2023/03/17 by Anna Winnicki, Winnicki, Anna, R. Srikant +1 · 1 citation
Computer Science · #Artificial Intelligence (cs.AI) #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Reinforcement Learning in Robotics #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2303.09716
openalex publication_date 2023/03/17 · openalex created_date 2023/03/21 · openalex updated_date 2026/07/28
Optimal policies in standard MDPs can be obtained using either value iteration or policy iteration. However, in the case of zero-sum Markov games, there is no efficient policy iteration algorithm; e.g., it has been shown that one has to solve Omega(1/(1-alpha)) MDPs, where alpha is the discount factor, to implement the only known convergent version of policy iteration. Another algorithm, called naive policy iteration, is easy to implement but is only provably convergent under very restrictive assumptions. Prior attempts to fix naive policy iteration algorithm have several limitations. Here, we show that a simple variant of naive policy iteration for games converges exponentially fast. The only addition we propose to naive policy iteration is the use of lookahead policies, which are anyway used in practical algorithms. We further show that lookahead can be implemented efficiently in the function approximation setting of linear Markov games, which are the counterpart of the much-studied linear MDPs. We illustrate the application of our algorithm by providing bounds for policy-based RL (reinforcement learning) algorithms. We extend the results to the function approximation setting.