Design Experiments to Compare Multi-armed Bandit Algorithms
arXiv:2603.05919v1 Announce Type: new Abstract: Online platforms routinely compare multi-armed bandit algorithms, such as UCB and Thompson Sampling, to select the best-performing policy. Unlike standard A/B tests for static treatments, each run of a bandit algorithm over $T$ users produces only one dependent trajectory, because the algorithm's decisions depend on all past interactions. Reliable inference therefore demands many independent restarts of the algorithm, making experimentation costly and delaying deployment decisions. We propose Artificial Replay (AR) as a new experimental design for this problem. AR first runs one policy and records its trajectory. When the second policy is executed, it reuses a recorded reward whenever it selects an action the first policy already took, and queries the real environment only otherwise. We develop a new analytical framework for this design and prove three key properties of the resulting estimator: it is unbiased; it requires only $T + o(T)$
arXiv:2603.05919v1 Announce Type: new Abstract: Online platforms routinely compare multi-armed bandit algorithms, such as UCB and Thompson Sampling, to select the best-performing policy. Unlike standard A/B tests for static treatments, each run of a bandit algorithm over $T$ users produces only one dependent trajectory, because the algorithm's decisions depend on all past interactions. Reliable inference therefore demands many independent restarts of the algorithm, making experimentation costly and delaying deployment decisions. We propose Artificial Replay (AR) as a new experimental design for this problem. AR first runs one policy and records its trajectory. When the second policy is executed, it reuses a recorded reward whenever it selects an action the first policy already took, and queries the real environment only otherwise. We develop a new analytical framework for this design and prove three key properties of the resulting estimator: it is unbiased; it requires only $T + o(T)$ user interactions instead of $2T$ for a run of the treatment and control policies, nearly halving the experimental cost when both policies have sub-linear regret; and its variance grows sub-linearly in $T$, whereas the estimator from a na\"ive design has a linearly-growing variance. Numerical experiments with UCB, Thompson Sampling, and $\epsilon$-greedy policies confirm these theoretical gains.
Executive Summary
This article proposes Artificial Replay (AR), a novel experimental design for comparing multi-armed bandit algorithms. By reusing past reward interactions, AR significantly reduces the experimental cost and variance of estimators compared to traditional methods. The authors develop a new analytical framework and prove that AR's estimator is unbiased, requires fewer user interactions, and has sub-linear variance growth. Numerical experiments validate these theoretical gains, demonstrating the potential of AR for efficient comparison of bandit algorithms in real-world settings.
Key Points
- ▸ Artificial Replay (AR) is a new experimental design for comparing multi-armed bandit algorithms, offering improved efficiency and reduced costs.
- ▸ AR reuses past reward interactions to reduce the number of required user interactions and variance of estimators.
- ▸ The authors develop a new analytical framework and prove key properties of AR's estimator, including unbiasedness, reduced interaction requirements, and sub-linear variance growth.
Merits
Efficient Experimental Design
AR reduces experimental costs and variance by reusing past reward interactions, making it an attractive option for comparing bandit algorithms in real-world settings.
Improved Estimator Properties
The authors prove that AR's estimator is unbiased, requires fewer user interactions, and has sub-linear variance growth, offering significant advantages over traditional methods.
Theoretical Framework
The development of a new analytical framework for AR provides a solid foundation for further research and applications in the field of multi-armed bandit algorithms.
Demerits
Complexity of Implementation
AR's design may require additional computational resources and complexity in implementation, potentially limiting its adoption in certain scenarios.
Assumptions and Limitations
The authors' framework and analysis are based on certain assumptions, such as the availability of past reward interactions and the characteristics of the bandit algorithms being compared, which may not always hold in real-world settings.
Expert Commentary
The article presents a significant contribution to the field of multi-armed bandit algorithms and online experimentation. By proposing AR and developing a new analytical framework, the authors offer a novel and efficient approach to comparing bandit algorithms. While there may be limitations and complexities associated with AR's implementation, the potential benefits of reduced costs and improved estimator properties make it an attractive option for researchers and practitioners alike. As the field continues to evolve, it will be essential to explore the applicability and limitations of AR in various contexts, including those with non-stationary rewards, complex decision-making environments, and limited access to past reward interactions.
Recommendations
- ✓ Further research is needed to explore the applicability and limitations of AR in various real-world settings, including those with non-stationary rewards, complex decision-making environments, and limited access to past reward interactions.
- ✓ The authors should consider developing additional analytical tools and frameworks to extend the applicability of AR to different types of bandit algorithms and decision-making scenarios.
