Explore-then-commit for a finite stochastic bandit

Input integers $k,n,m\ge 1$ with $mk\le n$, and access to an $n$-round $k$-armed stochastic bandit. The output is the sequence of selected arms $A_1,\dots ,A_n$ and the committed arm $J$.

1. For rounds $t=1,\dots ,mk$, choose arm $A_t=1+((t-1)<mrow><mi\; mathvariant="normal">m</mi><mi\; mathvariant="normal">o</mi><mi\; mathvariant="normal">d</mi></mrow>k)$ and observe its reward $Y_t$. Thus each arm is explored exactly $m$ times.
2. For each $i\in [k]$, form its exploration mean $${\widehat{\mu }}_i=\frac{1}{m}\sum _{r=1}^m{Y}_{(r-1)k+i}\mathrm{.}$$
3. Let $J$ be the least index attaining ${\max }_{i\in [k]}{\widehat{\mu }}_i$.
4. For every remaining round $t=mk+1,\dots ,n$, choose $A_t=J$ and observe its reward.

Finite stochastic bandit model, gaps, and regret: the horizon, finite arm set, reward observations, and non-anticipating round order used by the procedure.

Tor Lattimore and Csaba Szepesvári, Bandit Algorithms: Chapter 6 §6.1, Algorithm 1, PDF p. 101 / printed p. 92.