Stochastic optimization by message passing

Abstract

Most optimization problems in applied sciences realistically involve uncertainty in the parameters defining the cost function, of which only statistical information is known beforehand. In a recent work we introduced a message passing algorithm based on the cavity method of statistical physics to solve the two-stage matching problem with independently distributed stochastic parameters. In this paper we provide an in-depth explanation of the general method and caveats, show the details of the derivation and resulting algorithm for the matching problem and apply it to a stochastic version of the independent set problem, which is a computationally hard and relevant problem in communication networks. We compare the results with some greedy algorithms and briefly discuss the extension to more complicated stochastic multi-stage problems.