A Bayesian Sampling Approach to Exploration in Reinforcement Learning

Abstract: We present a modular approach to reinforcement learning that uses a Bayesian representation of the uncertainty over models. The approach, BOSS (Best of Sampled Set), drives exploration by sampling multiple models from the posterior and selecting actions optimistically. It extends previous work by providing a rule for deciding when to resample and how to combine the models. We show that our algorithm achieves nearoptimal reward with high probability with a sample complexity that is low relative to the speed at which the posterior distribution converges during learning. We demonstrate that BOSS performs quite favorably compared to state-of-the-art reinforcement-learning approaches and illustrate its flexibility by pairing it with a non-parametric model that generalizes across states.

• The paper’s main contribution is introducing the BOSS algorithm, which leverages Bayesian sampling to manage the exploration-exploitation trade-off in RL.
• It employs a modular approach that samples K models based on state-action count thresholds, reducing computational complexity while aiming for near-optimal performance.
• Experimental results on Chain and Marble Maze problems demonstrate BOSS’s rapid learning and its ability to dynamically cluster states for improved policy convergence.

A Bayesian Sampling Approach to Exploration in Reinforcement Learning

The paper "A Bayesian Sampling Approach to Exploration in Reinforcement Learning" by Asmuth et al. presents an innovative approach to addressing the perennial exploration-exploitation trade-off in reinforcement learning (RL). The authors introduce the BOSS (Best of Sampled Set) algorithm, a modular Bayesian reinforcement learning method that leverages model sampling from Bayesian posteriors to optimize exploration. This work builds upon previous RL methodologies by delineating a clear framework for model resampling and integration, setting it apart as a promising alternative to other established algorithms.

The paper identifies three prevalent categories of exploration strategies in RL: belief-lookahead, myopic, and undirected. Belief-lookahead strategies, though theoretically optimal, suffer from computational intractability. Myopic strategies, while simpler, do not account for long-term consequences of reduced uncertainty. Undirected strategies, like e-greedy and Boltzmann, merely ensure convergence to optimal behaviors asymptotically. BOSS is characterized as a myopic Bayesian approach, effectively negotiating a balance by sampling model posteriors and simulating exploratory actions based on an optimistic view of their outcomes.

A significant contribution of the BOSS algorithm is its sampling methodology. It samples K models from the Bayesian posterior based on a preset transition count threshold B for each state-action pair. Upon reaching this threshold, models are merged into a composite MDP, and decisions are made optimistically using this mixed model. This framework significantly reduces the computational burden relative to other Bayesian approaches while ensuring near-optimal performance with a probability that is inversely proportional to the sampling parameters.

The analytical foundation of BOSS is deeply rooted in sample complexity analysis and PAC-MDP frameworks. The authors demonstrate that the choice of parameters, such as K and B, is crucial to achieving an e-close optimal value function, except for a polynomial number of steps. Lemma 3.1 illustrates that a sampled set will likely contain an optimistic model, given a sufficiently large K. Subsequent lemmas and theorem strengthen the claim that BOSS maintains this optimism and concentration within a constrained sample complexity, thereby validating its prospects in practical applications.

The empirical evaluation of BOSS utilizes environments like the Chain and Marble Maze problems. The experimental results underscore BOSS's superior or competitive performance against prominent algorithms like BEETLE and Bayesian DP, especially in scenarios where clustering of state dynamics can be leveraged. Importantly, the introduction of a non-parametric model capable of automatically discovering cluster structures within the state space showcases the flexibility and robustness of BOSS.

BOSS's capacity to dynamically cluster states without predefined knowledge is particularly insightful, demonstrated by its adaptation in the Chain2 problem. This implicit clustering extends the practical applicability of BOSS in environments where direct modeling of dependencies is intractable. Moreover, simulations in a grid-based Marble Maze elucidate the quick convergence to optimal policies, underscoring the algorithm's rapid learning capability, attributable to its Bayesian inference mechanics.

In conclusion, BOSS's integration of Bayesian modeling and optimistic exploration presents a powerful tool for RL, offering a computationally feasible pathway to near-optimal solutions. The theoretical groundwork laid by Asmuth et al. promises potential extensions, such as hierarchical models and improved Bayesian priors. Notably, future research directions could involve enhancing feature-based state decomposition to further optimize exploratory efficiency within complex RL environments. Such advancements stand to significantly refine the interaction of Bayesian learning paradigms with RL's exploration strategies, fostering improved adaptability and generalization across diverse domains.