Why is Posterior Sampling Better than Optimism for Reinforcement Learning? (1607.00215v3)

Abstract: Computational results demonstrate that posterior sampling for reinforcement learning (PSRL) dramatically outperforms algorithms driven by optimism, such as UCRL2. We provide insight into the extent of this performance boost and the phenomenon that drives it. We leverage this insight to establish an $\tilde{O}(H\sqrt{SAT})$ Bayesian expected regret bound for PSRL in finite-horizon episodic Markov decision processes, where $H$ is the horizon, $S$ is the number of states, $A$ is the number of actions and $T$ is the time elapsed. This improves upon the best previous bound of $\tilde{O}(H S \sqrt{AT})$ for any reinforcement learning algorithm.

Overview of Posterior Sampling vs Optimism in Reinforcement Learning

The paper "Why is Posterior Sampling Better than Optimism for Reinforcement Learning?" by Ian Osband and Benjamin Van Roy investigates the comparative performance of Posterior Sampling for Reinforcement Learning (PSRL) vis-à-vis optimism-driven approaches in the context of Reinforcement Learning (RL). The paper provides both theoretical insights and empirical evidence to substantiate the efficacy of PSRL, particularly in finite-horizon episodic Markov Decision Processes (MDPs).

Core Contributions and Results

1. Bayesian Regret Bounds: The paper propounds an improved Bayesian regret bound of $\tilde{O}(H\sqrt{SAT})$ for PSRL, which surpasses the best-known regret bound of $\tilde{O}(H S \sqrt{AT})$ achieved by any optimistic exploration algorithm. This result effectively reduces the dependency on the state-space size $S$.
2. Comparative Analysis: A significant claim of the paper is the constructive critique of optimistic algorithms, such as UCRL2, with respect to exploration strategies reliant on 'optimism in the face of uncertainty' (OFU). While OFU approaches rely on constructing confidence bounds over the possible MDPs, PSRL adopts a more efficient sampling-based strategy that inherently combines exploration and exploitation.
3. Computational Complexity: The paper posits that any optimistic algorithm matching the statistical efficiency of PSRL would be computationally prohibitive, primarily due to the inherent complexity in simultaneously maintaining tight confidence bounds over vast state-action spaces.
4. Empirical Validation: To complement the theoretical assertions, extensive empirical studies using synthetic MDP environments highlight PSRL's superiority in terms of convergence speed and regret minimization. The experimental results corroborate the theoretical regret bounds, portraying significant improvement over UCRL2 and similar algorithms.

Theoretical Implications

PSRL's enhanced regret bounds not only signify a step forward in reinforcement learning exploration strategies but also suggest potential revisions to theoretical frameworks for analyzing RL algorithms. The improved scaling from $S$ to $\sqrt{S}$ introduces a paradigm shift in how exploration is traditionally handled, implying that the incorporation of posterior sampling can mitigate inefficiencies seen in existing frameworks.

Practical Implications and Future Directions

From a practical standpoint, the findings advocate for broader adoption and implementation of PSRL in real-world applications where computational resources and statistical efficiency are critical. The paper implicitly sets a new benchmark for exploration algorithms, promoting further research to refine the balance of exploration-exploitation trade-offs.

Future research might explore several avenues, including:

• Extending PSRL's application to continuous state and action spaces.
• Investigating hybrid models that combine the strengths of optimism and posterior sampling.
• The potential integration of function approximation techniques to handle larger state spaces in a scalable manner.

Conclusion

This paper elucidates the efficacy of PSRL over optimism-based algorithms through meticulous theoretical analysis and robust empirical validation. By demonstrating a marked improvement in Bayesian regret bounds, the paper challenges existing conventions in RL exploration strategies, laying the groundwork for future innovations in both theoretical and applied machine learning landscapes. The authors’ insights into the computational and statistical trade-offs highlight the nuanced complexities inherent in designing efficient RL algorithms, encouraging continued exploration in this vibrant field.