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

Key points

• Adversarial workers pose a severe challenge in distributed computing systems by returning corrupted outputs that can substantially distort the recovered computations.1
• Coded computing addresses this threat by introducing redundancy across worker assignments.1
• 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.1
• 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.1

Sources (1)

• [1]Learning-Theoretic Foundation for General Coded Computing: The Adversarial Setting
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 20, 12:41 AM

  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.

  Adversarial workers pose a severe challenge in distributed computing systems by returning corrupted outputs that can substantially distort the recovered computations.

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