Distributed Learning with Adversarial Gradient Perturbations

2026-05-04

AI Summary

This work addresses the degradation in optimization performance in distributed learning caused by clients returning maliciously perturbed gradients due to privacy concerns. Focusing on the minimization of convex and L-smooth functions under adversarial gradient perturbations, the paper assumes that the reported gradients may deviate arbitrarily from the true gradients within a prescribed distance bound. The authors establish a tight feasibility threshold characterizing the minimal achievable suboptimality gap under such adversarial corruption and propose an efficient query-based algorithm that integrates techniques from convex optimization and adversarial robustness analysis. Theoretically, the algorithm simultaneously attains optimal query complexity and a tight bound on the suboptimality gap, thereby advancing beyond existing approaches in both efficiency and robustness guarantees.

Abstract

Privacy concerns in distributed learning often lead clients to return intentionally altered gradient information. We consider the problem of learning convex and $L$-smooth functions under adversarial gradient perturbation, where a client's gradient reply to a server query can deviate arbitrarily from the true gradient subject to a distance bound. Our study focuses on two fundamental questions: (i) what is the smallest achievable sub-optimality gap (i.e., excess error in optimization) under such responses, and (ii) how many queries are sufficient to guarantee a given sub-optimality gap? We establish tight feasibility thresholds on the sub-optimality gap and provide algorithms that achieve these thresholds with provable query complexity guarantees.

Problem

• distributed learning
• adversarial gradient perturbations
• convex optimization
• sub-optimality gap
• query complexity

Innovation

• adversarial gradient perturbations
• distributed learning
• sub-optimality gap
• query complexity
• convex optimization