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.
Unlike best-arm identification, this objective does not require finding the best design.
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 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.
On one-positive-arm families, we establish an asymptotic sample-complexity lower bound that HTG matches up to a logarithmic factor.
We further analyze uniform sampling and sequential halving, revealing regimes where they require more samples than HTG by linear and logarithmic factors, respectively.
Simulations illustrate HTG's sample-efficiency advantages and their dependence on instance structure.