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.

Accelerating Cutting-Plane Algorithms via Reinforcement Learning Surrogates

JP Morgan Chase & Co.

reinforcement learning

decomposition

Kyle Mana

1

SHORT BIO

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