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In this paper, we introduce proximal gradient temporal difference learning,which provides a principled way of designing and analyzing true stochasticgradient temporal difference learning algorithms. We show how gradient TD (GTD)reinforcement learning methods can be formally derived, not by starting fromtheir original objective functions, as previously attempted, but rather from aprimal-dual saddle-point objective function. We also conduct a saddle-pointerror analysis to obtain finite-sample bounds on their performance. Previousanalyses of this class of algorithms use stochastic approximation techniques toprove asymptotic convergence, and do not provide any finite-sample analysis. Wealso propose an accelerated algorithm, called GTD2-MP, that uses proximal``mirror maps'' to yield an improved convergence rate. The results of ourtheoretical analysis imply that the GTD family of algorithms are comparable andmay indeed be preferred over existing least squares TD methods for off-policylearning, due to their linear complexity. We provide experimental resultsshowing the improved performance of our accelerated gradient TD methods.

Proximal Gradient Temporal Difference Learning: Stable Reinforcement Learning with Polynomial Sample Complexity