compute expected utility

This study addresses the lack of long-term resilience investment planning methods in power systems that can simultaneously account for multiple objectives and uncertainties arising from extreme weather events, surging electricity demand, and aging infrastructure. To bridge this gap, the authors propose a novel four-stage framework that integrates digital twins of power grids, Monte Carlo simulations, and multi-objective optimization, systematically incorporating extreme weather modeling into investment decision-making for the first time. The work also provides a comparative evaluation of model-based and model-free approaches. Empirical results demonstrate that, under limited grid knowledge, a simple net present value ranking method outperforms computationally intensive model-based optimization techniques, offering a practical and efficient alternative for real-world planning applications.

This paper addresses the absence of non-probabilistic, non-heuristic risk decision frameworks under extreme uncertainty—such as “unknown unknowns” and severe resource constraints. Methodologically, it introduces the RDOT classification paradigm, a structured taxonomy that categorizes cross-disciplinary risk strategies into six types: structural, responsive, formal, adversarial, multi-stage, and proactive. It systematically identifies over 110 domain-agnostic strategies, transcending the traditional dichotomy between probabilistic modeling and cognitive heuristics, and bridges theoretical gaps in robust design and emergency planning. The framework integrates multi-objective optimization, multi-attribute utility theory, and structured workflow modeling—requiring neither probability estimation nor predictive modeling. Empirically validated in engineering and public policy contexts, RDOT demonstrates robustness and embeddability, delivering the first lightweight, actionable, cross-domain risk decision toolkit. (149 words)

This study addresses a critical gap in algorithmic fairness research, which has predominantly focused on trade-offs between performance and fairness in prediction space while overlooking the real-world utilities of multiple stakeholders and welfare distribution across groups. The authors propose a novel multi-stakeholder framework grounded in welfare economics and distributive justice, formalizing fairness as the social planner’s utility and employing posterior multi-objective optimization to identify optimal trade-offs between decision-maker utility and societal fairness. For the first time, they characterize the fairness–performance Pareto frontier in utility space under both deterministic and randomized policies, theoretically demonstrating that randomization can yield strictly superior trade-offs under certain conditions. Empirical results confirm that simple randomized mechanisms leverage outcome uncertainty to enhance fairness–performance balance, offering a more transparent and equitable design paradigm for algorithmic decision systems.

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.

Real-world multi-objective optimization often suffers from the difficulty of explicitly modeling expert preferences; existing approaches rely on strong utility function priors, frequent human interaction, or costly computation of the full Pareto front. This paper proposes an offline preference learning framework that (i) introduces coarse-grained prior constraints over the utility function space, and (ii) jointly models and explicitly propagates uncertainty in utility learning throughout the surrogate optimization pipeline—significantly reducing expert involvement. By integrating preference learning, Bayesian uncertainty quantification, multi-objective surrogate optimization, and utility-space regularization, our method achieves a 3.2× improvement in sample efficiency across four real-world tasks. Crucially, it remains robust to misspecified utility surrogates, consistently converging to high-quality solutions, and effectively mitigates optimization bias induced by skewed preference data.

This study addresses utility maximization for an investor facing an exogenous contingent claim with known marginal distributions but ambiguous dependence structure. Introducing an α-robust criterion that continuously interpolates between worst- and best-case scenarios, the dynamic stochastic control problem is transformed into a static concave quantile optimization over a convex set. The optimal quantile function is derived via variational methods. Innovatively integrating the α-robust framework with quantile optimization, the analysis leverages the rearrangement inequality and comonotonicity theory to establish distributional invariance of risk measures, thereby naturally accommodating risk constraints such as Value-at-Risk (VaR) and Expected Shortfall (ES). The solution yields a numerically tractable two-dimensional first-order ordinary differential equation system, elucidating the joint impact of ambiguity aversion, market conditions, and claim characteristics on the optimal payoff structure.

This study addresses the limitations of traditional static portfolio optimization in handling sequential decision-making, tail risk, and market frictions such as transaction costs. To this end, it proposes a deep reinforcement learning–based bi-objective dynamic optimization framework that jointly maximizes expected return and minimizes downside risk by integrating three risk measures—variance, Conditional Value-at-Risk (CVaR), and Entropic Value-at-Risk (EVaR)—while explicitly incorporating transaction costs and position constraints. The approach innovatively applies deep reinforcement learning to multi-objective portfolio optimization, modeling asset return uncertainty through a combination of GARCH(1,1), extreme value theory, and t-copula. Scenario generation employs quasi-Monte Carlo simulation, and the policy is trained using the Proximal Policy Optimization (PPO) algorithm. Empirical validation on equity index data from ten countries across pre-, mid-, and post-pandemic periods demonstrates that the proposed method significantly outperforms benchmarks such as NSGA-II in terms of risk–return trade-off, control of extreme downside risk, and scalability to high-dimensional portfolios.

This work proposes a risk-aware generalized utility Markov decision process (MDP) framework that enables flexible trade-offs between expected performance and risk aversion. The approach formulates the objective function based on state visitation frequencies and, for the first time, integrates entropic risk measures into the generalized utility MDP setting, thereby supporting risk-sensitive decision-making in multi-task scenarios. To solve this framework, the authors develop an online planning algorithm grounded in Monte Carlo tree search and establish its convergence properties. Experimental results demonstrate that the method effectively optimizes policies across diverse risk preferences in a range of tasks—including standard MDPs, maximum state-entropy exploration, imitation learning, and multi-objective MDPs—highlighting its versatility and efficacy.

This work addresses the challenge of decision uncertainty in engineering design arising from incomplete preference information, which complicates the assessment of solution robustness and recommendation stability. The authors propose a probabilistic framework that models preference parameters as random variables to analyze how their uncertainty propagates to optimal design decisions and to characterize the probability distribution over regions of the Pareto front being selected. For the first time in preference-driven optimization, variance-based global sensitivity analysis and Fréchet variance are integrated with Sobol’ indices and Shapley values to quantify the contributions of design variables to decision uncertainty and to measure overall decision stability. Applied to a ground vehicle design case, the approach reveals how problem structure induces either discrete or continuous decision distributions, thereby enabling robust design recommendations under preference uncertainty.

This study addresses the challenge that investors’ true utility functions are typically unobservable, which limits the accuracy of portfolio optimization. To overcome this, the authors propose a preference-fitting approach based on probability–wealth pairs, leveraging martingale duality theory to establish a bijection between terminal wealth and utility functions. This framework circumvents the traditional Lagrangian multiplier method while offering both intuitive clarity and analytical tractability. The approach employs piecewise hyperbolic absolute risk aversion (PHARA) utility functions for approximation and rigorously establishes convergence of the fitted solution to the true optimum under multiple modes—almost sure, $L^r$, and uniform convergence. The methodology is successfully applied to explicit asymptotic portfolio construction and asset allocation under Value-at-Risk (VaR) constraints, significantly enhancing practical applicability and robustness.