Recent studies in reinforcement learning (RL) have made significant progress by leveraging function approximation to alleviate the sample complexity hurdle for better performance. Despite the success, existing provably efficient algorithms typically rely on the accessibility of immediate feedback upon taking actions. The failure to account for the impact of delay in observations can significantly degrade the performance of real-world systems due to the regret blow-up. In this work, we tackle the challenge of delayed feedback in RL with linear function approximation by employing posterior sampling, which has been shown to empirically outperform the popular UCB algorithms in a wide range of regimes. We first introduce Delayed-PSVI, an optimistic value-based algorithm that effectively explores the value function space via noise perturbation with posterior sampling.

While agents' learning is data-driven, sampling from millions

As one of the most mainstream paradigms for sequential decision-making, RL has extensive applications in many real-world problems (Kober et al., 2013; Mnih et al.,

TRPO, PPO), and a critic that involves minimizing a closely connected objective.

Our contributions are summarized as follows.

Reinforcement learning (RL) is a sequential decision-making problem in which an agent tries to maximize its expected cumulative reward by interacting with an unknown environment over time.

As a prominent category of imitation learning methods, adversarial imitation learning (AIL) has garnered significant practical success powered by neural network approximation. However, existing theoretical studies on AIL are primarily limited to simplified scenarios such as tabular and linear function approximation and involve complex algorithmic designs that hinder practical implementation, highlighting a gap between theory and practice.

These authors contributed equally to this work.

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