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In distributed learning systems, robustness issues may arise from twosources. On one hand, due to distributional shifts between training data andtest data, the trained model could exhibit poor out-of-sample performance. Onthe other hand, a portion of working nodes might be subject to byzantineattacks which could invalidate the learning result. Existing works mostly dealwith these two issues separately. In this paper, we propose a new algorithmthat equips distributed learning with robustness measures against bothdistributional shifts and byzantine attacks. Our algorithm is built on recentadvances in distributionally robust optimization as well as norm-basedscreening (NBS), a robust aggregation scheme against byzantine attacks. Weprovide convergence proofs in three cases of the learning model beingnonconvex, convex, and strongly convex for the proposed algorithm, sheddinglight 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 1/3 or higher,instead of 1/2, which is the common belief in current literature. Theexperimental results demonstrate the effectiveness of our algorithm againstboth robustness issues. To the best of our knowledge, this is the first work toaddress distributional shifts and byzantine attacks simultaneously.

Robust Distributed Learning Against Both Distributional Shifts and Byzantine Attacks