3 problems

Consider a $K$-armed bandit model. For arm $k$, let $N_{k,T}$ be the number of pulls by time $T$, let $\bar\mu_{k,T}$ be its empirical mean reward, and let $I(\cdot)$ be the index…

Let $M$ clients play a multi-armed bandit for $T$ time slots. For client $m$, let $k'_{*,m}$ denote its optimal arm, let $X'_{k,m}$ denote the reward distribution of arm $k$ for cl…

Let $M>2$ and let $N$ be the number of channels. For a problem instance $(M,N,\boldsymbol\mu)$, consider all possible permutations of arms in the set $\mathcal{S}(M)$ and the round…