Non-Convex Robust Hypothesis Testing using Sinkhorn Uncertainty Sets
<|reference_start|>Non-Convex Robust Hypothesis Testing using Sinkhorn Uncertainty Sets: 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.<|reference_end|>
@article{wang2024non-convex,
    title={Non-Convex Robust Hypothesis Testing using Sinkhorn Uncertainty Sets},
    author={Jie Wang and Rui Gao and Yao Xie},
    journal={arXiv preprint arXiv:2403.14822},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.14822},
    primaryClass={stat.ML cs.LG math.OC}
}