Reviews: Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation

Overall, I found this paper to be a nice read. It lays out the motivation for the problem and then illustrates how one can apply the idea for various different notions of a "close distribution," e.g., KL-divergence, Wasserstein metric, and distributions that match the first and second empirical moments. One strange thing about this approach is that the optimistic probabilities found at the end may not integrate to 1 (for example, the kernel density estimator will integrate to 1). For this reason, it doesn't appear the optimistic likelihood is a likelihood in any traditional sense. Because of this property, I would like to understand better how this new sense of likelihood behaves.