Empirical Q-Value Iteration

We propose a new simple and natural algorithm for learning the optimal Q-value function of a discounted-cost Markov Decision Process (MDP) when the transition kernels are unknown. Unlike the classical learning algorithms for MDPs, such as Q-learning and ‘actor-critic’ algorithms, this algorithm doesn’t depend on a stochastic approximation-based method. We show that our algorithm, which we call the empirical Q-value iteration (EQVI) algorithm, converges almost surely to the optimal Q-value function. To the best of our knowledge, this is the first algorithm for learning in MDPs that guarantees an almost sure convergence without using stochastic approximations. We also give a rate of convergence or a non-aymptotic sample complexity bound, and also show that an asynchronous (or online) version of the algorithm will also work. Preliminary experimental results suggest a faster rate of convergence to a ball park estimate for our algorithm compared to stochastic approximation-based algorithms. In fact, the asynchronous setting EQVI vastly outperforms the popular and widely-used Q-learning algorithm.