For distributions with a known bound on an increasing convex moment, the AL1 algorithm identifies the best arm with probability at least 1-δ using asymptotically minimal expected samples as δ goes to 0.
,K}, solve the following for yj = yj(c) (set y1(c) = 1) and let xj(c) for each j≥ 2 denote the corresponding minimizer: inf x∈[m(µj),m(µ1)] KLinf(µ1, x) + yj KLinf(µj, x) = c
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Optimal $\delta$-Correct Best-Arm Selection for Heavy-Tailed Distributions
For distributions with a known bound on an increasing convex moment, the AL1 algorithm identifies the best arm with probability at least 1-δ using asymptotically minimal expected samples as δ goes to 0.