Almost Sure Convergence of Differential Temporal Difference Learning for Average Reward Markov Decision Processes
This work strengthens the theoretical foundations of differential TD learning for average reward RL, making it more applicable to practical implementations, though it is incremental as it builds on prior methods.
The paper tackles the limitation of existing convergence guarantees for differential temporal difference learning in average reward reinforcement learning, which require impractical local clock learning rates, by proving almost sure convergence for on-policy and off-policy settings using standard diminishing learning rates without a local clock.
The average reward is a fundamental performance metric in reinforcement learning (RL) focusing on the long-run performance of an agent. Differential temporal difference (TD) learning algorithms are a major advance for average reward RL as they provide an efficient online method to learn the value functions associated with the average reward in both on-policy and off-policy settings. However, existing convergence guarantees require a local clock in learning rates tied to state visit counts, which practitioners do not use and does not extend beyond tabular settings. We address this limitation by proving the almost sure convergence of on-policy $n$-step differential TD for any $n$ using standard diminishing learning rates without a local clock. We then derive three sufficient conditions under which off-policy $n$-step differential TD also converges without a local clock. These results strengthen the theoretical foundations of differential TD and bring its convergence analysis closer to practical implementations.