Prophet Inequality for Bipartite Matching: Merits of Being Simple and Nonadaptive

We consider the Bayesian online selection problem of a matching in bipartite graphs, that is, weighted where edges arrive and edge weights are generated from known distribution. This setting corresponds to intersection two matroids work Kleinberg Weinberg [ 40 ] Feldman et al. 27 ]. study simple class nonadaptive policies we call vertex-additive policies. A policy assigns static prices every vertex graph accepts only those whose weight exceeds sum on endpoints. show there exists with expected payoff at least one-third prophet’s present gradient descent algorithm quickly converges desired vector prices. Our results improve adaptive for ways: our is has better approximation guarantee 3 instead previous guarantees 5.82 5.43 give complementary lower bound 2.25 any setting. Funding: was supported by Fundamental Research Funds Central Universities China, Science Technology Innovation 2030 major project [“New Generation Artificial Intelligence,” Project 2018AAA0100903], Shanghai Municipal Education Commission Program, Program Innovative Team University Finance Economics (IRTSHUFE).