Review for NeurIPS paper: Fast Epigraphical Projection-based Incremental Algorithms for Wasserstein Distributionally Robust Support Vector Machine

Summary and Contributions: The authors have proposed two new algorithms to solve the timely and important distributionally robust SVM problem. These new algorithms are instances of incremental projected subgradient descent and incremental proximal point algorithm. The main novelty of ISG and IPPA proposed in this work is that they developed efficient algorithms (in linear time) for the subproblems in these solving strategies, which are interesting and potentially beneficial for other problems with similar structures. Besides, the authors carefully analyze the iteration complexity of their new algorithms under the so-called BLR condition. They show if the BLR condition is satisfied, the exponent in the Holderian growth condition could be explicitly determined.