14 problems

Let $\mathcal{F}_{K,B}$ denote the class of monotone functions considered in the paper, with influence budget $K$ and range or norm bound $B$. Under the paper's noisy-observation m…

Let a dynamic monotone function be a monotone fitness function whose fitness landscape may change between generations, and let Adversarial Dynamic BinVal (ADBV) denote the construc…

Let $f:[0,1]\to\mathbb{R}$ be a fixed non-decreasing function, and let $\operatorname{GreedyBox}$ be the adaptive approximation algorithm whose queried points form an empirical dis…

Consider the self-adjusting $(1,\lambda)$-EA with mutation probability $c/n$, success rate $s$, and update strength $F>1$, optimizing dynamic monotone functions. No-phase-transitio…

Let the self-adjusting $(1,\lambda)$-EA have success rate $s$ and update strength $F>1$. Middle-range dependence conjecture. There is a middle range of values of $s$ for which whet…

Let the self-adjusting $(1,\lambda)$-EA have success rate $s$ and update strength $F>1$. Non-universal threshold conjecture. There is no threshold $s_0$ such that the algorithm is…

Consider the self-adjusting $(1,\lambda)$-EA with mutation probability $c/n$, success rate $s$, and update strength $F>1$, optimizing dynamic monotone functions. Linear-evaluation…

Let the self-adjusting $(1,\lambda)$-EA use mutation probability $c/n$, success rate $s$, and update strength $F>1$. An efficiency threshold conjecture asserts that there does not…

Let $w$ be a positive integer, let $\varepsilon>0$, and let a monotone width-$w$ DNF be a monotone DNF whose terms contain at most $w$ literals. An upper-bound DNF for $f$ satisfie…

A monotone DNF is a DNF containing no negated literals. In the improved upper-bound DNF compression conjecture, $f_{\mathrm{upper}}$ is an upper bound of $f$ when…

The paper considers a misspecified regression setting in which the target function may not belong to the convex-function class, and establishes a sharp Bayesian oracle inequality f…

Let $f_0$ be a decreasing density on $[0,infty)$, let $X_1,\dots,X_n$ be a sample from $f_0$, and let $\hat f_n$ be the Grenander estimator, defined as the left derivative of the l…

Let $X=[m]$ for some finite $m\geq 1$, and let $f_1,\ldots,f_n$ be nonnegative nondecreasing functions $2^X\to\mathbb{R}$. For a probability measure $\mu$ on $2^X$, write … for…

Single-function conjecture. Assuming $k$-general position, every $k$th-order monotone finite set lies on the graph of a $k$-times differentiable function