Learning with Local Search MCMC Layers
This addresses the problem of learning with inexact combinatorial solvers for researchers and practitioners in operations research and machine learning, offering a novel method but with incremental improvements over existing hybrid approaches.
The paper tackles the challenge of integrating combinatorial optimization layers into neural networks by proposing a theoretically-principled approach using MCMC to transform local search heuristics into differentiable layers, reducing computational burden and demonstrating it on a large-scale dynamic vehicle routing problem with time windows.
Integrating combinatorial optimization layers into neural networks has recently attracted significant research interest. However, many existing approaches lack theoretical guarantees or fail to perform adequately when relying on inexact solvers. This is a critical limitation, as many operations research problems are NP-hard, often necessitating the use of neighborhood-based local search heuristics. These heuristics iteratively generate and evaluate candidate solutions based on an acceptance rule. In this paper, we introduce a theoretically-principled approach for learning with such inexact combinatorial solvers. Inspired by the connection between simulated annealing and Metropolis-Hastings, we propose to transform problem-specific neighborhood systems used in local search heuristics into proposal distributions, implementing MCMC on the combinatorial space of feasible solutions. This allows us to construct differentiable combinatorial layers and associated loss functions. Replacing an exact solver by a local search strongly reduces the computational burden of learning on many applications. We demonstrate our approach on a large-scale dynamic vehicle routing problem with time windows.