4 problems

Open problem 1. For large enough $r$, prove

Let $\Omega$ be a domain, let $F_i\subseteq\mathbb{R}^{\Omega}$ for $i\in[k]$, and let $F_{\max}$ be their $k$-fold maximum. Logarithmic aggregation conjecture. For some universal…

Let $N_{\infty}(\delta,\mathcal{S}_{\gamma+1})$ denote the covering number of the smooth-function class $\mathcal{S}_{\gamma+1}$ at accuracy $\delta$, and let the lower bound in eq…

Natural-quantity conjecture. The corresponding statements for martingale type should also hold when the quantity…