# Nearly Optimal Fixed-Confidence Best-Arm Identification with 1-Bit Feedback

arXiv: https://arxiv.org/abs/2610.02771 · HTML: https://mlsanity.com/paper/2610.02771/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2026.

## Abstract (arXiv)

We study fixed-confidence best-arm identification under strict 1-bit feedback constraints. At each round, the learner selects an arm and a query set, and receives only a single bit indicating whether the sampled reward belongs to that set. We consider a distribution-free finite-variance setting with arm-wise localization, where direct empirical mean estimation is no longer available and clipping becomes unavoidable. We first formulate a time-uniform 1-bit mean-estimation primitive based on randomized threshold queries and a clipped tail-integral identity. We then embed this primitive into candidate-challenger best-arm identification algorithms. A fixed-clipping algorithm gives a simple anytime (ε,δ)-PAC guarantee, while a phased adaptive-clipping algorithm matches the clipping level to the current resolution and yields a gap-adaptive sample complexity. We also prove a K-arm worst-case information-theoretic lower bound showing that the logarithmic penalty caused by finite-variance 1-bit feedback is intrinsic. This bound matches the leading dependence of the phased algorithm up to lower-order loglog factors.