Online Distributed Optimization With Strongly Pseudoconvex-Sum Cost Functions

Abstract

This paper considers the problem of asynchronous distributed multi-agent optimization on server-based system architecture. In this problem, each agent has a local cost, and the goal for the agents is to collectively find a minimum of their aggregate cost. A standard algorithm to solve this problem is the iterative distributed gradientdescent (DGD) method being implemented collaboratively by the server and the agents. In the synchronous setting, the algorithm proceeds from one iteration to the next only after all the agents complete their expected communication with the server. However, such synchrony can be expensive and even infeasible in realworld applications. We show that waiting for all the agents is unnecessary in many applications of distributed optimization, including distributed machine learning, due to redundancy in the cost functions (or data). Specifically, we consider a generic notion of redundancy named (r, )-redundancy implying solvability of the original multi-agent optimization problem with accuracy, despite the removal of up to r (out of total n) agents from the system. We present an asynchronous DGD algorithm where in each iteration the server only waits for (any) n − r agents, instead of all the n agents. Assuming (r, )-redundancy, we show that our asynchronous algorithm converges to an approximate solution with error that is linear in and r. Moreover, we also present a generalization of our algorithm to tolerate some Byzantine faulty agents in the system. Finally, we demonstrate the improved communication efficiency of our algorithm through experiments on MNIST and Fashion-MNIST using the benchmark neural network LeNet.Preprint. Under review.

Gradient and Projection Free Distributed Online Min-Max Resource Optimization

“…Additional dynamic regret bounds have also been derived for centralized OCO, e.g., Mokhtari et al (2016); Zhang et al (2017a); Besbes et al (2015). In distributed implementation, several recent works have proposed methods that provide dynamic regret guarantee under various assumptions on the convexity and smoothness of the objective functions (Shahrampour and Jadbabaie (2018); Zhang et al (2019); Dixit et al (2019); Lu et al (2020); Sharma et al (2020); Eshraghi and Liang (2020); ; Li et al (2021)). To the best of our knowledge, for gradient/projection-based distributed OCO, the tightest known dynamic regret bound for general convex cost functions is O( T (1 + P T )) (Shahrampour and Jadbabaie (2018)).…”

Improving Dynamic Regret in Distributed Online Mirror Descent Using Primal and Dual Information

“…However, it is generally impossible to know C T beforehand in practice, so most subsequent works do not require this assumption. A distributed online gradient tracking algorithm is proposed in (Lu et al, 2019), which has a dynamic regret bound of O( √ 1 + C T T 3/4 √ ln T ). The dynamic regret of distributed online proximal gradient descent with an O(log t) communication steps per round is bounded by O(log T (1 + C T )) (Dixit et al, 2019).…”

A Distributed Online Convex Optimization Algorithm with Improved Dynamic Regret

“…Thus, to ensure that such a positive N exists, we must select α such that both (29) and (27a) are satisfied in addition to (31), which requires…”