Offline-to-online hyperparameter transfer for stochastic bandits (2501.02926v1)

Abstract: Classic algorithms for stochastic bandits typically use hyperparameters that govern their critical properties such as the trade-off between exploration and exploitation. Tuning these hyperparameters is a problem of great practical significance. However, this is a challenging problem and in certain cases is information theoretically impossible. To address this challenge, we consider a practically relevant transfer learning setting where one has access to offline data collected from several bandit problems (tasks) coming from an unknown distribution over the tasks. Our aim is to use this offline data to set the hyperparameters for a new task drawn from the unknown distribution. We provide bounds on the inter-task (number of tasks) and intra-task (number of arm pulls for each task) sample complexity for learning near-optimal hyperparameters on unseen tasks drawn from the distribution. Our results apply to several classic algorithms, including tuning the exploration parameters in UCB and LinUCB and the noise parameter in GP-UCB. Our experiments indicate the significance and effectiveness of the transfer of hyperparameters from offline problems in online learning with stochastic bandit feedback.

• The paper presents a transfer learning framework that uses offline data to guide hyperparameter optimization in stochastic bandits.
• It establishes sample complexity bounds for inter- and intra-task learning, informing efficient tuning for algorithms such as UCB, LinUCB, and GP-UCB.
• Experimental validations demonstrate that leveraging historical data enhances the balance between exploration and exploitation in online settings.

Overview of Offline-to-Online Hyperparameter Transfer for Stochastic Bandits

The paper presents a novel approach for hyperparameter optimization in the context of stochastic bandits, where the aim is to enhance algorithm performance by adapting hyperparameters using offline data derived from various tasks. It explores the intricate problem of selecting hyperparameters that strike a balance between exploration and exploitation — a challenge compounded by the inherent complexity of bandit problems. The approach leverages a transfer learning framework, moving from offline to online settings, to provide robust solutions to multi-armed bandit (MAB) challenges.

Summary of Key Contributions

1. Theoretical Foundations and Impossibility Results: The paper begins by establishing the theoretical underpinnings that denote the difficulty of hyperparameter tuning in bandit algorithms. A significant finding is that achieving near-optimal hyperparameter selection is information-theoretically impossible without exploring multiple task-related samples. This sets the stage for utilizing historical data to make better-informed hyperparameter choices.
2. Framework for Hyperparameter Transfer: The authors introduce a structured framework that enables the extrapolation of hyperparameter settings from offline to online tasks. This framework quantifies task similarity through a distribution from which tasks are sampled, facilitating a deeper understanding of how past experiences can guide future decision-making processes.
3. Sample Complexity Bounds: A notable contribution is the derivation of sample complexity bounds, both inter-task and intra-task, that are necessary for learning hyperparameters efficiently. These bounds provide crucial insights into the volume of historical data required to feasibly transfer learned settings to new, unseen tasks while maintaining optimal performance in the online environment.
4. Application to Algorithms: The methodological advances proposed apply to well-known bandit algorithms like UCB, LinUCB, and GP-UCB. For these algorithms, the paper presents specific results on tuning exploration and noise parameters, respectively, demonstrating the framework's versatility across different algorithmic paradigms.
5. Experimental Validation: Empirical results underscore the framework's effectiveness, showcasing improvements in algorithm performance through enhanced hyperparameter transfer. The experiments validate theoretical claims, providing concrete evidence of the utility of offline data in online optimization.

Implications and Future Work

The implications of this research extend to any domain that relies on bandit algorithms, such as recommendation systems, computational advertising, or adaptive clinical trials. By demonstrating a method to leverage offline data, it paves the way for more efficient deployment of bandit-based decision systems, especially when faced with budgetary or temporal constraints on exploration.

The paper's focus on sample complexity offers a strategic insight into managing computational resources, further reinforcing its practical relevance. However, the reliance on the assumptions about the distribution of tasks presents an area for further refinement. Future developments could explore how shifts in this underlying distribution affect hyperparameter transfer and how adaptive methods might mitigate these challenges.

Further exploration could also involve extending the framework to environments with dynamically changing tasks, or integrating more advanced statistical techniques to better predict hyperparameter impacts without heavy reliance on past data.

In conclusion, the contributions of this paper lay an essential foundation for elevating the role of hyperparameter optimization in bandit problems, actively shaping how these algorithms can be fine-tuned to maximize real-world applicability and efficiency. The presented framework stands as both a benchmark for current methodologies and a promising direction for ongoing research in algorithmic adaptation and learning.