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

Overview & Synopsis

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 error by decomposing it into three components: (1) the encoder approximation error, (2) the decoder reconstruction error under fully honest results, and (3) the adversarial perturbation error. For maximum of $q\geq 1$ adversarial workers among $N$ workers results in a worst-case error of order $\mathcal{O}((q/N)^{6/5})$ with appropriate selection of smoothness parameter, demonstrating that the approximation error vanishes asymptotically whenever the number of adversaries grows sublinearly with the network size. Experiments on scalar computation and neural-network inference are consistent with the predicted convergence behavior.