Almost Optimal Variance-Constrained Best Arm Identification

We design and analyze Variance-Aware-Lower and Upper Confidence Bound (VA-LUCB), a parameter-free algorithm, for identifying the best arm under the fixed-confidence setup and under a stringent constraint that the variance of the chosen arm is strictly smaller than a given threshold. An upper bound o...

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Bibliographic Details
Published in:IEEE transactions on information theory 2023-04, Vol.69 (4), p.1-1
Main Authors: Hou, Yunlong, Tan, Vincent Y. F., Zhong, Zixin
Format: Article
Language:English
Subjects:
Algorithms
Best Arm Identification
Clinical trials
Complexity
Complexity theory
Confidence
Constraints
Empirical analysis
History
Information theory
Lower bounds
Minimization
Parameter identification
Risk-aware Bandits
Stochastic Multi-Armed Bandits
Task analysis
Upper bound
Upper bounds
Variance analysis
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Summary:We design and analyze Variance-Aware-Lower and Upper Confidence Bound (VA-LUCB), a parameter-free algorithm, for identifying the best arm under the fixed-confidence setup and under a stringent constraint that the variance of the chosen arm is strictly smaller than a given threshold. An upper bound on VA-LUCB's sample complexity is shown to be characterized by a fundamental variance-aware hardness quantity H VA . By proving an information-theoretic lower bound, we show that sample complexity of VA-LUCB is optimal up to a factor logarithmic in H VA . Extensive experiments corroborate the dependence of the sample complexity on the various terms in H VA . By comparing VA-LUCB's empirical performance to a close competitor RiskAverse-UCB-BAI by David et al . [1], our experiments suggest that VA-LUCB has the lowest sample complexity for this class of risk-constrained best arm identification problems, especially for the riskiest instances.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2022.3222231