Multi-Armed Bandits with Interference
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911956449886208 |
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| author | Jia, Su Frazier, Peter Kallus, Nathan |
| author_facet | Jia, Su Frazier, Peter Kallus, Nathan |
| contents | Experimentation with interference poses a significant challenge in contemporary online platforms. Prior research on experimentation with interference has concentrated on the final output of a policy. The cumulative performance, while equally crucial, is less well understood. To address this gap, we introduce the problem of {\em Multi-armed Bandits with Interference} (MABI), where the learner assigns an arm to each of $N$ experimental units over a time horizon of $T$ rounds. The reward of each unit in each round depends on the treatments of {\em all} units, where the influence of a unit decays in the spatial distance between units. Furthermore, we employ a general setup wherein the reward functions are chosen by an adversary and may vary arbitrarily across rounds and units. We first show that switchback policies achieve an optimal {\em expected} regret $\tilde O(\sqrt T)$ against the best fixed-arm policy. Nonetheless, the regret (as a random variable) for any switchback policy suffers a high variance, as it does not account for $N$. We propose a cluster randomization policy whose regret (i) is optimal in {\em expectation} and (ii) admits a high probability bound that vanishes in $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01845 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multi-Armed Bandits with Interference Jia, Su Frazier, Peter Kallus, Nathan Machine Learning Experimentation with interference poses a significant challenge in contemporary online platforms. Prior research on experimentation with interference has concentrated on the final output of a policy. The cumulative performance, while equally crucial, is less well understood. To address this gap, we introduce the problem of {\em Multi-armed Bandits with Interference} (MABI), where the learner assigns an arm to each of $N$ experimental units over a time horizon of $T$ rounds. The reward of each unit in each round depends on the treatments of {\em all} units, where the influence of a unit decays in the spatial distance between units. Furthermore, we employ a general setup wherein the reward functions are chosen by an adversary and may vary arbitrarily across rounds and units. We first show that switchback policies achieve an optimal {\em expected} regret $\tilde O(\sqrt T)$ against the best fixed-arm policy. Nonetheless, the regret (as a random variable) for any switchback policy suffers a high variance, as it does not account for $N$. We propose a cluster randomization policy whose regret (i) is optimal in {\em expectation} and (ii) admits a high probability bound that vanishes in $N$. |
| title | Multi-Armed Bandits with Interference |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2402.01845 |