Model-based reinforcement learning with value-targeted regression

Analysis

Why This Paper Matters

This paper addresses a fundamental question in reinforcement learning: how to efficiently balance exploration and exploitation when the environment's dynamics are unknown. Model-based RL has long been considered a promising approach due to its sample efficiency, but theoretical guarantees were often lacking or suboptimal. By introducing value-targeted regression, the authors provide a unified and rigorous framework that achieves near-optimal regret bounds, closing the gap between theory and practice.

The significance is twofold. First, it establishes that model-based methods can achieve minimax optimal regret in episodic settings, matching lower bounds for linear MDPs. Second, it introduces a general analysis technique based on eluder dimension, which has become a standard tool in RL theory. This work has inspired a wave of follow-up research on optimistic model-based algorithms and has practical implications for designing sample-efficient RL agents.

Technical Contributions

• Value-targeted regression: Instead of directly fitting the transition model to observed transitions, the algorithm regresses on value functions, which reduces the impact of model error on policy evaluation.
• Confidence set construction: Maintains a set of plausible models based on regression residuals, enabling optimistic exploration.
• Eluder dimension analysis: Provides a regret bound that depends on the eluder dimension of the model class, which generalizes linear and low-rank structures.
• Unified framework: The algorithm and analysis encompass several existing model-based RL methods, offering a common theoretical lens.

Results

The paper proves a regret bound of O~(d√(H^3T)) for finite-horizon episodic RL, where d is the eluder dimension, H is the horizon, and T is the number of episodes. For linear MDPs, this matches the information-theoretic lower bound up to logarithmic factors, demonstrating minimax optimality. The bound improves upon prior model-based RL results that had extra dependencies on the number of states or actions. The analysis also shows that the algorithm achieves sublinear regret for general function classes with finite eluder dimension.

Significance

This work has had a lasting impact on the RL theory community. It established that model-based RL can be as sample-efficient as the best model-free methods while offering better generalization in complex environments. The value-targeted regression technique has been adopted in various subsequent algorithms, and the eluder dimension has become a central complexity measure. Practically, the insights guide the design of exploration strategies in deep RL, where function approximation is essential. The paper bridges the gap between model-based and value-based approaches, paving the way for more robust and sample-efficient RL systems.