Robust Distributed Learning Against Both Distributional Shifts and Byzantine Attacks

In distributed learning systems, robustness threat may arise from two major sources. On the one hand, due to distributional shifts between training data and test data, the trained model could exhibit poor out-of-sample performance. On the other hand, a portion of working nodes might be subject to Byzantine attacks, which could invalidate the learning result. In this article, we propose a new research direction that jointly considers distributional shifts and Byzantine attacks. We illuminate the major challenges in addressing these two issues simultaneously. Accordingly, we design a new algorithm that equips distributed learning with both distributional robustness and Byzantine robustness. Our algorithm is built on recent advances in distributionally robust optimization (DRO) as well as norm-based screening (NBS), a robust aggregation scheme against Byzantine attacks. We provide convergence proofs in three cases of the learning model being nonconvex, convex, and strongly convex for the proposed algorithm, shedding light on its convergence behaviors and endurability against Byzantine attacks. In particular, we deduce that any algorithm employing NBS (including ours) cannot converge when the percentage of Byzantine nodes is
$\sfrac{1}{3}$
or higher, instead of
$\sfrac{1}{2}$
, which is the common belief in current literature. The experimental results verify our theoretical findings (on the breakpoint of NBS and others) and also demonstrate the effectiveness of our algorithm against both robustness issues, justifying our choice of NBS over other widely used robust aggregation schemes. To the best of our knowledge, this is the first work to address distributional shifts and Byzantine attacks simultaneously.