Optimal Best Arm Identification with Fixed Confidence

Abstract : We give a complete characterization of the complexity of best-arm identification in one-parameter bandit problems. We prove a new, tight lower bound on the sample complexity. We propose the `Track-and-Stop' strategy, which we prove to be asymptotically optimal. It consists in a new sampling rule (which tracks the optimal proportions of arm draws highlighted by the lower bound) and in a stopping rule named after Chernoff, for which we give a new analysis.
Complete list of metadatas

Cited literature [29 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01273838
Contributor : Aurélien Garivier <>
Submitted on : Wednesday, June 1, 2016 - 2:25:34 PM
Last modification on : Monday, April 29, 2019 - 3:55:11 PM
Long-term archiving on : Friday, September 2, 2016 - 10:27:56 AM

Files

MDLBAI.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01273838, version 2
  • ARXIV : 1602.04589

Citation

Aurélien Garivier, Emilie Kaufmann. Optimal Best Arm Identification with Fixed Confidence. 29th Annual Conference on Learning Theory (COLT), Jun 2016, New York, United States. ⟨hal-01273838v2⟩

Share

Metrics

Record views

695

Files downloads

274