Exploratory Combinatorial Optimization with Reinforcement Learning

TL;DR

This paper introduces ECO-DQN, a reinforcement learning approach that enables continuous improvement of solutions in combinatorial optimization problems, demonstrating state-of-the-art results on the Maximum Cut problem.

Contribution

The paper proposes a novel RL method that allows exploration and solution refinement at test time, unlike previous incremental approaches.

Findings

Achieves state-of-the-art RL performance on Maximum Cut.

Can start from arbitrary configurations and improve solutions.

Combines with simple search methods for further gains.

Abstract

Many real-world problems can be reduced to combinatorial optimization on a graph, where the subset or ordering of vertices that maximize some objective function must be found. With such tasks often NP-hard and analytically intractable, reinforcement learning (RL) has shown promise as a framework with which efficient heuristic methods to tackle these problems can be learned. Previous works construct the solution subset incrementally, adding one element at a time, however, the irreversible nature of this approach prevents the agent from revising its earlier decisions, which may be necessary given the complexity of the optimization task. We instead propose that the agent should seek to continuously improve the solution by learning to explore at test time. Our approach of exploratory combinatorial optimization (ECO-DQN) is, in principle, applicable to any combinatorial problem that can be defined on a graph. Experimentally, we show our method to produce state-of-the-art RL performance on the Maximum Cut problem. Moreover, because ECO-DQN can start from any arbitrary configuration, it can be combined with other search methods to further improve performance, which we demonstrate using a simple random search.