Halve-Then-Greedy: Adaptive Sampling for Posterior Success with Near-Optimal Instance Dependence

Key points

• We study fixed-budget adaptive experimentation aimed at maximizing the probability of obtaining sufficient posterior evidence that a recommended design's mean performance exceeds a target.1
• We prove instance-dependent, finite-budget exponential bounds on posterior-failure probability that capture both separation from unfavorable arms and the presence of multiple favorable arms.1
• On one-positive-arm families, we establish an asymptotic sample-complexity lower bound that HTG matches up to a logarithmic factor.1
• We further analyze uniform sampling and sequential halving, revealing regimes where they require more samples than HTG by linear and logarithmic factors, respectively.1

Sources (1)

• [1]Halve-Then-Greedy: Adaptive Sampling for Posterior Success with Near-Optimal Instance Dependence
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 14, 10:33 PM

  For Gaussian bandits with a Gaussian prior, we propose Halve-Then-Greedy (HTG), which combines a large initial balanced allocation, successive halving, and posterior-greedy sampling.

  We study fixed-budget adaptive experimentation aimed at maximizing the probability of obtaining sufficient posterior evidence that a recommended design's mean performance exceeds a target.

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