Policy Mirror Descent with Lookahead

Policy Mirror Descent (PMD) stands as a versatile algorithmic framework encompassing several seminal policy gradient algorithms such as natural policy gradient, with connections with state-of-the-art reinforcement learning (RL) algorithms such as TRPO and PPO. PMD can be seen as a soft Policy Iteration algorithm implementing regularized 1-step greedy policy improvement. However, 1-step greedy policies might not be the best choice and recent remarkable empirical successes in RL such as AlphaGo and AlphaZero have demonstrated that greedy approaches with respect to multiple steps outperform their 1-step counterpart. In this work, we propose a new class of PMD algorithms called h -PMD which incorporates multi-step greedy policy improvement with lookahead depth h to the PMD update rule. To solve discounted infinite horizon Markov Decision Processes with discount factor \gamma, we show that h -PMD which generalizes the standard PMD enjoys a faster dimension-free \gamma h -linear convergence rate, contingent on the computation of multi-step greedy policies.