Near-Optimal Algorithms for Private Online Optimization in the Realizable Regime. (arXiv:2302.14154v1 [cs.LG])

We consider online learning problems in the realizable setting, where there
is a zero-loss solution, and propose new Differentially Private (DP) algorithms
that obtain near-optimal regret bounds. For the problem of online prediction
from experts, we design new algorithms that obtain near-optimal regret ${O}
\big( \varepsilon^{-1} \log^{1.5}{d} \big)$ where $d$ is the number of experts.
This significantly improves over the best existing regret bounds for the DP
non-realizable setting which are ${O} \big( \varepsilon^{-1} \min\big\{d,
T^{1/3}\log d\big\} \big)$. We also …

algorithms big design experts log loss near non online learning optimization prediction private problem problems solution