We study the task of $(\epsilon, \delta)$-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 {\epsilon} 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.

翻译：我们研究$(\epsilon, \delta)$-差分隐私在线凸优化（OCO）问题。在线场景中，每次不同决策或迭代的发布都可能带来隐私损失的风险。该问题自Jain等人[2012]开创性研究以来已有长期研究历史，在$\epsilon$非极小场景下，目前最优结果由Agarwal等人[2023]提出。本文在维度因子方面改进了Agarwal等人[2023]的结果，并移除了平滑性假设要求。我们的成果已成为该场景下DP-OCO领域已知的最优速率。算法构建于Asi等人[2023]的工作基础之上，该工作通过拒绝抽样显式限制切换次数。本算法的核心创新在于采用强对数凹密度采样，从而更优地权衡维度因子，最终实现性能提升。