7 problems

Let $\adapttt{}$ be the modified adaptive algorithm for differentially private best-arm identification, and let $\delta$ denote the confidence level. Its modified transportation co…

Consider regret minimisation and best-arm identification (BAI) under differential privacy, at an arbitrary privacy level. Let an arm-level measure of distinguishability mean a quan…

Nouiehed–Ross conjecture. For all $k,n$, the myopic strategy maximizes the probability that at least $k$ wins occur in the first $n$ trials.

Bradt–Feldman conjecture. The myopic strategy is optimal when $\alpha+\beta\neq 1$.

Let $n\geq 2$, let $A_n=(1,1,\ldots,1)$ be the uniform discount sequence, let $M>0$, and let $F$ be a nondegenerate prior distribution. Write $W(MF,\alpha_2;A_n)$ for the bandit's…

Let $A_n$ be a regular discount sequence, let $\alpha$ denote the Dirichlet-process prior specification for the bandit, and let $\Lambda(\alpha;A_n)$ be the relevant break-even val…

Let $u_i,v_i>0$ and let the two arms of a finite-horizon Bernoulli bandit have independent ${\rm Beta}(u_i,v_i)$ priors, for $i=1,2$, under uniform discounting. Berry's prior-order…