Reinforcement Learning with Segment Feedback

TL;DR

This paper introduces a new RL model called RL with segment feedback, analyzing how different feedback types and segment counts affect learning efficiency through theoretical bounds and experiments.

Contribution

It proposes the RL with segment feedback model, providing algorithms and regret bounds for binary and sum feedback settings, highlighting the impact of segment number on learning performance.

Findings

Increasing segments reduces regret exponentially under binary feedback.

Segment count has little effect on regret under sum feedback.

Theoretical and experimental validation of the model's behavior.

Abstract

Standard reinforcement learning (RL) assumes that an agent can observe a reward for each state-action pair. However, in practical applications, it is often difficult and costly to collect a reward for each state-action pair. While there have been several works considering RL with trajectory feedback, it is unclear if trajectory feedback is inefficient for learning when trajectories are long. In this work, we consider a model named RL with segment feedback, which offers a general paradigm filling the gap between per-state-action feedback and trajectory feedback. In this model, we consider an episodic Markov decision process (MDP), where each episode is divided into $m$ segments, and the agent observes reward feedback only at the end of each segment. Under this model, we study two popular feedback settings: binary feedback and sum feedback, where the agent observes a binary outcome and a reward sum according to the underlying reward function, respectively. To investigate the impact of the number of segments $m$ on learning performance, we design efficient algorithms and establish regret upper and lower bounds for both feedback settings. Our theoretical and experimental results show that: under binary feedback, increasing the number of segments $m$ decreases the regret at an exponential rate; in contrast, surprisingly, under sum feedback, increasing $m$ does not reduce the regret significantly.