SBEED: Convergent Reinforcement Learning with Nonlinear Function Approximation
This addresses a foundational stability issue in reinforcement learning for researchers and practitioners, offering a novel solution to a decades-old bottleneck.
The paper tackles the long-standing open problem of ensuring stable convergence in reinforcement learning with nonlinear function approximation by reformulating the Bellman equation into a primal-dual optimization problem, resulting in a new algorithm (SBEED) that provides the first convergence guarantee for general nonlinear function approximation and shows favorable empirical performance in benchmark control problems.
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 Q-learning. In this paper, we revisit the Bellman equation, and reformulate it into a novel primal-dual optimization problem using Nesterov's smoothing technique and the Legendre-Fenchel 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 state-of-the-art baselines in several benchmark control problems.