Distributionally Robust Chance-Constrained Optimization with Deep Kernel Ambiguity Set

Yang, Shu‐Bo; Li, Zukui

doi:10.1109/adconip55568.2022.9894158

Cited by 1 publication

(2 citation statements)

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“…It is also noteworthy that CVaR approximation has been used to solve the Sinkhorn robust chance-constrained program in literature [22]. Unlike their algorithm idea that solves a largescale convex program using interior-point methods, we provide a first-order method that enables us to solve such problem more efficiently.…”

Section: Return Smentioning

confidence: 99%

“…We use the following stochastic approximation-based algorithm to find a near-optimal solution for this convex optimization problem. The objective defined in (22) serves as a biased estimator of the objective defined in (21), whereas the bias vanishes as m → ∞. We will provide the theoretical analysis regarding this biased stochastic optimization algorithm in future work.…”

Section: Appendix B Implementation Detailsmentioning

confidence: 99%

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A Data-Driven Approach to Robust Hypothesis Testing Using Sinkhorn Uncertainty Sets

Wang¹,

Xie²

2022

2022 IEEE International Symposium on Information Theory (ISIT)

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We present a new framework to address the non-convex robust hypothesis testing problem, wherein the goal is to seek the optimal detector that minimizes the maximum of worst-case type-I and type-II risk functions. The distributional uncertainty sets are constructed to center around the empirical distribution derived from samples based on Sinkhorn discrepancy. Given that the objective involves non-convex, non-smooth probabilistic functions that are often intractable to optimize, existing methods resort to approximations rather than exact solutions. To tackle the challenge, we introduce an exact mixed-integer exponential conic reformulation of the problem, which can be solved into a global optimum with a moderate amount of input data. Subsequently, we propose a convex approximation, demonstrating its superiority over current state-of-the-art methodologies in literature. Furthermore, we establish connections between robust hypothesis testing and regularized formulations of non-robust risk functions, offering insightful interpretations. Our numerical study highlights the satisfactory testing performance and computational efficiency of the proposed framework.

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Section: Return Smentioning

confidence: 99%

Section: Appendix B Implementation Detailsmentioning

confidence: 99%