Room 206 (2nd floor, badged access)
7 January 2019 - 14h00
A simple parameter-free and adaptive approach to optimization under a minimal local smoothness assumption
by Michal Valko from SequeL, Inria Lille - Nord Europe
Abstract: We will describe the history and the most recent results in the bandit approach black-box optimization with provable global guarantees. In particular, we will study the problem of optimizing a function under a budgeted number of evaluations. We only assume that the function is locally smooth around one of its global optima. The difficulty of optimization is measured in terms of 1) the amount of noise $b$ of the function evaluation and 2) the local smoothness, $d$, of the function. A smaller $d$ results in smaller optimization error. We come with a new, simple, and parameter-free approach. First, for all values of $b$ and $d$, this approach recovers at least the state-of-the-art regret guarantees. Second, our approach additionally obtains these results while being agnostic to the values of both $b$ and $d$. This leads to the first algorithm that naturally adapts to an unknown range of noise $b$ and leads to significant improvements in a moderate and low-noise regime. Third, our approach also obtains a remarkable improvement over the state-of-the-art \SOO algorithm when the noise is very low which includes the case of optimization under deterministic feedback ($b=0$). There, under our minimal local smoothness assumption, this improvement is of exponential magnitude and holds for a class of functions that covers the vast majority of functions that practitioners optimize ($d=0$). We show that our algorithmic improvement is also borne out in the numerical experiments, where we empirically show faster convergence on common benchmark functions.
Join work with Peter L. Bartlett and Victor Gabillon