We propose the k-Shortest-Path (k-SP) constraint: a novel constraint on the agents trajectory that improves the sample efficiency in sparse-reward MDPs. We show that any optimal policy necessarily satisfies the k-SP constraint. Notably, the k-SP constraint prevents the policy from exploring state-action pairs along the non-k-SP trajectories (e.g., going back and forth). However, in practice, excluding state-action pairs may hinder the convergence of RL algorithms. To overcome this, we propose a novel cost function that penalizes the policy violating SP constraint, instead of completely excluding it. Our numerical experiment in a tabular RL setting demonstrates that the SP constraint can significantly reduce the trajectory space of policy. As a result, our constraint enables more sample efficient learning by suppressing redundant exploration and exploitation. Our experiments on MiniGrid, DeepMind Lab, Atari, and Fetch show that the proposed method significantly improves proximal policy optimization (PPO) and outperforms existing novelty-seeking exploration methods including count-based exploration even in continuous control tasks, indicating that it improves the sample efficiency by preventing the agent from taking redundant actions.
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