arXiv subjects

Irina Wang

Publications and source records attributed to Irina Wang.

4 recordsLinked to original sources

arXiv2025

Fast Online Distributionally Robust Optimization via Data Compression

We propose an online data compression approach for efficiently solving Wasserstein distributionally robust optimization (DRO) problems with streaming data. Our method constructs adaptive ambiguity sets around a compressed distribution obtained by online clustering, so the problem size stays fixed as data accumulate. We construct a dynamic regret bound with respect to a one-step-ahead non-compressed DRO oracle, and establish online clustering conditions such that, with high probability, the regret converges sublinearly to a clustering-discrepancy-based performance gap. This gap is defined in terms of the discrepancies between the true and compressed distributions, so that by varying the number of clusters, our method trades off robustness against computational effort. We additionally provide fast subgradient-based updates that replace direct solutions of both the full and compressed problems, and extend the regret analysis to this setting. Numerical experiments on portfolio optimization and sparse support vector machine problems, including mixed-integer formulations, show over an order of magnitude reduction in cumulative computation time, even compared to non-robust methods, with minimal loss in solution quality.

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arXiv2023

Learning Decision-Focused Uncertainty Sets in Robust Optimization

We propose a data-driven technique to automatically learn contextual uncertainty sets in robust optimization, resulting in excellent worst-case and average-case performance while also guaranteeing constraint satisfaction. Our method reshapes the uncertainty sets by minimizing the expected performance across a contextual family of problems, subject to conditional-value-at-risk constraints. Our approach is very flexible, and can learn a wide variety of uncertainty sets while preserving tractability. We solve the constrained learning problem using a stochastic augmented Lagrangian method that relies on differentiating the solutions of the robust optimization problems with respect to the parameters of the uncertainty set. Due to the nonsmooth and nonconvex nature of the augmented Lagrangian function, we apply the nonsmooth conservative implicit function theorem to establish convergence to a critical point, which is a feasible solution of the constrained problem under mild assumptions. Using empirical process theory, we show finite-sample probabilistic guarantees of constraint satisfaction for the resulting solutions. Numerical experiments show that our method outperforms traditional approaches in robust and distributionally robust optimization in terms of out-of-sample performance and constraint satisfaction guarantees.

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arXiv2023

The Benefit of Uncertainty Coupling in Robust and Adaptive Robust Optimization

Despite the modeling power for problems under uncertainty, robust optimization (RO) and adaptive robust optimization (ARO) can exhibit too conservative solutions in terms of objective value degradation compared to the nominal case. One of the main reasons behind this conservatism is that, in many practical applications, uncertain constraints are directly designed as constraint-wise without taking into account couplings over multiple constraints. In this paper, we define a coupled uncertainty set as the intersection between a constraint-wise uncertainty set and a coupling set. We study the benefit of coupling in alleviating conservatism in RO and ARO. We provide theoretical tight and computable upper and lower bounds on the objective value improvement of RO and ARO problems under coupled uncertainty over constraint-wise uncertainty. In addition, we relate the power of adaptability over static solutions with the coupling of uncertainty set. Computational results demonstrate the benefit of coupling in applications.

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arXiv2022

Mean Robust Optimization

Robust optimization is a tractable and expressive technique for decision-making under uncertainty, but it can lead to overly conservative decisions when pessimistic assumptions are made on the uncertain parameters. Wasserstein distributionally robust optimization can reduce conservatism by being data-driven, but it often leads to very large problems with prohibitive solution times. We introduce mean robust optimization, a general framework that combines the best of both worlds by providing a trade-off between computational effort and conservatism. We propose uncertainty sets constructed based on clustered data rather than on observed data points directly thereby significantly reducing problem size. By varying the number of clusters, our method bridges between robust and Wasserstein distributionally robust optimization. We show finite-sample performance guarantees and explicitly control the potential additional pessimism introduced by any clustering procedure. In addition, we prove conditions for which, when the uncertainty enters linearly in the constraints, clustering does not affect the optimal solution. We illustrate the efficiency and performance preservation of our method on several numerical examples, obtaining multiple orders of magnitude speedups in solution time with little-to-no effect on the solution quality.

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