12 problems

Localization-omission conjecture. The authors conjecture that their techniques may allow for a simpler and more direct analysis by omitting the localization, while obtaining almost…

Sample-average asymptotic optimality conjecture. Replacing the AIPW estimator with the sample average estimator in the strategy should still yield an upper bound that matches the l…

Let the full asymptotic optimality property (full AOP) denote achieving the best performance of a convex combination of all the subset models, uniformly over the whole parameter re…

The restless bandit problem consists of multiple arms whose states evolve whether or not they are activated, subject to a resource constraint that allows a constant fraction of the…

Let $s_n$ denote the solution to the fixed-point equation arising in the preceding bound, and let its leading-order term refer to the dominant asymptotic contribution as $n$ become…

Let the standing assumptions of the paper hold. Let ${\cal S}_{\text{LP}}$ denote the set of solutions to the linear program, and suppose that this set contains multiple solutions.…

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…

Non-degeneracy conjecture. Non-degeneracy is also a necessary condition for the existence of a policy satisfying

Let a planning problem be given by $\{\boldsymbol{q}_{init},\mathcal{Q}_{goal}, \mathcal{X}_{obs}, \mathbf{F}, J\}$ together with a collision-checker. Here $\boldsymbol{q}_{init}$…

Extension conjecture. The formulation of the policy and its asymptotic optimality should extend to (i) multiple actions associated with a state, instead of only an active and a pas…

Let $\mathcal{S}_A^r$ denote the Shiryaev–Roberts–$r$ procedure with threshold $A$ and initialization point $r\geq0$. For a false-alarm constraint…

Worst-changepoint-at-infinity conjecture. The worst changepoint for the SR-$r$ procedure is at infinity: the supremum of the conditional average detection delay over changepoints i…