Towards Accelerating Benders Decomposition via Reinforcement Learning Surrogate Models

Abstract

Stochastic optimization (SO) attempts to offer optimal decisions in the presence of uncertainty. Often, the classical formulation of these problems becomes intractable due to (a) the number of scenarios required to capture the uncertainty and (b) the discrete nature of real-world planning problems. To overcome these tractability issues, practitioners turn to decomposition methods that divide the problem into smaller, more tractable sub-problems. The focal decomposition method of this paper is Benders decomposition (BD), which decomposes stochastic optimization problems on the basis of scenario independence. In this paper we propose a method of accelerating BD with the aid of a surrogate model in place of an $\mathcal{NP}$-hard integer master problem. Through the acceleration method we observe $30\%$ faster average convergence when compared to other accelerated BD implementations. We introduce a reinforcement learning agent as a surrogate and demonstrate how it can be used to solve a stochastic inventory management problem.