3 problems

Averaged TV-risk conjecture. The upper bound above may not be tight; it is an open problem whether it can be improved to

Let $B_j^t$ be the polynomials whose coefficients are denoted by $C(t,m,j)$, with $m$ and $j$ satisfying $m\leq t$ and $j=0,1,2,\ldots,t$. Coefficient-bound conjecture. The coeffic…

Let $K$ be the alphabet size, let $\boldsymbol{W}_{\epsilon,\star}$ denote the step mechanism, let $\mathscr{W}_\epsilon$ be the class of all $\epsilon$-private mechanisms, and let…