Nonsmooth Nonconvex Optimization from Noisy Comparisons: Unbiased Gap Estimation and the Price of Preference Feedback

We study the minimization of $L$-Lipschitz, possibly nonsmooth and nonconvex $f:R^d\to R$ from noisy pairwise comparisons: comparing $x$ and $y$ returns a bit equal to $1$ with probability $σ((f(y)-f(x))/τ)$, for a known link $σ$ and temperature $τ$, and the goal is a $(δ,ε)$-Goldstein stationary po