SBEED: Convergent Reinforcement Learning with Nonlinear Function Approximation
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Proceedings of the 35th International Conference on Machine Learning, PMLR 80:11251134, 2018.
Abstract
When function approximation is used, solving the Bellman optimality equation with stability guarantees has remained a major open problem in reinforcement learning for decades. The fundamental difficulty is that the Bellman operator may become an expansion in general, resulting in oscillating and even divergent behavior of popular algorithms like Qlearning. In this paper, we revisit the Bellman equation, and reformulate it into a novel primaldual optimization problem using Nesterov’s smoothing technique and the LegendreFenchel transformation. We then develop a new algorithm, called Smoothed Bellman Error Embedding, to solve this optimization problem where any differentiable function class may be used. We provide what we believe to be the first convergence guarantee for general nonlinear function approximation, and analyze the algorithm’s sample complexity. Empirically, our algorithm compares favorably to stateoftheart baselines in several benchmark control problems.
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