10 problems

Silver-rate optimality conjecture. The asymptotic rate achieved by the silver stepsize schedule is optimal among all non-adaptive stepsize schedules.

Silver-schedule optimality conjecture. The silver stepsize schedule is exactly optimal for this performance metric among stepsize schedules in the strongly convex setting.

Basic g-composable schedule conjecture. For each $n$, every minimax-optimal stepsize schedule solving

OBS-F minimax optimality conjecture. The OBS-F schedules are minimax optimal in the sense of the paper's minimax formulation.

Let the stepsize schedules generated by the algorithm in Definition be the schedules obtained by the paper's concatenation procedure for a given total iteration number $n$. Global…

Let $h_{\circ}^{(n)}$ denote the primitive stepsize schedule generated by Definition, let $\Call{ConPP}$ denote the concatenation operation, and let $\mathbf 1$ be the all-ones vec…

Consider gradient descent for smooth convex optimization with time-varying stepsize schedules, and let $n$ denote the number of iterations. Optimized-schedule rate conjecture. Furt…

Let $n=2^k-1$, let $r_k=\frac{1}{1+\sqrt{4\rho^{2k}-3}}$ with $\rho=1+\sqrt{2}$, and consider gradient descent on arbitrary smooth convex functions using stepsize schedules of leng…

Consider gradient descent with dynamic, time-varying stepsizes in the convex optimization setting, and let $T$ denote the number of iterations. Dynamic stepsizes accelerated-rate c…

Let $n$ be a positive integer, and consider the infinite-horizon Silver Stepsize Schedule, whose $i$-th normalized stepsize is $a_{B(i)}$, where $B(i)$ denotes the smallest power o…