Accelerating Cutting-Plane Algorithms via Reinforcement Learning Surrogates

TL;DR

This paper introduces a reinforcement learning-based approach to accelerate cutting-plane algorithms for discrete optimization, improving convergence speed while maintaining optimality guarantees in complex problems.

Contribution

It proposes a novel reinforcement learning surrogate method that speeds up cutting-plane algorithms for NP-hard problems without sacrificing optimality.

Findings

Achieves up to 45% faster convergence in stochastic optimization.

Effectively accelerates mixed-integer quadratic programming.

Maintains theoretical guarantees of optimality.

Abstract

Discrete optimization belongs to the set of $\mathcal{NP}$-hard problems, spanning fields such as mixed-integer programming and combinatorial optimization. A current standard approach to solving convex discrete optimization problems is the use of cutting-plane algorithms, which reach optimal solutions by iteratively adding inequalities known as \textit{cuts} to refine a feasible set. Despite the existence of a number of general-purpose cut-generating algorithms, large-scale discrete optimization problems continue to suffer from intractability. In this work, we propose a method for accelerating cutting-plane algorithms via reinforcement learning. Our approach uses learned policies as surrogates for $\mathcal{NP}$-hard elements of the cut generating procedure in a way that (i) accelerates convergence, and (ii) retains guarantees of optimality. We apply our method on two types of problems where cutting-plane algorithms are commonly used: stochastic optimization, and mixed-integer quadratic programming. We observe the benefits of our method when applied to Benders decomposition (stochastic optimization) and iterative loss approximation (quadratic programming), achieving up to $45\%$ faster average convergence when compared to modern alternative algorithms.