Decision-Making under Uncertainty

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Overview

Decision-making under uncertainty studies how agents should choose actions when outcomes, states, preferences, or even the governing model are imperfectly known. Common approaches include Bayesian beliefs and partially observable Markov decision processes for sequential learning, robust optimization for misspecified distributions, risk-sensitive criteria such as CVaR, and conformal methods that calibrate when to act, gather information, or abstain. These methods are tested in settings such as autonomous driving and robotics, clinical diagnosis, energy and supply-chain scheduling, finance, and human–AI interaction. A central tension is that better-calibrated or more conservative uncertainty estimates do not automatically improve decisions: methods must balance safety and tail risk against utility, computational cost, and the value of additional information.

Latest papers

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204 papers24 papers in the last four weeks, up 26% on the four weeks before. 0.1% of all new papers.

Apr 22, 2026

Robust Out-of-Distribution Stochastic Optimization

Data-driven decision-making under uncertainty typically presumes the collection of historical data from an unknown target probability distribution. However, one may have no access to any data from the target distribution prior to decision-making. To address this challenge, we propose robust out-of-distribution stochastic optimization, a novel data-driven framework that effectively utilizes relevant data distributions for robust decision-making under unseen distributions. A key feature of our framework is that all data distributions are assumed to be randomly generated from a meta-distribution over distributions. To describe uncertainty in distribution generation, we propose to learn a data-driven uncertainty set in a reproducing kernel Hilbert space (RKHS) from relevant data distributions, with adjustable conservatism. We then incorporate this set into a min-max stochastic program to derive robust decisions. Notably, under randomness of distribution generation, we establish rigorous out-of-distribution generalization guarantees for the uncertainty set as well as the solution. To ease problem-solving in RKHS, an approximate parametrization with a provably bounded suboptimality and a row generation strategy are presented. Extensive numerical experiments on multi-item newsvendor and portfolio optimization demonstrate the superior out-of-distribution performance of our decision-making framework under unseen data distribution, even when only a small or moderate number of relevant sources are available.

Xianyu Li, Huan Xu, Xiaolin Huang +1

Department of Automation, Tsinghua University · Antai College of Economics & Management, Shanghai Jiao Tong University · Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University

Stochastic OptimizationOOD GeneralizationDistributionally Robust OptimizationDecision-Making under Uncertainty
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Apr 15, 2026

Multistage Conditional Compositional Optimization

We introduce Multistage Conditional Compositional Optimization (MCCO) as a new paradigm for decision-making under uncertainty that combines aspects of multistage stochastic programming and conditional stochastic optimization. MCCO minimizes a nest of conditional expectations and nonlinear cost functions. It has numerous applications and arises, for example, in optimal stopping, linear-quadratic regulator problems, distributionally robust contextual bandits, as well as in problems involving dynamic risk measures. The naïve nested sampling approach for MCCO suffers from the curse of dimensionality familiar from scenario tree-based multistage stochastic programming, that is, its scenario complexity grows exponentially with the number of nests. We develop new multilevel Monte Carlo techniques for MCCO whose scenario complexity grows only polynomially with the desired accuracy.

Buse Şen, Yifan Hu, Daniel Kuhn

EPFL, Switzerland · Rutgers University, USA

Stochastic OptimizationDecision-Making under Uncertainty
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Apr 14, 2026

Instantiating Bayesian CVaR lower bounds in Interactive Decision Making Problems

Recent work established a generalized-Fano framework for lower bounding prior-predictive (Bayesian) CVaR in interactive statistical decision making. In this paper, we show how to instantiate that framework in concrete interactive problems and derive explicit Bayesian CVaR lower bounds from its abstract corollaries. Our approach compares a hard model with a reference model using squared Hellinger distance, and combines a lower bound on a reference hinge term with a bound on the distinguishability of the two models. We apply this approach to canonical examples, including Gaussian bandits, and obtain explicit bounds that make the dependence on key problem parameters transparent. These results show how the generalized-Fano Bayesian CVaR framework can be used as a practical lower-bound tool for interactive learning and risk-sensitive decision making.

Raghav Bongole, Tobias J. Oechtering, Mikael Skoglund

Department of Information Science and Engineering (ISE), KTH Royal Institute of Technology

Gaussian Process BanditsDecision-Making under UncertaintyConditional Value-at-RiskInformation-Theoretic Lower Bounds
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Apr 13, 2026

Deep Learning for Sequential Decision Making under Uncertainty: Foundations, Frameworks, and Frontiers

Artificial intelligence (AI) is moving increasingly beyond prediction to support decisions in complex, uncertain, and dynamic environments. This shift creates a natural intersection with operations research and management science (OR/MS), which has long provided methodological foundations for sequential decision making under uncertainty. At the same time, deep learning advances, including feedforward neural networks, recurrent architectures, transformers, large language models (LLMs), and deep reinforcement learning, have expanded data-driven modeling for large-scale decisions. This tutorial presents an OR/MS-centered perspective on deep learning for sequential decision making under uncertainty, bridging neural architectures and OR/MS approaches to decision making. Its premise: deep learning complements optimization rather than replacing it. Deep learning brings adaptability and scalable approximation, whereas OR/MS provides the mathematical rigor to represent constraints, recourse, uncertainty, and decision quality. The tutorial reviews key decision making foundations, connects them to the major neural architectures in modern AI, and organizes the field around three central themes: predict-then-optimize and decision-aware learning, learning-based decision generation under constraints for continuous and discrete problems with temporal coupling, and deep reinforcement learning for sequential and combinatorial decision making. Impact spans supply chains, service systems, healthcare and epidemic response, agriculture, energy, environmental sustainability, and autonomous operations. This tutorial frames these developments as part of a shift from predictive AI toward decision-capable AI, highlighting OR/MS's role in shaping the next generation of integrated learning--optimization systems.

I. Esra Buyuktahtakin

Grado Department of Industrial and Systems Engineering, Virginia Tech Blacksburg, VA 24061, USA

Reinforcement LearningPredict-Then-OptimizeSequential Decision MakingLearning to OptimizeDecision-Focused LearningDecision-Making under Uncertainty
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Apr 12, 2026

Mapping High-Performance Regions in Battery Scheduling across Data Uncertainty, Battery Design, and Planning Horizons

This study presents a controlled parametric framework for analyzing energy storage planning under uncertainty in a multi-stage model predictive control setting. The framework enables a broad and systematic exploration through parametrized generation of synthetic datasets in the context of energy price arbitrage. It facilitates the study of the joint effects of battery characteristics, signal structure, forecast uncertainty, and planning horizon on revenue performance in energy storage optimization, which are rarely considered together. The analysis is driven by two objectives. First, it characterizes how these interacting factors influence operational revenue and its sensitivity to planning horizon selection, including economic losses caused by deviations from optimal horizons. This provides guidance on expected horizon ranges and their impact on revenue and computational cost. Second, it enables a compact parametrization of the relationships between battery properties, data characteristics, forecast uncertainty, and horizon-dependent performance, providing a basis for future modelling of optimal planning horizon length. Results show that the framework captures consistent structural dependencies across configurations and provides meaningful guidance for horizon selection under uncertainty. In particular, increasing forecast uncertainty systematically reduces the optimal planning horizon across battery types, reflecting the diminishing value of long-term information under increasingly unreliable forecasts. Comparison with real market data shows that the parametrization reproduces the main qualitative trends of optimal horizon behavior, suggesting its potential as a lightweight surrogate for more complex simulation-based analysis.

Jaime de Miguel Rodriguez, Artjom Vargunin, Brigitta Robin Raudne +3

Enefit, Estonia · University of Seville, Spain · University of Tartu, Estonia +1

Power SystemsDecision-Making under UncertaintyModel Predictive Control
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Apr 8, 2026

The Theorems of Dr. David Blackwell and Their Contributions to Artificial Intelligence

Dr. David Blackwell was a mathematician and statistician of the first rank, whose contributions to statistical theory, game theory, and decision theory predated many of the algorithmic breakthroughs that define modern artificial intelligence. This survey examines three of his most consequential theoretical results the Rao Blackwell theorem, the Blackwell Approachability theorem, and the Blackwell Informativeness theorem (comparison of experiments) and traces their direct influence on contemporary AI and machine learning. We show that these results, developed primarily in the 1940s and 1950s, remain technically live across modern subfields including Markov Chain Monte Carlo inference, autonomous mobile robot navigation (SLAM), generative model training, no-regret online learning, reinforcement learning from human feedback (RLHF), large language model alignment, and information design. NVIDIAs 2024 decision to name their flagship GPU architecture (Blackwell) provides vivid testament to his enduring relevance. We also document an emerging frontier: explicit Rao Blackwellized variance reduction in LLM RLHF pipelines, recently proposed but not yet standard practice. Together, Blackwell theorems form a unified framework addressing information compression, sequential decision making under uncertainty, and the comparison of information sources precisely the problems at the core of modern AI.

Napoleon Paxton

School of Information, University of California, Berkeley

Blackwell ApproachabilityDecision-Making under Uncertainty
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Apr 6, 2026

Noisy Nonreciprocal Pairwise Comparisons: Scale Variation, Noise Calibration, and Admissible Ranking Regions

Pairwise comparisons are widely used in decision analysis, preference modeling, and evaluation problems. In many practical situations, the observed comparison matrix is not reciprocal. This lack of reciprocity is often treated as a defect to be corrected immediately. In this article, we adopt a different point of view: part of the nonreciprocity may reflect a genuine variation in the evaluation scale, while another part is due to random perturbations. We introduce an additive model in which the unknown underlying comparison matrix is consistent but not necessarily reciprocal. The reciprocal component carries the global ranking information, whereas the symmetric component describes possible scale variation. Around this structured matrix, we add a random perturbation and show how to estimate the noise level, assess whether the scale variation remains moderate, and assign probabilities to admissible ranking regions in the sense of strict ranking by pairwise comparisons. We also compare this approach with the brutal projection onto reciprocal matrices, which suppresses all symmetric information at once. The Gaussian perturbation model is used here not because human decisions are exactly Gaussian, but because observed judgment errors often result from the accumulation of many small effects. In such a context, the central limit principle provides a natural heuristic justification for Gaussian noise. This makes it possible to derive explicit estimators and probability assessments while keeping the model interpretable for decision problems.

Jean-Pierre Magnot

SFR MATHSTIC, LAREMA, Université d’Angers, 2 Bd Lavoisier, 49045 Angers cedex 1, France · Lycée Jeanne d’Arc, 40 avenue de Grande Bretagne, 63000 Clermont-Ferrand, France · Lepage Research Institute, 17 novembra 1, 081 16 Presov, Slovakia

Pairwise ComparisonDecision-Making under UncertaintyMulti-Criteria Decision Analysis
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Apr 6, 2026

Optimizing Service Operations via LLM-Powered Multi-Agent Simulation

Service system performance depends on how participants respond to design choices, but modeling these responses is hard due to the complexity of human behavior. We introduce an LLM-powered multi-agent simulation (LLM-MAS) framework for optimizing service operations. We pose the problem as stochastic optimization with decision-dependent uncertainty: design choices are embedded in prompts and shape the distribution of outcomes from interacting LLM-powered agents. By embedding key numerical information in prompts and extracting it from LLM-generated text, we model this uncertainty as a controlled Markov chain. We develop an on-trajectory learning algorithm that, on a single simulation run, simultaneously constructs zeroth-order gradient estimates and updates design parameters to optimize steady-state performance. We also incorporate variance reduction techniques. In a sustainable supply chain application, our method outperforms benchmarks, including blackbox optimization and using LLMs as numerical solvers or as role-playing system designers. A case study on optimal contest design with real behavioral data shows that LLM-MAS is both as a cost-effective evaluator of known designs and an exploratory tool that can uncover strong designs overlooked by traditional approaches.

Yanyuan Wang, Xiaowei Zhang

Department of Industrial Engineering and Decision Analytics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR

Stochastic OptimizationDecision-Making under UncertaintyMulti-Agent LLM SystemsLarge Language Model-Based Social SimulationZeroth-Order Optimization
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Apr 6, 2026

Generative models for decision-making under distributional shift

Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially observed, or stress-induced. This tutorial presents modern generative models, particularly flow- and score-based methods, as mathematical tools for constructing decision-relevant distributions. From an operations research perspective, their primary value lies not in unconstrained sample synthesis but in representing and transforming distributions through transport maps, velocity fields, score fields, and guided stochastic dynamics. We present a unified framework based on pushforward maps, continuity, Fokker-Planck equations, Wasserstein geometry, and optimization in probability space. Within this framework, generative models can be used to learn nominal uncertainty, construct stressed or least-favorable distributions for robustness, and produce conditional or posterior distributions under side information and partial observation. We also highlight representative theoretical guarantees, including forward-reverse convergence for iterative flow models, first-order minimax analysis in transport-map space, and error-transfer bounds for posterior sampling with generative priors. The tutorial provides a principled introduction to using generative models for scenario generation, robust decision-making, uncertainty quantification, and related problems under distributional shift.

Xiuyuan Cheng, Yunqin Zhu, Yao Xie

Department of Mathematics, Duke University, Durham, NC, USA · H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA

Decision-Making under UncertaintyDistribution Shift RobustnessDistributionally Robust Optimization
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Apr 5, 2026

Uncertainty as a Planning Signal: Multi-Turn Decision Making for Goal-Oriented Conversation

Goal-oriented conversational systems require making sequential decisions under uncertainty about the user's intent, where the algorithm must balance information acquisition and target commitment over multiple turns. Existing approaches address this challenge from different perspectives: structured methods enable multi-step planning but rely on predefined schemas, while LLM-based approaches support flexible interactions but lack long-horizon decision making, resulting in poor coordination between information acquisition and target commitment. To address this limitation, we formulate goal-oriented conversation as an uncertainty-aware sequential decision problem, where uncertainty serves as a guiding signal for multi-turn decision making. We propose a Conversation Uncertainty-aware Planning framework (CUP) that integrates language models with structured planning: a language model proposes feasible actions, and a planner evaluates their long-term impact on uncertainty reduction. Experiments on multiple conversational benchmarks show that CUP consistently improves success rates while requiring fewer interaction turns. Further analysis demonstrates that uncertainty-aware planning contributes to more efficient information acquisition and earlier confident commitment.

Xinyi Ling, Ye Liu, Reza Averly +1

Department of Computer Science and Engineering, The Ohio State University · Department of Biomedical Informatics, The Ohio State University · Translational Data Analytics Institute, The Ohio State University

Task-Oriented Dialogue SystemsDecision-Making under UncertaintyLLM PlanningModel-Based Planning
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Apr 2, 2026

A Comprehensive Framework for Long-Term Resiliency Investment Planning under Extreme Weather Uncertainty for Electric Utilities

Electric utilities must make massive capital investments in the coming years to respond to explosive growth in demand, aging assets and rising threats from extreme weather. Utilities today already have rigorous frameworks for capital planning, and there are opportunities to extend this capability to solve multi-objective optimization problems in the face of uncertainty. This work presents a four-part framework that 1) incorporates extreme weather as a source of uncertainty, 2) leverages a digital twin of the grid, 3) uses Monte Carlo simulation to capture variability and 4) applies a multi-objective optimization method for finding the optimal investment portfolio. We use this framework to investigate whether grid-aware optimization methods outperform model-free approaches. We find that, in fact, given the computational complexity of model-based metaheuristic optimization methods, the simpler net present value ranking method was able to find more optimal portfolios with only limited knowledge of the grid.

Emma Benjaminson

Boston Consulting Group’s AI Science Institute, Pittsburgh, PA, USA

Power SystemsDecision-Making under UncertaintyMulti-Objective Optimization
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Apr 2, 2026

Learning in Prophet Inequalities with Noisy Observations

We study the prophet inequality, a fundamental problem in online decision-making and optimal stopping, in a practical setting where rewards are observed only through noisy realizations and reward distributions are unknown. At each stage, the decision-maker receives a noisy reward whose true value follows a linear model with an unknown latent parameter, and observes a feature vector drawn from a distribution. To address this challenge, we propose algorithms that integrate learning and decision-making via lower-confidence-bound (LCB) thresholding. In the i.i.d.\ setting, we establish that both an Explore-then-Decide strategy and an ε\varepsilon-Greedy variant achieve the sharp competitive ratio of 1−1/e1 - 1/e, under a mild condition on the optimal value. For non-identical distributions, we show that a competitive ratio of 1/21/2 can be guaranteed against a relaxed benchmark. Moreover, with limited window access to past rewards, the tight ratio of 1/21/2 against the optimal benchmark is achieved.

Jung-hun Kim, Vianney Perchet

CREST, ENSAE, IP Paris · FairPlay joint team · Criteo AI Lab

Optimal StoppingDecision-Making under Uncertainty
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Apr 1, 2026

All Substitution Is Local

When does consulting one information source raise the value of another, and when does it diminish it? We study this question for Bayesian decision-makers facing finite actions. The interaction decomposes into two opposing forces: a complement force, measuring how one source moves beliefs to where the other becomes more useful, and a substitute force, measuring how much the current decision is resolved. Their balance obeys a localization principle: substitution requires an observation to cross a decision boundary, though crossing alone does not guarantee it. Whenever posteriors remain inside the current decision region, the substitute force vanishes, and sources are guaranteed to complement each other, even when one source cannot, on its own, change the decision. The results hold for arbitrarily correlated sources and are formalized in Lean 4. Substitution is confined to the thin boundaries where decisions change. Everywhere else, information cooperates. Code and proofs: https://github.com/nidhishs/all-substitution-is-local.

Nidhish Shah, Shaurjya Mandal, Asfandyar Azhar

Harvard University · University of Oxford

Value of InformationBayesian Decision TheoryDecision-Making under Uncertainty
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Apr 1, 2026

Scenario theory for multi-criteria data-driven decision making

The scenario approach provides a powerful data-driven framework for designing solutions under uncertainty with rigorous probabilistic robustness guarantees. Existing theory, however, primarily addresses assessing robustness with respect to a single appropriateness criterion for the solution based on a dataset, whereas many practical applications - including multi-agent decision problems - require the simultaneous consideration of multiple criteria and the assessment of their robustness based on multiple datasets, one per criterion. This paper develops a general scenario theory for multi-criteria data-driven decision making. A central innovation lies in the collective treatment of the risks associated with violations of individual criteria, which yields substantially more accurate robustness certificates than those derived from a naive application of standard results. In turn, this approach enables a sharper quantification of the robustness level with which all criteria are simultaneously satisfied. The proposed framework applies broadly to multi-criteria data-driven decision problems, providing a principled, scalable, and theoretically grounded methodology for design under uncertainty.

Simone Garatti, Lucrezia Manieri, Alessandro Falsone +3

Dipartimento di Elettronica Informazione e Ingegneria, Politecnico di Milano, Milano, Italy · Dipartimento di Ingegneria dell’Informazione, Universit`a degli studi di Brescia, Brescia, Italy

Decision-Making under UncertaintyMulti-Criteria Decision AnalysisRobust Optimization
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Mar 26, 2026

UMBRELLA: Uncertainty-aware Multi-robot Reactive Coordination under Dynamic Temporal Logic Tasks

Multi-robot systems can be extremely efficient for accomplishing team-wise tasks by acting concurrently and collaboratively. However, most existing methods either assume static task features or simply replan when environmental changes occur. This paper addresses the challenging problem of coordinating multi-robot systems for collaborative tasks involving dynamic and moving targets. We explicitly model the uncertainty in target motion prediction via Conformal Prediction(CP), while respecting the spatial-temporal constraints specified by Linear Temporal Logic (LTL). The proposed framework (UMBRELLA) combines the Monte Carlo Tree Search (MCTS) over partial plans with uncertainty-aware rollouts, and introduces a CP-based metric to guide and accelerate the search. The objective is to minimize the Conditional Value at Risk (CVaR) of the average makespan. For tasks released online, a receding-horizon planning scheme dynamically adjusts the assignments based on updated task specifications and motion predictions. Spatial and temporal constraints among the tasks are always ensured, and only partial synchronization is required for the collaborative tasks during online execution. Extensive large-scale simulations and hardware experiments demonstrate substantial reductions in both the average makespan and its variance by 23% and 71%, compared with static baselines.

Qisheng Zhao, Meng Guo, Hengxuan Du +2

School of Advanced Manufacturing and Robotics, Peking University, Beijing 100871, China · Automatic Control Laboratory, ETH Zürich, Zürich 8092, Switzerland

Risk-Sensitive PlanningMulti-Robot CoordinationMulti-Agent PlanningMulti-Robot Task AllocationDecision-Making under Uncertainty
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Mar 26, 2026

The Value of Information in Resource-Constrained Pricing

Firms that price perishable resources -- airline seats, hotel rooms, seasonal inventory -- now routinely use demand predictions, but these predictions vary widely in quality. Under hard capacity constraints, acting on an inaccurate prediction can irreversibly deplete inventory needed for future periods. We study how prediction uncertainty propagates into dynamic pricing decisions with linear demand, stochastic noise, and finite capacity. A certified demand forecast with known error bound~ε0ε^0 specifies where the system should operate: it shifts regret from O(T)O(\sqrt{T}) to O(log⁡T)O(\log T) when ε0≲T−1/4ε^0 \lesssim T^{-1/4}, and we prove this threshold is tight. A misspecified surrogate model -- biased but correlated with true demand -- cannot set prices directly but reduces learning variance by a factor of (1−ρ2)(1-ρ^2) through control variates. The two mechanisms compose: the forecast determines the regret regime; the surrogate tightens estimation within it. All algorithms rest on a boundary attraction mechanism that stabilizes pricing near degenerate capacity boundaries without requiring non-degeneracy assumptions. Experiments confirm the phase transition threshold, the variance reduction from surrogates, and robustness across problem instances.

Ruicheng Ao, Jiashuo Jiang, David Simchi-Levi

Institute for Data, Systems, and Society, Massachusetts Institute of Technology · Department of Industrial Engineering and Decision Analytics, Hong Kong University of Science and Technology · Department of Civil and Environmental Engineering and Operations Research Center, MIT

Dynamic PricingDecision-Making under UncertaintyDynamic Regret Minimization
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Mar 24, 2026

Can LLM Agents Be CFOs? Benchmarking Long-Horizon Resource Allocation in an Uncertain Enterprise Environment

Large language model (LLM) agents are increasingly tested on complex tasks, but their ability to allocate scarce resources over long horizons remains unclear. Unlike reactive tasks with immediate feedback, this setting requires agents to make binding commitments under partial observability, delayed consequences, hard resource budgets, and shifting dynamics. We introduce EnterpriseArena, a 132-month CFO simulator that evaluates long-horizon resource allocation under uncertainty in a FinTech lending firm. Agents must manage liquidity, close books, gather costly signals, and request equity or debt financing across changing macroeconomic regimes. The simulator is built from transformed firm-level financial data, anonymized business documents, decade-scale macroeconomic and industry signals, and expert-validated operating rules. Experiments across 23 LLMs and four agent frameworks show that current agents remain far from robust: only 15.4% of trials survive the full horizon, larger models do not reliably outperform smaller ones, and failures cascade across observation, action timing, and capital sizing. These findings establish long-horizon resource allocation under uncertainty as a distinct capability gap for LLM agents.

Yi Han, Yan Wang, Lingfei Qian +12

Georgia Institute of Technology · The Fin AI · Stevens Institute of Technology +7

Long-Horizon Agent EvaluationLLM AgentsFinancial Decision-MakingDecision-Making under UncertaintyAI Agent Benchmarks
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Mar 24, 2026

A Bayesian Learning Approach for Drone Coverage Network: A Case Study on Cardiac Arrest in Scotland

Drones are becoming popular as a complementary system for Emergency Medical Services (EMS). Although several pilot studies and flight trials have shown the feasibility of drone-assisted Automated External Defibrillator (AED) delivery, running a full-scale operational network remains challenging due to high capital expenditure and environmental uncertainties. In this paper, we formulate a reliability-informed Bayesian learning framework for designing drone-assisted AED delivery networks under environmental and operational uncertainty. We propose our objective function based on the survival probability of Out-off Hospital Cardiac Arrest (OHCA) patients to identify the ideal locations of drone stations. Moreover, we consider the coverage of existing EMS infrastructure to improve the response reliability in remote areas. We illustrate our proposed method using geographically referenced cardiac arrest data from Scotland. The result shows how environmental variability and spatial demand patterns influence optimal drone station placement across urban and rural regions. In addition, we assess the robustness of the network and evaluate its economic viability using a cost-effectiveness analysis based on expected Quality Adjusted Life Year (QALY). The findings suggest that drone-assisted AED delivery is expected to be cost-effective and has the potential to significantly improve the emergency response coverage in rural and urban areas with longer ambulance response times.

Tathagata Basu, Edoardo Patelli, Gianluca Filippi +7

UNSW Bengaluru, Bengaluru, India · Civil and Environmental Engineering, University of Strathclyde, Glasgow G1 1XQ, UK · Centre for Maritime Research and Experimentation, 19126 La Spezia, Italy +2

HealthcareDecision-Making under Uncertainty
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Mar 20, 2026

Multi-Robot Learning-Informed Task Planning Under Uncertainty

We want a multi-robot team to complete complex tasks in minimum time where the locations of task-relevant objects are not known. Effective task completion requires reasoning over long horizons about the likely locations of task-relevant objects, how individual actions contribute to overall progress, and how to coordinate team efforts. Planning in this setting is extremely challenging: even when task-relevant information is partially known, coordinating which robot performs which action and when is difficult, and uncertainty introduces a multiplicity of possible outcomes for each action, which further complicates long-horizon decision-making and coordination. To address this, we propose a multi-robot planning abstraction that integrates learning to estimate uncertain aspects of the environment with model-based planning for long-horizon coordination. We demonstrate the efficient multi-stage task planning of our approach for 1, 2, and 3 robot teams over competitive baselines in large ProcTHOR household environments. Additionally, we demonstrate the effectiveness of our approach with a team of two LoCoBot mobile robots in real household settings.

Abhish Khanal, Abhishek Paudel, Hung Pham +1

Department of Computer Science, George Mason University, Fairfax, VA, 22030, USA.

Multi-Robot CoordinationDecision-Making under UncertaintyMulti-Robot Motion PlanningModel-Based Planning
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Mar 17, 2026

Contextual Preference Distribution Learning

Decision-making problems often feature uncertainty stemming from heterogeneous and context-dependent human preferences. To address this, we propose a sequential learning-and-optimization pipeline to learn preference distributions and leverage them to solve downstream problems, for example risk-averse formulations. We focus on human choice settings that can be formulated as (integer) linear programs. In such settings, existing inverse optimization and choice modelling methods infer preferences from observed choices but typically produce point estimates or fail to capture contextual shifts, making them unsuitable for risk-averse decision-making. Using a bounded-variance score function gradient estimator, we train a predictive model mapping contextual features to a rich class of parameterizable distributions. This approach yields a maximum likelihood estimate. The model generates scenarios for unseen contexts in the subsequent optimization phase. In a synthetic ridesharing environment, our approach reduces average post-decision surprise by up to 114×\times compared to a risk-neutral approach with perfect predictions and up to 25×\times compared to leading risk-averse baselines.

Benjamin Hudson, Laurent Charlin, Emma Frejinger

Mila – Quebec Artificial Intelligence Institute, Montreal, Quebec, Canada · Département d’informatique et de recherche opérationnelle (DIRO), Université de Montréal, Montreal, Quebec, Canada · HEC Montréal, Montreal, Quebec, Canada

Preference LearningDecision-Making under UncertaintyConditional Distribution EstimationDiscrete Choice Modeling
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Mar 16, 2026

Persona-Conditioned Risk Behavior in Large Language Models: A Simulated Gambling Study with GPT-4.1

Large language models (LLMs) are increasingly deployed as autonomous agents in uncertain, sequential decision-making contexts. Yet it remains poorly understood whether the behaviors they exhibit in such environments reflect principled cognitive patterns or simply surface-level prompt mimicry. This paper presents a controlled experiment in which GPT-4.1 was assigned one of three socioeconomic personas (Rich, Middle-income, and Poor) and placed in a structured slot-machine environment with three distinct machine configurations: Fair (50%), Biased Low (35%), and Streak (dynamic probability increasing after consecutive losses). Across 50 independent iterations per condition and 6,950 recorded decisions, we find that the model reproduces key behavioral signatures predicted by Kahneman and Tversky's Prospect Theory without being instructed to do so. The Poor persona played a mean of 37.4 rounds per session (SD=15.5) compared to 1.1 rounds for the Rich persona (SD=0.31), a difference that is highly significant (Kruskal-Wallis H=393.5, p<2.2e-16). Risk scores by persona show large effect sizes (Cohen's d=4.15 for Poor vs Rich). Emotional labels appear to function as post-hoc annotations rather than decision drivers (chi-square=3205.4, Cramer's V=0.39), and belief-updating across rounds is negligible (Spearman rho=0.032 for Poor persona, p=0.016). These findings carry implications for LLM agent design, interpretability research, and the broader question of whether classical cognitive economic biases are implicitly encoded in large-scale pretrained language models.

Sankalp Dubedy

Independent Researcher

Prospect TheoryLLM Decision-MakingDecision-Making under UncertaintyHuman Behavior Simulation
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Mar 16, 2026

Survey of Various Fuzzy and Uncertain Decision-Making Methods

Decision-making in real applications is often affected by vagueness, incomplete information, heterogeneous data, and conflicting expert opinions. This survey reviews uncertainty-aware multi-criteria decision-making (MCDM) and organizes the field into a concise, task-oriented taxonomy. We summarize problem-level settings (discrete, group/consensus, dynamic, multi-stage, multi-level, multiagent, and multi-scenario), weight elicitation (subjective and objective schemes under fuzzy/linguistic inputs), and inter-criteria structure and causality modelling. For solution procedures, we contrast compensatory scoring methods, distance-to-reference and compromise approaches, and non-compensatory outranking frameworks for ranking or sorting. We also outline rule/evidence-based and sequential decision models that produce interpretable rules or policies. The survey highlights typical inputs, core computational steps, and primary outputs, and provides guidance on choosing methods according to robustness, interpretability, and data availability. It concludes with open directions on explainable uncertainty integration, stability, and scalability in large-scale and dynamic decision environments.

Takaaki Fujita, Florentin Smarandache

Neutrosophic Science International Association (NSIA) Publishing House Gallup - Guayaquil United States of America – Ecuador

Decision-Making under UncertaintyMulti-Criteria Decision AnalysisFuzzy LogicSequential Decision Making
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Mar 14, 2026

Chance-Constrained Correlated Equilibria for Robust Noncooperative Coordination

Correlated equilibria enable a coordinator to influence the self-interested agents by recommending actions that no player has an incentive to deviate from. However, the effectiveness of this mechanism relies on accurate knowledge of the agents' cost structures. When cost parameters are uncertain, the recommended actions may no longer be incentive compatible, allowing agents to benefit from deviating from them. We study a chance-constrained correlated equilibrium problem formulation that accounts for uncertainty in agents' costs and guarantees incentive compatibility with a prescribed confidence level. We derive sensitivity results that quantify how uncertainty in individual incentive constraints affects the expected coordination outcome. In particular, the analysis characterizes the value of information by relating the marginal benefit of reducing uncertainty to the dual sensitivities of the incentive constraints, providing guidance on which sources of uncertainty should be prioritized for information acquisition. The results further reveal that increasing the confidence level is not always beneficial and can introduce a tradeoff between robustness and system efficiency. Numerical experiments demonstrate this tradeoff: CC-CE reduces realized coordination cost by up to 35% at intermediate confidence levels, while the proposed information-gain metric consistently identifies effective uncertainty sources to reduce.

Jaehan Im, Ufuk Topcu, David Fridovich-Keil

Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin · The Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin

Game TheoryDecision-Making under UncertaintyChance-Constrained OptimizationValue of Information
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Mar 14, 2026

Distributional Uncertainty and Adaptive Decision-Making in System Co-design

Complex engineered systems require coordinated design choices across heterogeneous components under conflicting objectives and uncertain specifications. Monotone co-design provides a compositional framework for such problems. Performance of each subsystem is modeled with a design problem: a relation specifying what resources suffice to provide each functionality. Existing uncertain co-design models rely on interval bounds, which support worst-case reasoning but cannot represent probabilistic risk or multi-stage adaptive decisions. We develop a distributional extension of co-design that models uncertain design outcomes as distributions over design problems and supports adaptive decision processes through Markov-kernel re-parameterizations. Using quasi-measurable and quasi-universal spaces, we show that the standard co-design compositions remain compositional under this richer uncertainty, and introduce queries and observations extracting probabilistic trade-offs, including feasibility probabilities, confidence bounds, and distributions of minimal required resources. A task-driven unmanned aerial vehicle case study shows how the framework captures risk-sensitive and information-dependent design choices that interval models cannot express.

Yujun Huang, Gioele Zardini

Laboratory for Information & Decision Systems, Massachusetts Institute of Technology, Cambridge, MA 02139

Decision-Making under UncertaintyUncertainty Quantification
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Mar 12, 2026

Adaptive Conditional Residual Sampling for Spectral Risk Optimisation under Decision-Dependent Uncertainty

We consider minimising a spectral risk objective, the expected cost plus a weighted conditional value-at-risk, when the distribution of the uncertain parameters depends on the decision and can only be sampled through a stochastic simulator under a fixed budget of draws. We propose adaptive conditional residual sampling (ACRS). It takes one simulator draw at each point of a space-filling design, fits a heteroscedastic regression model of the decision-dependent distribution and reuses the standardised residual vectors as scenarios to construct a deterministic surrogate. ACRS searches this surrogate for several local optima, adds draws around the most promising ones, ranks the candidates on the simulator with common random numbers and finishes with sample-path local refinement using tail importance sampling. We show that the optimality gap of the surrogate minimiser is bounded by the Wasserstein error of the scenario distribution and that the refinement estimator is consistent. In the experiments, all methods share the budget accounting, the design sampler and the local refinement routine, and solutions are scored by normalised regret against reference optima. On 60 random instances of an analytic family with a closed-form objective, ACRS attains a mean regret of 11.8% against 22.3-42.3% for Bayesian optimisation, cross-entropy, kernel-density, stochastic-gradient and refinement-only baselines; its lead is largest at small budgets and, relative to the kernel-density method, tends to grow with the dimension. ACRS also has the lowest mean regret on two six-dimensional benchmarks and three development problems, and performs comparably to pure local refinement on three held-out problems frozen before testing.

Marcell T. Kurbucz

Institute for Global Prosperity, The Bartlett, University College London, 9–11 Endsleigh Gardens, London, WC1H 0EH, United Kingdom

Stochastic OptimizationDecision-Making under UncertaintyConditional Value-at-Risk
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Mar 12, 2026

Optimizing Task Completion Time Updates Using POMDPs

Managing announced task completion times is a fundamental control problem in project management. While extensive research exists on estimating task durations and task scheduling, the problem of when and how to update completion times communicated to stakeholders remains understudied. Organizations must balance announcement accuracy against the costs of frequent timeline updates, which can erode stakeholder trust and trigger costly replanning. Despite the prevalence of this problem, current approaches rely on static predictions or ad-hoc policies that fail to account for the sequential nature of announcement management. In this paper, we formulate the task announcement problem as a Partially Observable Markov Decision Process (POMDP) where the control policy must decide when to update announced completion times based on noisy observations of true task completion. Since most state variables (current time and previous announcements) are fully observable, we leverage the Mixed Observability MDP (MOMDP) framework to enable more efficient policy optimization. Our reward structure captures the dual costs of announcement errors and update frequency, enabling synthesis of optimal announcement control policies. Using off-the-shelf solvers, we generate policies that act as feedback controllers, adaptively managing announcements based on belief state evolution. Simulation results demonstrate significant improvements in both accuracy and announcement stability compared to baseline strategies, achieving up to 75% reduction in unnecessary updates while maintaining or improving prediction accuracy.

Duncan Eddy, Esen Yel, Emma Passmore +4

Stanford University, Stanford, CA, USA · Rensselaer Polytechnic Institute, Troy, NY, USA

Decision-Making under Uncertainty
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Mar 11, 2026

Safe RLHF Beyond Expectation: Stochastic Dominance for Universal Spectral Risk Control

Safe Reinforcement Learning from Human Feedback (RLHF) typically enforces safety through expected cost constraints, but the expectation captures only a single statistic of the cost distribution and fails to account for distributional uncertainty, particularly under heavy tails or rare catastrophic events. This limitation is problematic when robustness and risk sensitivity are critical. Stochastic dominance offers a principled alternative by comparing entire cost distributions rather than just their averages, enabling direct control over tail risks and potential out-of-distribution failures that expectation-based constraints may overlook. In this work, we propose Risk-sensitive Alignment via Dominance (RAD), a novel alignment framework that replaces scalar expected cost constraints with First-Order Stochastic Dominance (FSD) constraints. We operationalize this constraint by comparing the target policy's cost distribution to that of a reference policy within an Optimal Transport (OT) framework, using entropic regularization and Sinkhorn iterations to obtain a differentiable and computationally efficient objective for stable end-to-end optimization. Furthermore, we introduce quantile-weighted FSD constraints and show that weighted FSD universally controls a broad class of Spectral Risk Measures (SRMs), so that improvements under weighted dominance imply guaranteed improvements in the corresponding spectral risk. This provides a principled mechanism for tuning a model's risk profile via the quantile weighting function. Empirical results demonstrate that RAD improves harmlessness over baselines while remaining competitive in helpfulness, and exhibits greater robustness on out-of-distribution harmlessness evaluations.

Yaswanth Chittepu, Ativ Joshi, Rajarshi Bhattacharjee +1

University of Massachusetts Amherst

Constrained RLLLM Safety AlignmentRisk-Sensitive RLDecision-Making under Uncertainty
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Mar 11, 2026

Implicit Statistical Inference in Transformers: Approximating Likelihood-Ratio Tests In-Context

In-context learning (ICL) allows Transformers to adapt to novel tasks without weight updates, yet the underlying algorithms remain poorly understood. We adopt a statistical decision-theoretic perspective by investigating simple binary hypothesis testing, where the optimal policy is determined by the likelihood-ratio test. Notably, this setup provides a mathematically rigorous setting for mechanistic interpretability where the target algorithmic ground truth is known. By training Transformers on tasks requiring distinct geometries (linear shifted means vs. nonlinear variance estimation), we demonstrate that the models approximate the Bayes-optimal sufficient statistics from context up to some monotonic transformation, matching the performance of an ideal oracle estimator in nonlinear regimes. Leveraging this analytical ground truth, mechanistic analysis via logit lens and circuit alignment suggests that the model does not rely on a fixed kernel smoothing heuristic. Instead, it appears to adapt the point at which decisions become linearly decodable: exhibiting patterns consistent with a voting-style ensemble for linear tasks while utilizing a deeper sequential computation for nonlinear tasks. These findings suggest that ICL emerges from the construction of task-adaptive statistical estimators rather than simple similarity matching.

Faris Chaudhry, Siddhant Gadkari

Department of Computer Science Imperial College London

Likelihood Ratio TestingIn-Context LearningTransformer InterpretabilityDecision-Making under Uncertainty
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Mar 10, 2026

Noncooperative Human-AI Agent Dynamics

This paper investigates the dynamics of noncooperative interactions between artificial intelligence agents and human decision-makers in strategic environments. In particular, motivated by extensive literature in behavioral Economics, human agents are more faithfully modeled with respect to the state of the art using Prospect Theoretic preferences, while AI agents are modeled with standard expected utility maximization. Prospect Theory incorporates known cognitive heuristics employed by humans, including reference dependence and greater loss aversion relative to utility to relative gains. This paper runs different combinations of expected utility and prospect theoretic agents in a number of classic matrix games as well as examples specialized to tease out distinctions in strategic behavior with respect to preference functions, to explore the emergent behaviors from mixed population (human vs. AI) competition. Extensive numerical simulations are performed across AI, aware humans (those with full knowledge of the game structure and payoffs), and learning Prospect Agents (i.e., for AIs representing humans). A number of interesting observations and patterns show up, spanning barely distinguishable behavior, behavior corroborating Prospect preference anomalies in the theoretical literature, and unexpected surprises. Code can be found at https://github.com/dylanwaldner/noncooperative-human-AI.

Dylan Waldner, Vyacheslav Kungurtsev, Mitchelle Ashimosi

Prospect TheoryHuman-AI Decision MakingGame TheoryHuman Behavior SimulationDecision-Making under Uncertainty
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Mar 10, 2026

The Confidence Gate Theorem: When Should Ranked Decision Systems Abstain?

Ranked decision systems -- recommenders, ad auctions, clinical triage queues -- must decide when to intervene in ranked outputs and when to abstain. We study when confidence-based abstention monotonically improves decision quality, and when it fails. The formal conditions are simple: rank-alignment and no inversion zones. The substantive contribution is identifying why these conditions hold or fail: the distinction between structural uncertainty (missing data, e.g., cold-start) and contextual uncertainty (missing context, e.g., temporal drift). Empirically, we validate this distinction across three domains: collaborative filtering (MovieLens, 3 distribution shifts), e-commerce intent detection (RetailRocket, Criteo, Yoochoose), and clinical pathway triage (MIMIC-IV). Structural uncertainty produces near-monotonic abstention gains in all domains; structurally grounded confidence signals (observation counts) fail under contextual drift, producing as many monotonicity violations as random abstention on our MovieLens temporal split. Context-aware alternatives -- ensemble disagreement and recency features -- substantially narrow the gap (reducing violations from 3 to 1--2) but do not fully restore monotonicity, suggesting that contextual uncertainty poses qualitatively different challenges. Exception labels defined from residuals degrade substantially under distribution shift (AUC drops from 0.71 to 0.61--0.62 across three splits), providing a clean negative result against the common practice of exception-based intervention. The results provide a practical deployment diagnostic: check C1 and C2 on held-out data before deploying a confidence gate, and match the confidence signal to the dominant uncertainty type.

Ronald Doku

Haske Labs

Decision-Making under UncertaintyUncertainty QuantificationDistribution Shift
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