Temporal Difference Updating without a Learning Rate

In the field of reinforcement learning, temporal difference (TD) learning is perhaps the most popular way to estimate the future discounted reward of states. We derive an equation for TD learning from statistical principles. Specifically, we start with the variational principle and then bootstrap to produce an updating rule for discounted state value estimates. The resulting equation is similar to the standard equation for temporal difference learning with eligibility traces, so called TD(λ), however it lacks the parameter α that specifies the learning rate. In the place of this free parameter there is now an equation for the learning rate that is specific to each state transition. We experimentally test this new learning rule against TD(λ) and find that it offers superior performance in various settings. Finally, we combine our update equation with both Watkin’s Q(λ) and Sarsa(λ) and find that it again offers superior performance without a learning rate parameter.