8 problems

UCB1 allocation-variability conjecture. The large allocation variability of texttt{UCB1} contributes to its slow convergence to the central limit theorem, and the convergence rate…

Conjecture on modified algorithms. Suitably modified variants of bandit algorithms should similarly achieve Pareto-efficient trade-offs as those achieved by texttt{UCB-f}.

Consider the proposed RS-AIPW strategy for fixed-budget best-arm identification in multi-armed bandits, together with the RS-DR and RS-SA strategies. RS-DR and RS-SA asymptotic opt…

The setting is a two-armed bandit problem using the RS-DR strategy, with allocation probability $w_{a,t}$ for arm $a$ at time $t$ and a re-estimated allocation probability used by…

Eluder-dimension conjecture. The eluder dimension does not yield sublinear regret unless the information gain is sublinear in $n$.

Let $M$ denote the number of stages in a multi-stage dynamic treatment regime (DTR) bandit problem, and let $T$ denote the time horizon. As $M$ becomes very large, for example comp…

Tightness conjecture. This regret bound is at most $\widetilde{\mathcal{O}}(\sqrt{|\mathcal{E}|d})$ away from being tight.

KL-HHR performance conjecture. The performance of the ${\textsc{KL-HHR}}$ algorithm should be very close to that of the ${\textsc{KL-SR}}$ algorithm, as observed in numerical exper…