(More) Efficient Reinforcement Learning via Posterior Sampling
(1306.0940v5)
Published 4 Jun 2013 in stat.ML and cs.LG
Abstract: Most provably-efficient learning algorithms introduce optimism about poorly-understood states and actions to encourage exploration. We study an alternative approach for efficient exploration, posterior sampling for reinforcement learning (PSRL). This algorithm proceeds in repeated episodes of known duration. At the start of each episode, PSRL updates a prior distribution over Markov decision processes and takes one sample from this posterior. PSRL then follows the policy that is optimal for this sample during the episode. The algorithm is conceptually simple, computationally efficient and allows an agent to encode prior knowledge in a natural way. We establish an $\tilde{O}(\tau S \sqrt{AT})$ bound on the expected regret, where $T$ is time, $\tau$ is the episode length and $S$ and $A$ are the cardinalities of the state and action spaces. This bound is one of the first for an algorithm not based on optimism, and close to the state of the art for any reinforcement learning algorithm. We show through simulation that PSRL significantly outperforms existing algorithms with similar regret bounds.
Efficient Reinforcement Learning via Posterior Sampling: A Detailed Analysis
In the field of reinforcement learning (RL), the tradeoff between exploration and exploitation remains a central challenge. This paper addresses this challenge by investigating posterior sampling for reinforcement learning (PSRL) as a method to achieve efficient exploration. In contrast to the more conventional approach of employing optimism in the face of uncertainty (OFU), PSRL offers a principled alternative by emphasizing the use of prior distributions over Markov Decision Processes (MDPs) to guide policy selection.
Key Contributions and Methodology
The authors propose a robust reinforcement learning algorithm, PSRL, which operates in episodic settings with repeated interactions modeled as MDPs. The algorithm updates the agent's beliefs by sampling from a posterior distribution over MDPs at the beginning of each episode. The agent then executes the policy that is optimal for this sampled instance throughout the episode. This probabilistic method inherently balances exploration and exploitation by selecting policies in proportion to their likelihood of being optimal, which contrasts with the deterministic optimism-based approaches. Importantly, they establish a regret bound of O~(τSAT), which aligns closely with state-of-the-art bounds for reinforcement learning algorithms.
Numerical Results and Theoretical Implications
The performance of PSRL is demonstrated through simulations, indicating superior efficacy compared to traditional algorithms like UCRL2 in terms of regret minimization. The empirical setup, including environments such as RiverSwim, highlights that PSRL consistently outperforms optimistic methods, which rely on conservative confidence bounds and can incur higher computational costs.
The theoretical implications of this work are significant. It provides one of the first regret bounds for a reinforcement learning algorithm not predicated on optimism, further strengthening the case for PSRL. The potential for incorporation of prior knowledge makes PSRL particularly valuable in practical applications, facilitating a more nuanced exploration strategy than conventional model-free RL methods.
Speculation on Future Developments
This paper sets the stage for future advancements in AI by suggesting a shift from optimism-driven algorithms to those that leverage Bayesian methods. Future research could delve into refining the posterior distributions or exploring PSRL's applicability in non-episodic contexts or continuous state-action spaces. Additionally, integrating PSRL with function approximation techniques could open new avenues for handling large-scale problems efficiently.
The integration of these probabilistic methods into existing RL frameworks may induce a paradigm shift, promoting agents that learn more efficiently in complex, uncertain environments. As a promising alternative to traditional strategies, PSRL holds significant potential to advance both theoretical and applied aspects of reinforcement learning.
In conclusion, the adoption of methods like PSRL may drive a new wave of innovative solutions in AI, unlocking capabilities for agents to learn from prior distributions more effectively and naturally within uncertain and dynamic environments.