A Sampling Framework for Value-Based Reinforcement Learning

Value-based algorithms have achieved great successes in solving Reinforcement Learning problems via minimizing the mean squared Bellman error (MSBE). Temporal-difference (TD) algorithms such as Q-learning and SARSA often use stochastic gradient descent based optimization approaches to estimate the value function parameters, but fail to quantify their uncertainties. In our work, under the Kalman filtering paradigm, we establish a novel and scalable sampling framework based on stochastic gradient Markov chain Monte Carlo, which allows us to efficiently generate samples from the posterior distribution of deep neural network parameters. For TD-learning with both linear and nonlinear function approximation, we prove that the proposed algorithm converges to a stationary distribution, which allows us to measure uncertainties of the value function and its parameters.