decision theory

This work addresses the joint optimization of predictive uncertainty quantification and downstream decision-making for risk-averse decision-makers—such as clinicians—in high-stakes settings. We propose the Risk-Averse Calibration (RAC) framework, which (i) establishes, for the first time, the statistical optimality of prediction sets for Value-at-Risk (VaR) minimization; (ii) introduces a coupled max-min optimal decision mechanism that jointly optimizes prediction sets and action policies; and (iii) provides a distribution-free, finite-sample-constructible method grounded in conformal prediction, decision theory, and robust statistical inference. Empirically, on medical diagnosis and recommendation tasks, RAC achieves significantly higher utility than existing uncertainty quantification methods while rigorously satisfying user-specified risk constraints—demonstrating both theoretical soundness and practical efficacy in safety-critical applications.

This work addresses the challenge of selecting uncertainty representations that align with decision objectives to achieve optimal and trustworthy decisions under state-variable uncertainty. Drawing on decision theory, it systematically analyzes the optimal forms of uncertainty representation for both risk-neutral and risk-averse agents in known and unknown environments, revealing the minimal uncertainty information required under distinct risk preferences. The study innovatively unifies three approaches to epistemic uncertainty—calibrated prediction, confidence-set robust optimization, and Bayesian inference—establishing a theoretical link between uncertainty representation and decision goals. This integration yields a reliable decision-making framework that provides agents with verifiable utility guarantees.

This work addresses the misalignment between conventional uncertainty quantification metrics—such as negative log-likelihood and expected calibration error—and the utility of downstream decision-making, which often renders them poor proxies for real-world decision value. To bridge this gap, the paper introduces a “decision-aligned” evaluation principle, systematically exposing the mismatch between widely used scoring rules and common decision tasks. Building on decision theory and proper scoring rules, the authors propose a class of prior-weighted utility-based metrics that directly reflect the impact of predictive uncertainty on decision outcomes. Empirical evaluations across multiple benchmarks and real-world scenarios demonstrate that the proposed metric consistently correlates strongly with actual decision utility, significantly outperforming traditional approaches and offering a principled foundation for decision-relevant uncertainty assessment.

This study addresses how organizations adopting commercial AI decision-support systems often passively accept vendors’ embedded and non-negotiable value judgments, thereby constraining their own decision flexibility. The paper introduces the concept of the “behaviorally feasible set” to formally characterize the range of recommendations an AI system can generate under value-alignment constraints and identifies critical conditions under which organizational needs exceed the system’s adaptive capacity. Through controlled experiments comparing binary decisions and multi-stakeholder preference rankings, the research demonstrates that value alignment substantially shrinks the behaviorally feasible set, diminishing the system’s responsiveness to legitimate contextual variation. Commercial models exhibit heightened rigidity, and the alignment process systematically shifts—rather than neutralizes—stakeholder priorities, revealing that value alignment functions as a structural mechanism embedding vendor values and narrowing organizational negotiation space.

Existing uncertainty quantification methods neglect downstream decision costs, leading to suboptimal decisions in high-risk scenarios. This paper proposes a utility-oriented conformal prediction framework that, for the first time, rigorously incorporates user-specified downstream utility functions into conformal prediction—jointly ensuring the standard 1−α statistical coverage guarantee and optimizing decision cost. To preserve semantic coherence of prediction sets, we introduce hierarchical label modeling (e.g., dermatological taxonomies) and design a model-agnostic permutation test coupled with a cost-sensitive set-shrinking algorithm. Empirical evaluation across multiple datasets demonstrates an average 23.6% reduction in decision cost. In a real-world dermatological diagnosis task, our method produces clinically interpretable and triage-appropriate diagnostic sets. The core contribution lies in achieving a rigorous unification of statistical reliability and decision utility—bridging theoretical guarantees with practical operational impact.

This study addresses a key limitation of traditional multi-attribute decision-making models, which assume full compensability and thus fail to account for human tendencies to outright reject alternatives that perform poorly on critical attributes. To resolve this, the authors propose a bounded trade-off screening mechanism that formalizes tolerance for attribute trade-offs as a controllable parameter, capturing decision makers’ non-compensatory judgments across varying contexts. Through computational modeling and simulation experiments, they develop a lightweight choice model that successfully reproduces preference patterns distinct from those predicted by classical utility theory. The approach elucidates the computational underpinnings of non-compensatory screening and context-dependent preferences, while generating testable behavioral predictions that offer a novel mechanistic account of human multi-attribute decision making.

Existing decision theories lack a unified formal language, and key concepts—such as the distinction between subjective and objective perspectives and criteria for evaluating theoretical superiority—remain ambiguous, impeding rigorous comparison. This work addresses these limitations by constructing a unified decision-theoretic framework grounded in nonparametric structural equation models (NPSEMs), which precisely characterizes agents, causal relationships, and counterfactuals, and formally defines evidential decision theory (EDT) and causal decision theory (CDT). Building on this foundation, the paper proposes a personal decision theory that aims to maximize an individual’s subjective counterfactual utility and introduces a performance evaluation metric based on population-level interventions, proving its optimality under specific conditions. The framework enables formal analyses of Newcomb’s paradox and the smoking lesion problem, offering a clear modeling language and a comparable benchmark for decision theories.

This work addresses the challenge of coordinating design in complex engineering systems under conflicting objectives and uncertain specifications, where existing co-design methods based on interval uncertainty fail to capture probabilistic risk and multi-stage adaptive decision-making. For the first time, distributional uncertainty is integrated into a monotone co-design framework by reparameterizing uncertain design outcomes as probability distributions over the design space via Markov kernels, thereby enabling adaptive decisions and compositional construction. Grounded in quasi-measurable space theory, the approach supports queries on probabilistic feasibility, confidence bounds, and resource demand distributions, overcoming the representational limitations of traditional interval models. In a mission-driven unmanned aerial vehicle case study, the framework successfully captures risk-sensitive and information-dependent design trade-offs, demonstrating its expressive power and effectiveness.

This study addresses the challenge of dependency uncertainty in risk and decision models where marginal distributions are sparse and dependence structures are partially unknown, rendering traditional probability bounds analysis ineffective. The authors propose a black-box risk decision framework that integrates p-boxes, precise cumulative distribution functions, and fixed quantities as mixed inputs. Known dependencies are characterized using copulas, while unknown dependencies are propagated through Fréchet-type admissible coupling sets. For the first time, dependence sensitivity is incorporated into probability bounds analysis, enabling cross-dependence modeling between imprecise and precise variables and substantially enhancing the transparency and reasonableness of uncertainty propagation. Case studies demonstrate that neglecting dependence structure can severely underestimate tail risk, leading to overly optimistic decision assessments.

This work addresses dynamic pricing under capacity constraints, where prediction errors can lead to irreversible inventory loss. Focusing on a setting with linear demand, stochastic noise, and finite inventory, the paper introduces a demand prediction model with bounded error and a proxy model to stabilize pricing through a boundary-attracting mechanism—without requiring non-degeneracy assumptions. Theoretically, it establishes a sharp phase transition: when the prediction error $\varepsilon \lesssim T^{-1/4}$, the regret drops abruptly from $O(\sqrt{T})$ to $O(\log T)$, and this threshold is tight. Furthermore, by integrating control variates, the proxy model reduces estimation variance by a factor of $(1-\rho^2)$. Extensive experiments confirm the algorithm’s robustness and effectiveness across diverse scenarios.