Outcome-Based Online Reinforcement Learning: Algorithms and Fundamental Limits

TL;DR

This paper analyzes outcome-based online reinforcement learning with endpoint-only rewards, proposing a sample-efficient algorithm, characterizing fundamental limits, and extending to preference-based feedback, thus establishing a theoretical foundation for this setting.

Contribution

It introduces the first provably sample-efficient algorithm for outcome-based RL with general function approximation and characterizes the fundamental limits of outcome-based feedback.

Findings

Achieves $ ilde{O}(C_{cov} H^3 / \\epsilon^2)$ sample complexity.

Identifies exponential separation between outcome-based feedback and per-step rewards.

Extends results to preference-based feedback with similar efficiency.

Abstract

Reinforcement learning with outcome-based feedback faces a fundamental challenge: when rewards are only observed at trajectory endpoints, how do we assign credit to the right actions? This paper provides the first comprehensive analysis of this problem in online RL with general function approximation. We develop a provably sample-efficient algorithm achieving $\widetilde{O}({C_{\rm cov} H^3}/{\epsilon^2})$ sample complexity, where $C_{\rm cov}$ is the coverability coefficient of the underlying MDP. By leveraging general function approximation, our approach works effectively in large or infinite state spaces where tabular methods fail, requiring only that value functions and reward functions can be represented by appropriate function classes. Our results also characterize when outcome-based feedback is statistically separated from per-step rewards, revealing an unavoidable exponential separation for certain MDPs. For deterministic MDPs, we show how to eliminate the completeness assumption, dramatically simplifying the algorithm. We further extend our approach to preference-based feedback settings, proving that equivalent statistical efficiency can be achieved even under more limited information. Together, these results constitute a theoretical foundation for understanding the statistical properties of outcome-based reinforcement learning.