Private Online Learning via Lazy Algorithms
This work addresses privacy concerns in online learning for applications like recommendation systems, offering incremental improvements in regret bounds for differential privacy.
The paper tackles private online learning by proposing a transformation that converts lazy algorithms into private ones for online prediction from experts and online convex optimization, achieving improved regret rates of sqrt(T log d) + T^{1/3} log(d)/ε^{2/3} and sqrt(T) + T^{1/3} sqrt(d)/ε^{2/3} in high privacy regimes.
We study the problem of private online learning, specifically, online prediction from experts (OPE) and online convex optimization (OCO). We propose a new transformation that transforms lazy online learning algorithms into private algorithms. We apply our transformation for differentially private OPE and OCO using existing lazy algorithms for these problems. Our final algorithms obtain regret, which significantly improves the regret in the high privacy regime $\varepsilon \ll 1$, obtaining $\sqrt{T \log d} + T^{1/3} \log(d)/\varepsilon^{2/3}$ for DP-OPE and $\sqrt{T} + T^{1/3} \sqrt{d}/\varepsilon^{2/3}$ for DP-OCO. We also complement our results with a lower bound for DP-OPE, showing that these rates are optimal for a natural family of low-switching private algorithms.