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
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
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
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
Realistic decision problems are inherently multiobjective and uncertain. To manage both of these complexities, robust multiobjective optimization strives to aid the decision maker in finding a decision which is Pareto efficient and is hedged against the worst-case scenario. In this paper, we present a robustness approach which is grounded in the decision maker’s preferences by … Read more
Decision scenarios far from rare in practice often place data-driven decision-making in an awkward position, where the decision maker may have access to neither the target distribution itself nor any empirical samples drawn from it, especially when decisions must be made in novel or highly uncertain environments. In response, robust out-of-distribution stochastic optimization (RooDSO) has … Read more
This document provides an extended and rigorous framework dedicated to the geometric analysis of the 3D incompressible Navier-Stokes equations \cite{ESS2003}. We comprehensively develop geometric proofs related to decay estimates, blow-up profiles, and the foundational partial regularity theory of Caffarelli, Kohn, and Nirenberg (CKN). We examine in detail the Hausdorff dimension of potential singular sets, local … Read more
We consider optimization applications with unknown parameters where the decision maker believes that the optimal value of the nominal problem—the optimization problem they would have solved if the true parameters were known—is unlikely to be large. This belief derives from information that humans have that is not captured in datasets, obtained from domain knowledge and … Read more
This paper studies the Sinkhorn distributionally robust hypothesis testing (SDRHT) problem, seeking a robust detector against least-favorable distributions in Sinkhorn discrepancy-based ambiguity sets centered at the empirical distributions. Existing approaches solve this problem by solving large-scale conic programs, which are not scalable. To overcome this, we propose a generative framework that learns least-favorable distributions and … Read more
Wasserstein distributionally robust optimization (DRO) is a versatile and widely adopted framework for decision-making under uncertainty, yet its standard deterministic reformulations generally contain non-convex inner subproblems that are challenging to solve. To address this issue, we propose a shrinkage path heuristic that reduces the solution of a DRO problem to a one-dimensional search over the … Read more