Adversary-Robust Learning from Fully Asynchronous Directional Derivative Estimates

We propose FAR-SIGN (Fully Asynchronous Robust optimization via SIGNed directional projections) for adversary-resilient learning in parameter-server--worker systems. FAR-SIGN achieves robustness through sign-based updates along carefully designed directions and mitigates the resulting bias via a two-timescale mechanism. It admits both first-order and zeroth-order implementations and enables fully asynchronous execution without requiring a private reference dataset at the server. We establish almost-sure convergence of FAR-SIGN to the set of stationary points for smooth, nonconvex objectives. Moreover, we prove the near-optimal rate of O(n-1/4+ε) in the first-order setting and the standard O(n-1/6+ε) in the zeroth-order setting, where n is the iteration count and ε>0 can be chosen arbitrarily small. Experiments on MNIST show that FAR-SIGN outperforms robust aggregation-based methods in both accuracy and wall-clock time.