criterion and bottom-ranked on other.

Jakub Paplhám, Willem Waegeman, Eyke Hüllermeier +1

Czech Technical University in Prague · Ghent University · LMU Munich, MCML, DFKI

Selective Prediction Decision-Making under Uncertainty Epistemic Uncertainty

Jul 15, 2026cs.IT

Decision Making Needs Uncertainty Quantification [Lecture Notes]

Many signal processing systems ultimately exist to {act}. Whenever the state variable that determines the action to be taken by a decision maker, or agent, is uncertain, the way that uncertainty is represented decides how well the agent performs and how much its performance can be trusted. This lecture note develops, from first principles and within a single decision-theoretic setting, the link between the {objective} and the knowledge of an agent and the form of uncertainty representation that is sufficient to act optimally. To start, assuming a known environment distribution, we show that a risk-neutral agent needs the posterior distribution over the state, whereas a risk-averse agent can rely without loss of optimality on a {prediction set} and a worst-case decision rule. We then turn to the case in which the environment is unknown, and identify three complementary approaches to address the resulting epistemic uncertainty: calibration of a fixed predictor, credal (ambiguity) sets with distributionally robust optimization, and Bayesian inference over model parameters. The common thread is that reliable decisions require an uncertainty representation matched to the decision objective and to the knowledge profile of the agent, together with a guarantee that certifies the utility the agent will actually obtain.

Osvaldo Simeone

Institute for Intelligent Networked Systems, Northeastern University London, One Portsoken Street, London, E1 8PH, UK

Uncertainty Quantification Decision-Making under Uncertainty Epistemic Uncertainty

Jul 13, 2026eess.SY

Active Noise Floor Estimation for Reliability-Optimal POMDPs: A Value-of-Noise-Information Approach

Finite Reliability Representations (FRR) certify when a cell-constant policy is sufficient for reliable decision-making in a partially observed system with a known physical noise floor. In practice, however, sensing and execution noise can be latent and context-dependent. This paper develops a certificate-aware active disambiguation framework for an unknown physical noise parameter theta = (sigma_y, sigma_u), with the sensor-only case obtained by fixing sigma_u. We define the Value of Noise Information (VoNI) as the expected excess FRR certificate gap caused by using a reliability cover calibrated to the current estimate rather than to the realized noise parameter. We bound VoNI using action-value model mismatch and FRR radius inflation, showing that noise estimation has low decision value in sub-crossover regimes where the FRR certificate is insensitive to theta, but becomes valuable when posterior uncertainty can invalidate the current cover. A bi-level decision maker uses a posterior over theta, obtained from innovation statistics, execution residuals, or another online estimator, and triggers diagnostic probing only when uncertainty threatens the FRR certificate. We also interpret VoNI as a tractable, certificate-aware approximation to a high-level finite POMDP for latent sensing-execution regime disambiguation. Under stationary, identifiable, and persistently exciting regimes, we establish posterior consistency and convergence of the induced policy loss to the FRR approximation floor. Closed-loop UGV simulations with EKF-based innovation residuals show earlier detection of abrupt sensing-noise jumps, lower drift-tracking error, and substantially fewer probing actions than posterior-entropy exploration over 50 Monte Carlo trials.

Hyung-Jin Yoon

Department of Mechanical and Nuclear Engineering, Tennessee Technological University, Cookeville, TN 37135, USA

Value of Information Active Sensing Partially Observable Markov Decision Processes Decision-Making under Uncertainty

Jul 13, 2026cs.AI

Reproducing human biases in route choice using large language models: Toward scalable behavioral modeling

Human choice behavior, including route choice, exhibits systematic behavioral biases that deviate from the assumptions of full rationality. Cumulative prospect theory (CPT) has been widely recognized as an effective framework for characterizing such behavioral patterns. However, its large-scale application, particularly in simulation and agent-based modeling, critically depends on specifying individual-level CPT parameters, which remain a major bottleneck. Conventional approaches typically rely on surveys and controlled experiments to calibrate CPT parameters, yet these methods are difficult to generalize and often fail to capture the full diversity of human decision-making. To address this challenge, this paper investigates whether large language models (LLMs) can reproduce human behavioral biases in choice-making without explicit specification of prospect-theoretic parameters. Using route choice as a representative scenario, we design a behavioral evaluation framework and systematically compare LLM-generated decisions with established human behavioral patterns predicted by CPT. Experimental results demonstrate that LLMs are capable of reproducing non-rational human choice biases and can exhibit decision behaviors consistent with prospect-theoretic effects under uncertainty. These findings suggest that generative AI models may provide a scalable alternative for modeling human decision processes and offer a promising foundation for next-generation large-scale agent-based simulation and AI-driven behavioral research.

Jiangtao Han, Shoufeng Ma, Shuxian Xu +4

College of Management and Economics, Tianjin University, China · Faculty of Science and Engineering, University of Nottingham Ningbo China

Cognitive Modeling Human Behavior Simulation Decision-Making under Uncertainty

Jul 13, 2026econ.EM

Removable Defects: The Economics and Limits of Deliberate Deficiency

A specialist tolerates blind spots that a generalist does not. Usually this is treated as a cost to be minimized. We treat it as a design variable: a deficiency can be kept because it pays and removed on demand in the rare situation where it would be fatal, by routing to a compensation channel. We give three results. First, an advantage condition under which keeping the deficiency is a computable economic position; structurally it is the Ehrlich-Becker market-vs-self-insurance margin applied to a competence gap, with the detector as a Townsend costly-state-verification technology. Second, a two-sided characterization of removability. A coupling lemma shows that when the deficiency is a coarsening of perception, no switch can separate benefit from harm, yielding a converse (a confounded detector earns zero premium, and any within-defect policy insisting on positive premium is driven, under multiplicative dynamics, to negative long-run growth) and an achievability result (a detector outside the deficiency earns a positive premium). Together, over structured uncertainty classes with severity capped or miss rate O(1/L): a defect is profitably removable iff the detector-relevant distinction survives the restriction and the advantage condition holds; the premium is the support function of the class's ROC set at an economic price vector. Third, observation defects and capacity defects differ exactly on whether access to the deployment distribution rescues them; the gap decomposes as cross-leak plus a closure deficit, and per-task randomization buys back the latter, never the former. The detector can be learned from declared fatal categories at a training bill linear in loss severity (up to a log factor). The results synthesize Chow's reject option, Kelly growth under ruin, and selective prediction.

Cheng Qian

Cost-Sensitive Learning Selective Prediction 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 8, 2026econ.EM

Sensitivity to Subjective Expected Utility Maximization: A Methodological Study, with an Illustrative Application to LLM Decision-Making

Evaluating decisions made under uncertainty is hard when labeled outcomes are scarce, costly, or confounded with luck. We treat subjective expected utility (SEU) maximization as a stated standard and define a graded measure -- SEU sensitivity -- of an agent's conformity to it. The vehicle is a softmax choice model with a sensitivity parameter

α

on SEU-valued alternatives; the contribution is a sequence of identifiability results for

α

and for belief and utility parameters

(β, δ)

, validated in Stan via prior predictive checks, parameter recovery, and simulation-based calibration (SBC), with finite-sample caveats intact. In the uncertain-choice-only model

m_0

,

α

is identifiable given the expected-utility vector

η

and sharply recovered, while

(β, δ)

are only weakly informed: the posterior barely contracts and concentrates on a

β

-

δ

trade-off. In the extended model

m_1

,

δ

becomes identifiable in principle via a

β

-free risky block, but its practical recovery gain at realistic sample sizes is negligible (matched-count CI-width reduction under 1%), and that block yields no detected

α

-precision gain at matched choice count. These are two distinct phenomena: for

δ

, identifiability does not imply precise estimability at realistic

n

; for

α

, identifiability is silent about what governs finite-

n

precision. Marginal SBC passes for both models even where the joint posterior is weakly informed -- a demarcation we make precise. A two-by-two application (GPT-4o and Claude 3.5 Sonnet, each on insurance-claims triage and Ellsberg-style urns, with sampling temperature as the lever) runs end-to-end on real LLM choice data, detecting a structured comparative

α

effect in two of four cells.

Jeff Helzner

Parameter Estimation Parameter Identifiability Discrete Choice Modeling Decision-Making under Uncertainty

Jul 7, 2026cs.LG

Robust Human-AI Complementarity under Uncertainty

Machine learning models are often intended to augment rather than replace human decision makers, by providing information that is complementary to human judgement. Yet, in practice, human decision makers routinely fail to realize such complementary gains, even when models provide useful signal. In this work, we study how asymmetric information about the quality of information available to a human decision maker vs. an AI impacts the ability of a decision maker to extract complementary value from AI predictions. We show that a key factor is the error correlation structure between human and AI predictions. In particular, when the AI's prediction errors are \textit{negatively correlated} with those of the human, the decision maker can construct robust strategies which guarantee improvements in expected utility. We empirically investigate whether these conditions for complementarity arise in practice, using real-world forecasting benchmarks.

Yewon Byun, Bryan Wilder

Machine Learning Department, Carnegie Mellon University.

Human-AI Decision Making Decision-Making under Uncertainty

Jul 7, 2026cs.LG

Decision-Focused Scenario Generation and Selection for Efficient and Robust Grid Dispatch

The increasing uncertainty from flexible demand and renewable generation has made distributionally robust optimization (DRO) an important tool for robust power system dispatch. DRO relies on forecast scenarios to construct ambiguity sets, but conventional scenario generation pipelines are often trained in an accuracy-oriented manner and may neglect spatial correlations among uncertainties. This mismatch can produce ambiguity sets that are statistically plausible but suboptimal for downstream operation. This work proposes a decision-focused generative framework for correlated scenario generation in DRO-based dispatch. Instead of training generative models solely to fit the historical uncertainty distribution, the proposed framework optimizes generated scenarios according to their induced downstream operational cost. The proposed framework is tailored to mainstream generative models, including variational autoencoders, generative adversarial networks, and diffusion models, while capturing the joint distribution of uncertainties across buses. To improve computational tractability, we further develop a differentiable scenario selector that selects decision-relevant scenarios from a generated pool and can be trained within the same decision-focused pipeline. Case studies demonstrate that the proposed framework effectively reduces 0.80%-2.02% operational cost across different generative models compared to accuracy-oriented methods.

Yangze Zhou, Yihong Zhou, Thomas Morstyn +1

Distributionally Robust Optimization Decision-Focused Learning Generative Modeling Decision-Making under Uncertainty Power Systems

Jul 6, 2026cs.AI

Robust Metaheuristics under Uncertainty for Berth Allocation and Quay Crane Assignment: A Review

The berth allocation and quay crane assignment problem (BACAP) is a representative port-terminal scheduling problem in maritime transportation and freight logistics, where vessel arrivals, berth positions, service durations, and quay?crane availability are tightly coupled. Under uncertainties such as arrival deviations, handling-time fluctuations, and resource disruptions, schedules optimized under nominal assumptions may become fragile during execution, motivating the study of robust metaheuristic optimization for BACAP in port-terminal operations. Although population-based metaheuristics have been widely used for BACAP and related port-scheduling problems, existing studies remain fragmented in their uncertainty repre?sentations, robustness criteria, search mechanisms, and empir?ical evaluation protocols. To the best of our knowledge, this paper provides the first focused review dedicated to robust population-based metaheuristics for BACAP under uncertainty. We first summarize uncertainty sources and information repre?sentations in BACAP, and then organize existing methods from a mechanism-oriented perspective, covering solution representation and decoding, robust evaluation and selection, robustness-guided search dynamics, and feasibility preservation and recovery. We further present a benchmark suite for uncertain BACAP to support controlled empirical comparison and report illustrative baseline results by combining representative metaheuristics with different robustness strategies. Finally, we identify open chal?lenges related to benchmark extension, robustness-aware search design, time-adaptive robustness, and non-stationary uncertainty.

Peilan Xu, Yang Li, Wenjian Luo

School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing 210044, China · Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies, Institute of Cyberspace Security, School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen 518055, Guangdong, China

Metaheuristic Optimization 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