In this work, we address the problem of learning optimal behavior from sub-optimal datasets in the context of goal-conditioned offline reinforcement learning. To do so, we propose a novel way of approximating the optimal value function for goal-conditioned offline RL problems under sparse rewards, symmetric and deterministic actions. We study a property for representations to recover optimality and propose a new optimization objective that leads to such property. We use the learned value function to guide the learning of a policy in an actor-critic fashion, a method we name MetricRL. Experimentally, we show how our method consistently outperforms other offline RL baselines in learning from sub-optimal offline datasets. Moreover, we show the effectiveness of our method in dealing with high-dimensional observations and in multi-goal tasks.
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