Performance Analysis of Online Anticipatory Algorithms for Large Multistage Stochastic Integer Programs

Abstract

Despite significant algorithmic advances in recent years, finding optimal policies for large-scale, multistage stochastic combinatorial optimization problems remains far beyond the reach of existing methods. This paper studies a complementary approach, online anticipatory algorithms, that make decisions at each step by solving the anticipatory relaxation for a polynomial number of scenarios. Online anticipatory algorithms have exhibited surprisingly good results on a variety of applications and this paper aims at understanding their success. In particular, the paper derives sufficient conditions under which online anticipatory algorithms achieve good expected utility and studies the various types of errors arising in the algorithms including the anticipativity and sampling errors. The sampling error is shown to be negligible with a logarithmic number of scenarios. The anticipativity error is harder to bound and is shown to be low, both theoretically and experimentally, for the existing applications.