Marcus Hutter, Shane Legg
We derive an equation for temporal difference 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 eligibil- ity 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 make some preliminary investigations into how to extend our new temporal difference algorithm to reinforcement learning. To do this we combine our update equation with both Watkins’ Q(λ) and Sarsa(λ) and ﬁnd that it again offers superior performance without a learning rate parameter.