Ranked Reward: Enabling Self-Play Reinforcement Learning for Combinatorial Optimization

TL;DR

This paper introduces the Ranked Reward (R2) algorithm, enabling self-play reinforcement learning for single-player combinatorial optimization problems by ranking rewards over multiple games, leading to improved performance over traditional methods.

Contribution

The paper proposes the R2 algorithm that adapts self-play reinforcement learning to single-player problems through reward ranking, a novel approach in this domain.

Findings

R2 outperforms Monte Carlo tree search, heuristics, and integer programming in bin packing.

Reward ranking improves learning efficiency and solution quality.

Analysis shows effectiveness varies with problem difficulty and ranking thresholds.

Abstract

Adversarial self-play in two-player games has delivered impressive results when used with reinforcement learning algorithms that combine deep neural networks and tree search. Algorithms like AlphaZero and Expert Iteration learn tabula-rasa, producing highly informative training data on the fly. However, the self-play training strategy is not directly applicable to single-player games. Recently, several practically important combinatorial optimisation problems, such as the travelling salesman problem and the bin packing problem, have been reformulated as reinforcement learning problems, increasing the importance of enabling the benefits of self-play beyond two-player games. We present the Ranked Reward (R2) algorithm which accomplishes this by ranking the rewards obtained by a single agent over multiple games to create a relative performance metric. Results from applying the R2 algorithm to instances of a two-dimensional and three-dimensional bin packing problems show that it outperforms generic Monte Carlo tree search, heuristic algorithms and integer programming solvers. We also present an analysis of the ranked reward mechanism, in particular, the effects of problem instances with varying difficulty and different ranking thresholds.