Fixed-Confidence Best Arm Identification with Decreasing Variance
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arXiv
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| Format: | Preprint |
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2025
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| author | Roychowdhury, Tamojeet Reddy, Kota Srinivas Jagannathan, Krishna P Moharir, Sharayu |
| author_facet | Roychowdhury, Tamojeet Reddy, Kota Srinivas Jagannathan, Krishna P Moharir, Sharayu |
| contents | We focus on the problem of best-arm identification in a stochastic multi-arm bandit with temporally decreasing variances for the arms' rewards. We model arm rewards as Gaussian random variables with fixed means and variances that decrease with time. The cost incurred by the learner is modeled as a weighted sum of the time needed by the learner to identify the best arm, and the number of samples of arms collected by the learner before termination. Under this cost function, there is an incentive for the learner to not sample arms in all rounds, especially in the initial rounds. On the other hand, not sampling increases the termination time of the learner, which also increases cost. This trade-off necessitates new sampling strategies. We propose two policies. The first policy has an initial wait period with no sampling followed by continuous sampling. The second policy samples periodically and uses a weighted average of the rewards observed to identify the best arm. We provide analytical guarantees on the performance of both policies and supplement our theoretical results with simulations which show that our polices outperform the state-of-the-art policies for the classical best arm identification problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07199 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fixed-Confidence Best Arm Identification with Decreasing Variance Roychowdhury, Tamojeet Reddy, Kota Srinivas Jagannathan, Krishna P Moharir, Sharayu Machine Learning Information Theory Statistics Theory We focus on the problem of best-arm identification in a stochastic multi-arm bandit with temporally decreasing variances for the arms' rewards. We model arm rewards as Gaussian random variables with fixed means and variances that decrease with time. The cost incurred by the learner is modeled as a weighted sum of the time needed by the learner to identify the best arm, and the number of samples of arms collected by the learner before termination. Under this cost function, there is an incentive for the learner to not sample arms in all rounds, especially in the initial rounds. On the other hand, not sampling increases the termination time of the learner, which also increases cost. This trade-off necessitates new sampling strategies. We propose two policies. The first policy has an initial wait period with no sampling followed by continuous sampling. The second policy samples periodically and uses a weighted average of the rewards observed to identify the best arm. We provide analytical guarantees on the performance of both policies and supplement our theoretical results with simulations which show that our polices outperform the state-of-the-art policies for the classical best arm identification problem. |
| title | Fixed-Confidence Best Arm Identification with Decreasing Variance |
| topic | Machine Learning Information Theory Statistics Theory |
| url | https://arxiv.org/abs/2502.07199 |