Adaptive Trust Region Policy Optimization: Global Convergence and Faster Rates for Regularized MDPs
This provides theoretical justification for TRPO and faster convergence in regularized RL, which is foundational for RL algorithms.
The paper shows that Trust Region Policy Optimization (TRPO) is a trust-region method in RL and proves global convergence with a rate of $ ilde O(1/\sqrt{N})$ for sample-based TRPO, achieving faster rates of $ ilde O(1/N)$ for regularized MDPs.
Trust region policy optimization (TRPO) is a popular and empirically successful policy search algorithm in Reinforcement Learning (RL) in which a surrogate problem, that restricts consecutive policies to be 'close' to one another, is iteratively solved. Nevertheless, TRPO has been considered a heuristic algorithm inspired by Conservative Policy Iteration (CPI). We show that the adaptive scaling mechanism used in TRPO is in fact the natural "RL version" of traditional trust-region methods from convex analysis. We first analyze TRPO in the planning setting, in which we have access to the model and the entire state space. Then, we consider sample-based TRPO and establish $\tilde O(1/\sqrt{N})$ convergence rate to the global optimum. Importantly, the adaptive scaling mechanism allows us to analyze TRPO in regularized MDPs for which we prove fast rates of $\tilde O(1/N)$, much like results in convex optimization. This is the first result in RL of better rates when regularizing the instantaneous cost or reward.