A Unified Framework for Regularized Reinforcement Learning
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We propose and study a general framework for regularized Markov decision processes (MDPs) where the goal is to find an optimal policy that maximizes the expected discounted total reward plus a policy regularization term. The extant entropy-regularized MDPs can be cast into our framework. Moreover, under our framework there are many regularization terms can bring multi-modality and sparsity which are potentially useful in reinforcement learning. In particular, we present sufficient and necessary conditions that induce a sparse optimal policy. We also conduct a full mathematical analysis of the proposed regularized MDPs, including the optimality condition, performance error and sparseness control. We provide a generic method to devise regularization forms and propose off-policy actor-critic algorithms in complex environment settings. We empirically analyze the statistical properties of optimal policies and compare the performance of different sparse regularization forms in discrete and continuous environments.
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