Design Experiments to Compare Multi-armed Bandit Algorithms
This work addresses the high cost and delayed deployment decisions in comparing multi-armed bandit algorithms for online platforms, offering a more efficient experimental design.
Comparing multi-armed bandit algorithms is costly due to the need for many independent restarts. This paper proposes Artificial Replay (AR), a new experimental design that reduces user interactions from 2T to T + o(T) and achieves sub-linear variance growth, outperforming naive designs with linear variance.
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 naïve design has a linearly-growing variance. Numerical experiments with UCB, Thompson Sampling, and $ε$-greedy policies confirm these theoretical gains.