Differentially private distributed online mirror descent algorithm

This paper examines a private distributed online convex optimization problem in which each agent strives to minimize the sum of objective functions while also tending to keep their individual objective functions confidential. We use differential privacy as the metric to safeguard each agent's privacy and offer a distributed online mirror descent technique that is differentially private. We demonstrate that for strongly convex objective functions, our proposed algorithm satisfies the expected regret bound of O(ln (T)) while maintaining differential privacy, where T is the number of iterations. The established expected regret bound matches the optimal theoretical regret bound with respect to T. We further illu-minate the trade-off between the extent of privacy-preserving and the expected regret bound through numerical simulations.& COPY; 2023 Elsevier B.V. All rights reserved.