Robust Distributed Optimization With Randomly Corrupted Gradients
This addresses the challenge of robust distributed optimization for systems with unreliable agents, but it is incremental as it builds on existing robust aggregation methods.
The paper tackles the problem of distributed optimization under Byzantine failures, where agents may behave arbitrarily or adversarially, by proposing a first-order algorithm with three defense layers and proving convergence guarantees for strongly convex and smooth non-convex functions.
In this paper, we propose a first-order distributed optimization algorithm that is provably robust to Byzantine failures-arbitrary and potentially adversarial behavior, where all the participating agents are prone to failure. We model each agent's state over time as a two-state Markov chain that indicates Byzantine or trustworthy behaviors at different time instants. We set no restrictions on the maximum number of Byzantine agents at any given time. We design our method based on three layers of defense: 1) temporal robust aggregation, 2) spatial robust aggregation, and 3) gradient normalization. We study two settings for stochastic optimization, namely Sample Average Approximation and Stochastic Approximation. We provide convergence guarantees of our method for strongly convex and smooth non-convex cost functions.