Promoting Generalization for Exact Solvers via Adversarial Instance Augmentation

TL;DR

This paper introduces AdaSolver, a novel adversarial instance augmentation framework that enhances the generalization of learning-based MILP solvers by generating diverse, perturbed instances through a learned augmentation policy trained via a contextual bandit approach.

Contribution

AdaSolver is the first general framework that improves the generalization of both IL-based and RL-based B&B solvers using adversarially learned instance augmentation without prior problem type knowledge.

Findings

Significant efficiency improvements on various MILP distributions.

Effective regularization of solvers through diverse, augmented instances.

First framework to adversarially train augmentation policies for MILP solvers.

Abstract

Machine learning has been successfully applied to improve the efficiency of Mixed-Integer Linear Programming (MILP) solvers. However, the learning-based solvers often suffer from severe performance degradation on unseen MILP instances -- especially on large-scale instances from a perturbed environment -- due to the limited diversity of training distributions. To tackle this problem, we propose a novel approach, which is called Adversarial Instance Augmentation and does not require to know the problem type for new instance generation, to promote data diversity for learning-based branching modules in the branch-and-bound (B&B) Solvers (AdaSolver). We use the bipartite graph representations for MILP instances and obtain various perturbed instances to regularize the solver by augmenting the graph structures with a learned augmentation policy. The major technical contribution of AdaSolver is that we formulate the non-differentiable instance augmentation as a contextual bandit problem and adversarially train the learning-based solver and augmentation policy, enabling efficient gradient-based training of the augmentation policy. To the best of our knowledge, AdaSolver is the first general and effective framework for understanding and improving the generalization of both imitation-learning-based (IL-based) and reinforcement-learning-based (RL-based) B&B solvers. Extensive experiments demonstrate that by producing various augmented instances, AdaSolver leads to a remarkable efficiency improvement across various distributions.