Accelerating Cutting-Plane Algorithms via Reinforcement Learning Surrogates

TL;DR

The paper addresses the computational bottleneck of cutting-plane methods for discrete NP-hard optimization by introducing reinforcement-learning surrogates that replace expensive master problem solves with learned policies. The Surrogate-MP framework is applied to two settings—Benders decomposition for stochastic inventory planning and L0-regularized regression—with three selection strategies (Greedy, Weighted, Informed) to integrate surrogate solutions. Empirical results show substantial reductions in convergence time, up to about 45% in the tested domains, while still producing certificates of optimality since the true MIP/MIP feasibility checks are preserved. The work demonstrates a general, domain-agnostic approach to speeding CP algorithms and highlights future directions for deeper integration between surrogates, sub-gradient information, and MP/SP dynamics, with potential applicability across CP-based solvers and optimization tasks.

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.

Figures (5)

• Figure 1: Iterative procedure of Benders decomposition, alternating between a MIMP \ref{['eq: BDMast']} and SP \ref{['eq: BDdual']}.
• Figure 2: Iterative procedure of Surrogate-MP.
• Figure 3: Convergence instances of BD accelerated by an informed Surrogate-MP, with different surrogate usages.
• Figure 4: Convergence rates of a baseline BD, and Surrogate-MP with three selection methods (greedy, weighted, informed). Results generated with $\Gamma=0.75$.
• Figure 5: Convergence rates of BD accelerated by an informed Surrogate-MP with different surrogate usages. Surrogate-MP deactivated at $5\%$ as indicated by dotted line.