PDE-Based Optimal Strategy for Unconstrained Online Learning. (arXiv:2201.07877v2 [cs.LG] UPDATED)

Web: http://arxiv.org/abs/2201.07877

Unconstrained Online Linear Optimization (OLO) is a practical problem setting
to study the training of machine learning models. Existing works proposed a
number of potential-based algorithms, but in general the design of these
potential functions relies heavily on guessing. To streamline this workflow, we
present a framework that generates new potential functions by solving a Partial
Differential Equation (PDE). Specifically, when losses are 1-Lipschitz, our
framework produces a novel algorithm with anytime regret bound
$C\sqrt{T}+||u||\sqrt{2T}[\sqrt{\log(1+||u||/C)}+2]$, where $C$ is a
user-specified …

arxiv learning lg online online learning strategy