Robust Optimization

Affine Decision Rules for Robust Optimization with Decision-Dependent Information Discovery

Categories Robust Optimization Tags , , , , ,

We study robust optimization problems with decision-dependent information discovery under polyhedral uncertainty and continuous recourse. We first establish structural properties of the resulting min–max–min problem, including existence of solutions and a condition under which information discovery has no value. Then, we develop a heuristic approach that combines affine decision rules with scenario generation and show … Read more

Adversarial Training for Deep Hedging in Nonstationary Markets

Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , , ,

Deep hedging learns trading policies from historical or simulated market trajectories, yet under nonstationarity these training paths may not represent future market conditions. We propose WRAP (Wasserstein-Reweighting Adversarial Perturbation), a drift-aware adversarial training framework derived from a two-budget distributionally robust optimization (DRO) formulation. The formulation is anchored to a weighted empirical reference distribution whose fixed … Read more

Robust Out-of-Distribution Stochastic Optimization Based on Wasserstein-Metric Meta-Distribution Support Learning

Categories Optimization in Data Science, Robust Optimization, Stochastic Programming Tags , , , , ,

We study stochastic optimization with a completely unobserved target distribution and samples from related source distributions. Treating the sources and the target as independent draws from a common meta-distribution, we propose Wasserstein-metric meta-distribution support learning (MDSL). The model jointly learns the center and radius of a Wasserstein ball, with an exclusion parameter controlling the fraction … Read more

On the Convergence of Column-and-Constraint Generation Algorithms in Two-Stage Robust Optimization

Categories Robust Optimization Tags , , , , , , ,

We study the well-posedness and convergence of column-and-constraint generation algorithms for general two-stage robust optimization problems. The analysis is formulated in terms of regularity properties of the objective, the second-stage feasible region mapping, and the separation value function, without relying on a particular algebraic representation of the second-stage problem. We give sufficient conditions for the … Read more

Signed Budget Uncertainty for Robust Mixed-Integer Optimization

Categories (Mixed) Integer Linear Programming, Robust Optimization Tags , , ,

Classical budget uncertainty is widely used in robust optimization. It bounds the aggregate absolute deviation of uncertain parameters from nominal values and yields tractable robust counterparts. In many applications, however, information concerns aggregate signed deviations. We therefore study signed budget uncertainty, in which bounds are imposed on signed aggregates rather than absolute deviations. For robust … Read more

Brenier Meets Adversarial Training: Optimal Transport Geometry for Robust Learning

Categories Convex and Nonsmooth Optimization, Optimization in Data Science, Robust Optimization

Distributionally robust optimization (DRO) provides a principled framework for learning under distribution shift, but its practical use is hindered by the difficulty of evaluating worst-case risks for nonconvex loss functions. We study a penalized DRO formulation in which the adversary may choose any distribution but incurs a Wasserstein penalty for deviating from the empirical distribution. … Read more

Soft Separation for Adaptive Robust Optimization

Categories Robust Optimization, Stochastic Programming Tags , ,

We propose an algorithmic framework for solving adaptive robust optimization with provable guarantees on both tractability and solution accuracy. The framework introduces soft separation, a probabilistic mechanism for identifying worst-case uncertainty realizations via a time-inhomogeneous Markov chain. Rather than solving an exact separation problem in each iteration, which is intractable in general, the chain carries … Read more

Learning Risk Scores Robust to Unobserved Confounders

Categories Robust Optimization Tags , ,

We consider the problem of learning risk scores to prioritize individuals for scarce resources or interventions, from historical observational data affected by unobserved confounding. In settings such as public health and homelessness prevention, decisions about who receives a scarce resource (e.g., a hospital bed or housing) are often guided by a risk score assigned to … Read more

New adaptive proximal gradient algorithms for solving multiobjective composite optimization problems

Categories Nonlinear Optimization, Nonsmooth Optimization, Robust Optimization Tags , , , ,

In this paper, we propose new adaptive proximal gradient algorithms to solve multiobjective optimization problems, where each objective function is the sum of a differentiable function and a proper, closed, convex function. Utilizing the local behavior of the differentiable terms we propose new adaptive ways to select stepsizes used in proximal gradient scheme. In particular, … Read more

Robust Optimization Under Sparse Uncertainty

Categories Robust Optimization Tags , , , ,

Classical robust optimization relies on convex and bounded uncertainty sets, an assumption that is inadequate for sparse uncertainty, where only a small, unknown subset of parameters deviates from its nominal value. This sparsity makes the uncertainty set nonconvex and turns separation into a combinatorial problem, so standard duality-based reformulations do not apply. We study two … Read more