13 problems

Let $K$ be prefix Kolmogorov complexity, let $\boldsymbol{\vartheta}_0$ be the true parameter, and let $\Delta(k)$ denote the complexity difference used in the MDL setup. Strengthe…

In the convex composite problem with closed proper convex functions $f,g$, suppose the Douglas–Rachford operator has a fixed point $w^\star$ and $f$ is $L$-smooth. Let $\rho$ denot…

Consider the convex composite problem … where $f$ and $g$ are closed proper convex functions. Assume that the Douglas–Rachford operator has a fixed point $w^\star$, that $f$ is $L$…

Let $A$ and $B$ be operators satisfying the paper's standing Assumption, let $B$ be $\beta$-cocoercive, and let $A=\partial g$ for a closed proper convex function $g$. Let…

Asymptotic-rate conjecture. The exact sublinear rates for regimes $p_5$ and $p_6$ correspond to

Finite-iteration tightness conjecture. The DCA rates corresponding to regimes $p_1$, $p_2$, $p_3$ and $p_4$ are tight for any number of iterations $N$.

Regular-graph extension conjecture. The bound given in Theorem remains valid in the simple symmetric case, for example for regular graphs without transitivity.

Kalman's convergence-rate conjecture. For any stable $G$ and $\Delta\in S[0,K]$ with $K<K_N$,

The $n^{-1}$ convergence-rate conjecture. Under these assumptions, the distance between the convergent subsequence of finite-depth minimisers and its limit is $O(n_k^{-1})$. This c…

Let $\mathbb{S}^1$ be the unit circle with Haar probability measure $d\mu_0$, and let $U:L^2(\mathbb{S}^1,d\mu_0)\to L^2(\mathbb{S}^1,d\mu_0)$ be the multiplication operator … Cons…

Let $k\in\mathbb{N}$. For each $d\in\mathbb{N}$, let $U=\operatorname{diag}(1,\zeta_d,\zeta_d^2,\dots,\zeta_d^{d-1})$, where $\zeta_d=\exp(2\pi \mathbf{i}/d)$ is a primitive root o…

Let $m$ be the number of training examples and suppose the feature matrix has entries in $\{-1,0,+1\}$. Let $L$ denote the exponential loss and let…

Let $\bm{\lambda}^*$ be any weight vector and let $B=\|\bm{\lambda}^*\|_1$. For exponential loss $L$ and AdaBoost's iterates, quadratic convergence conjecture. For every…