Learning-Theoretic Foundation for General Coded Computing: The Adversarial Setting

Parsa Moradi, Hanzaleh Akbarinodehi, Mohammad Ali Maddah-Ali

Adversarial workers pose a severe challenge in distributed computing systems by returning corrupted outputs that can substantially distort the recovered computations. Coded computing addresses this threat by introducing redundancy across worker assignments. Existing exact and approximate coded-computing methods typically handle adversarial outputs by explicitly locating and correcting or removing erroneous evaluations, which adds significant computational overhead at the master node. Moreover, existing analyses do not characterize how the recovery error scales with the number of workers and the adversarial budget. In this paper, we develop an adversarially robust extension of general coded computing (GCC), a learning-theoretic approximate coded-computing framework that designs the encoder and decoder by minimizing an upper bound on the end-to-end recovery error. Rather than identifying corrupted workers, the proposed method uses smoothness regularization to limit the influence of their outputs. The resulting encoder and decoder can be implemented using smoothing splines with linear master-side complexity. We derive a non-asymptotic bound on the worst-case end-to-end approximation…