A key problem in off-policy Reinforcement Learning (RL) is the mismatch, or distribution shift, between the dataset and the distribution over states and actions visited by the learned policy. This problem is exacerbated in the fully offline setting. The main approach to correct this shift has been through importance sampling, which leads to high-variance gradients. Other approaches, such as conservatism or behavior-regularization, regularize the policy at the cost of performance. In this paper, we propose a new approach for stable off-policy Q-Learning. Our method, Projected Off-Policy Q-Learning (POP-QL), is a novel actor-critic algorithm that simultaneously reweights off-policy samples and constrains the policy to prevent divergence and reduce value-approximation error. In our experiments, POP-QL not only shows competitive performance on standard benchmarks, but also out-performs competing methods in tasks where the data-collection policy is significantly sub-optimal.
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