Accelerating Cutting-Plane Algorithms via Reinforcement Learning Surrogates

Kyle Mana, Fernando Acero, Stephen Mak,Parisa Zehtabi,Michael Cashmore,Daniele Magazzeni,Manuela Veloso

AAAI 2024(2024)

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Discrete optimization belongs to the set of N P-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 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 N P-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.
SO: Combinatorial Optimization,ML: Reinforcement Learning,PRS: Mixed Discrete/Continuous Planning,PRS: Planning under Uncertainty,PRS: Scheduling under Uncertainty,SO: Algorithm Configuration,SO: Mixed Discrete/Continuous Search,SO: Sampling/Simulation-based Search
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