Optimistic Policy Optimization with Bandit Feedback
This addresses the exploration problem in RL for settings with limited feedback, providing the first sub-linear regret guarantees for policy optimization with unknown transitions and bandit feedback.
The paper tackles policy optimization in reinforcement learning with unknown transitions and bandit feedback, achieving sub-linear regret bounds of $ ilde O(\sqrt{S^2 A H^4 K})$ for stochastic rewards and $ ilde O( \sqrt{ S^2 A H^4 } K^{2/3} )$ for adversarial rewards.
Policy optimization methods are one of the most widely used classes of Reinforcement Learning (RL) algorithms. Yet, so far, such methods have been mostly analyzed from an optimization perspective, without addressing the problem of exploration, or by making strong assumptions on the interaction with the environment. In this paper we consider model-based RL in the tabular finite-horizon MDP setting with unknown transitions and bandit feedback. For this setting, we propose an optimistic trust region policy optimization (TRPO) algorithm for which we establish $\tilde O(\sqrt{S^2 A H^4 K})$ regret for stochastic rewards. Furthermore, we prove $\tilde O( \sqrt{ S^2 A H^4 } K^{2/3} ) $ regret for adversarial rewards. Interestingly, this result matches previous bounds derived for the bandit feedback case, yet with known transitions. To the best of our knowledge, the two results are the first sub-linear regret bounds obtained for policy optimization algorithms with unknown transitions and bandit feedback.