PAC-Bayesian Reinforcement Learning Trains Generalizable Policies

We derive a novel PAC-Bayesian generalization bound for reinforcement learning that explicitly accounts for Markov dependencies in the data, through the chain's mixing time. This contributes to overcoming challenges in obtaining generalization guarantees for reinforcement learning, where the sequential nature of data breaks the independence assumptions underlying classical bounds. The new bound provides non-vacuous certificates for modern off-policy algorithms such as Soft Actor-Critic. We demonstrate the practical utility of the bound through PB-SAC, a novel algorithm that optimizes the bound during training to guide exploration. Experiments across several continuous control tasks show that the proposed approach provides meaningful confidence certificates while maintaining competitive performance.

Before artificial intelligence can be safely deployed in real-world applications, we need strict guarantees of generalization—ensuring the systems perform reliably in unseen situations. However, AI agents that learn through sequential trial and error collect highly correlated data, which breaks the standard statistical assumptions required for traditional performance certificates. To solve this, we developed a novel mathematical framework that explicitly accounts for the dependent, sequential nature of this data. We integrated this theory into a practical algorithm (PB-SAC) that actively evaluates and optimizes its own performance guarantee during the training process. By using our method, AI models that learn through sequential interaction with an environment can maintain competitive learning performance while generating trustworthy, real-time confidence certificates. This advancement helps bridge the gap between theoretical guarantees and practical application, paving the way for safer deployment in high-stakes domains such as healthcare, robotics, and autonomous systems.