Generalization and Exploration via Randomized Value Functions (1402.0635v3)

Abstract: We propose randomized least-squares value iteration (RLSVI) -- a new reinforcement learning algorithm designed to explore and generalize efficiently via linearly parameterized value functions. We explain why versions of least-squares value iteration that use Boltzmann or epsilon-greedy exploration can be highly inefficient, and we present computational results that demonstrate dramatic efficiency gains enjoyed by RLSVI. Further, we establish an upper bound on the expected regret of RLSVI that demonstrates near-optimality in a tabula rasa learning context. More broadly, our results suggest that randomized value functions offer a promising approach to tackling a critical challenge in reinforcement learning: synthesizing efficient exploration and effective generalization.

Generalization and Exploration via Randomized Value Functions: An Expert Overview

The paper "Generalization and Exploration via Randomized Value Functions" introduces Randomized Least-Squares Value Iteration (RLSVI), a novel reinforcement learning algorithm that aims to address the dual challenges of efficient exploration and generalization in large state-action spaces. RLSVI sets itself apart from traditional methods by exploring through randomly sampling value functions rather than relying on action-dithering techniques such as $\epsilon$-greedy or Boltzmann exploration, which are often inefficient in large-scale reinforcement learning contexts.

Algorithmic Design and Theoretical Contributions

RLSVI extends the framework of least-squares value iteration (LSVI) by incorporating a Bayesian approach to sample plausible value functions. This randomized sampling facilitates exploration by encouraging the agent to consider statistically likely value functions that could reveal informative state-action pairs. The algorithm is grounded in the principles of Thompson sampling, a well-regarded method in online optimization tasks, thus bringing a principled strategy to the reinforcement learning domain.

A significant theoretical contribution of this paper is the derivation of an expected regret bound for RLSVI in tabular settings without generalization. Specifically, the paper establishes an upper bound of $\tilde{O}(\sqrt{H^3 S A T})$ on the expected cumulative regret, demonstrating near-optimal performance. This result is particularly noteworthy as it surpasses bounds for other known efficient algorithms in tabular environments, such as UCRL2, thus positioning RLSVI as robust and effective in a tabula rasa context.

Empirical Validation and Insights

The authors conduct extensive computational experiments to showcase the efficacy of RLSVI. By comparing the algorithm against LSVI combined with conventional exploration strategies, they highlight dramatic efficiency gains, especially in scenarios that inherently challenge traditional exploration techniques. In particular, RLSVI excels in environments requiring significant generalization, as demonstrated in experiments involving simple chain domains, Tetris gameplay, and a recommendation system, where it outperforms other strategies in terms of speed of learning and quality of the learned policies.

Implications and Future Developments

The implications of this research are profound for both reinforcement learning (RL) theory and practical applications. The randomized exploration approach of RLSVI offers insights into how value function sampling could enable more efficient learning in environments with complex state-action spaces. Theoretical advancements such as the one proposed here could pave the way for further exploration of randomized algorithms in RL, particularly those employing non-linear value function approximations like neural networks.

Looking ahead, several promising research directions emerge from this work. Extending RLSVI's theoretical guarantees to contexts involving function approximation other than linear, and incorporating more sophisticated models for continuous state-action spaces, could significantly broaden its applicability. Moreover, deploying RLSVI in real-world settings where data efficiency and rapid adaptation are crucial could further demonstrate its potential impact.

In conclusion, the paper makes a compelling case for randomized value functions in RL, offering a solid foundation for future exploration into this promising approach. As the field evolves towards more scalable and adaptable algorithms, contributions like RLSVI will be instrumental in bridging the gap between theoretical sophistication and practical utility.