Improved Differentially Private and Lazy Online Convex Optimization
This work addresses privacy concerns in online optimization for applications like machine learning, but it is incremental as it builds on existing methods.
The paper tackles the problem of differentially private online convex optimization by improving upon prior results in terms of dimension factors and removing smoothness requirements, achieving the best known rates in this regime.
We study the task of $(ε, δ)$-differentially private online convex optimization (OCO). In the online setting, the release of each distinct decision or iterate carries with it the potential for privacy loss. This problem has a long history of research starting with Jain et al. [2012] and the best known results for the regime of ε not being very small are presented in Agarwal et al. [2023]. In this paper we improve upon the results of Agarwal et al. [2023] in terms of the dimension factors as well as removing the requirement of smoothness. Our results are now the best known rates for DP-OCO in this regime. Our algorithms builds upon the work of [Asi et al., 2023] which introduced the idea of explicitly limiting the number of switches via rejection sampling. The main innovation in our algorithm is the use of sampling from a strongly log-concave density which allows us to trade-off the dimension factors better leading to improved results.