General Coded Computing in a Probabilistic Straggler Regime

TL;DR

This paper analyzes the approximation error convergence of two general coded computing schemes, BACC and LeTCC, in a probabilistic straggler model, showing they achieve zero average error as the number of servers grows.

Contribution

It provides the first theoretical analysis demonstrating convergence of approximation error for BACC and LeTCC under probabilistic straggler scenarios.

Findings

Average approximation error converges to zero for BACC and LeTCC.

Convergence rates are at least (\,log^3_{1/p}(N) \, \, N^{-3}) and (\,log^4_{1/p}(N) \, \, N^{-2}) respectively.

Results validated through experiments on neural networks and other functions.

Abstract

Coded computing has demonstrated promising results in addressing straggler resiliency in distributed computing systems. However, most coded computing schemes are designed for exact computation, requiring the number of responding servers to exceed a certain recovery threshold. Additionally, these schemes are tailored for highly structured functions. Recently, new coded computing schemes for general computing functions, where exact computation is replaced with approximate computation, have emerged. In these schemes, the availability of additional results corresponds to more accurate estimation of computational tasks. This flexibility introduces new questions that need to be addressed. This paper addresses the practically important scenario in the context of general coded computing, where each server may become a straggler with a probability $p$, independently from others. We theoretically analyze the approximation error of two existing general coded computing schemes: Berrut Approximate Coded Computing (BACC) and Learning Theoretic Coded Computing (LeTCC). Under the probabilistic straggler configuration, we demonstrate that the average approximation error for BACC and LeTCC converge to zero with the rate of at least $\mathcal{O}(\log^3_{\frac{1}{p}}(N)\cdot{N^{-3}})$ and $\mathcal{O}(\log^4_{\frac{1}{p}}(N)\cdot{N^{-2}})$, respectively. This is perhaps surprising, as earlier results does not indicate a convergence when the number of stragglers scales with the total number of servers $N$. However, in this case, despite the average number of stragglers being $Np$, the independence of servers in becoming stragglers allows the approximation error to converge to zero. These theoretical results are validated through experiments on various computing functions, including deep neural networks.