Black-Box Combinatorial Optimization with Order-Invariant Reinforcement Learning

Abstract

We introduce an order-invariant reinforcement learning framework for black-box combinatorial optimization. Classical estimation-of-distribution algorithms (EDAs) often rely on learning explicit variable dependency graphs, which can be costly and fail to capture complex interactions efficiently. In contrast, we parameterize a multivariate autoregressive generative model trained without a fixed variable ordering. By sampling random generation orders during training, a form of information-preserving dropout, the model is encouraged to be invariant to variable order, promoting search-space diversity, and shaping the model to focus on the most relevant variable dependencies, improving sample efficiency. We adapt Group Relative Policy Optimization (GRPO) to this setting, providing stable policy-gradient updates from scale-invariant advantages. Across a wide range of benchmark algorithms and problem instances of varying sizes, our method frequently achieves the best performance and consistently avoids catastrophic failures.