Gap Entropy and Almost Instance-Wise Optimal Best-Arm Identification
Quick summary
arXiv:2609.13703v1 Announce Type: cross Abstract: In the best-arm identification problem, we are given $n$ stochastic arms with unknown means and wish to identify the arm with the largest mean with probability at least $1-\delta$, using as few samples as possible. We consider independent Gaussian rewards with unit variance and means in $[0,1]$. Chen and Li [2016] conjectured that the instance-wise sample complexity of this problem is characterized by the gap entropy, up to an additive term arising from the two-arm problem. In this paper, we resolve their gap-entropy and almost instance-wise op
Key takeaways
- arXiv:2609.13703v1 Announce Type: cross Abstract: In the best-arm identification problem, we are given $n$ stochastic arms with unknown means and wish to identify the arm with the largest mean with probability at least $1-\delta$, using as few samples as possible.
- We consider independent Gaussian rewards with unit variance and means in $[0,1]$.
- Chen and Li [2016] conjectured that the instance-wise sample complexity of this problem is characterized by the gap entropy, up to an additive term arising from the two-arm problem.
Why it matters
The value of this work lies as much in how it was tested as in the claim itself. Sample design, baselines, uncertainty and replication help separate a laboratory result from real-world impact.
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