Gradient Descent Temporal Difference-difference Learning

Off-policy algorithms, in which a behavior policy differs from the target policy and is used to gain experience for learning, have proven to be of great practical value in reinforcement learning. However, even for simple convex problems such as linear value function approximation, these algorithms are not guaranteed to be stable. To address this, alternative algorithms that are provably convergent in such cases have been introduced, the most well known being gradient descent temporal difference (GTD) learning. This algorithm and others like it, however, tend to converge much more slowly than conventional temporal difference learning. In this paper we propose gradient descent temporal difference-difference (Gradient-DD) learning in order to improve GTD2, a GTD algorithm, by introducing second-order differences in successive parameter updates. We investigate this algorithm in the framework of linear value function approximation, theoretically proving its convergence by applying the theory of stochastic approximation. %analytically showing its improvement over GTD2. Studying the model empirically on the random walk task, the Boyan-chain task, and the Baird's off-policy counterexample, we find substantial improvement over GTD2 and, in several cases, better performance even than conventional TD learning.