Rethinking Successive Rejects Algorithms

Key points

• Successive Rejects (SR) is a simple fixed-budget best-arm identification algorithm that eliminates one candidate arm at each phase.1
• However, for Gaussian arms with common variance, SR's worst-instance error exponent normalized by the popular complexity measure $H1(P)$ is optimal up to a constant factor, which partly explains why SR's performance is competitive compared with state-of-the-art adaptive sampling algorithms.1
• Then, we introduce a version of SR with the optimized schedule, which we call $H1$-balanced Successive Rejects ($H1$-SR).1
• For Gaussian arms with common variance, $H1$-SR achieves at least $11/12$ of the optimal normalized rate over all adaptive algorithms for every $K\ge2$, and this approximation ratio converges to one as $1-O(1/\log K)$ as $K\to\infty$.1

Sources (1)

• [1]Rethinking Successive Rejects Algorithms
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 15, 03:19 PM

  In the best-arm identification problem, an algorithm adaptively selects arms to find the arm of the largest mean reward.

  Successive Rejects (SR) is a simple fixed-budget best-arm identification algorithm that eliminates one candidate arm at each phase.

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