通过离散余弦变换实现鲁棒的贝鲁特近似编码计算
Robust Berrut-Approximated Coded Computing via Discrete Cosine Transforms
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中文总结 AI 辅助
研究针对编码计算中BACC对拜占庭工作节点鲁棒性不足的问题，提出RBACC框架，通过引入新评估点建立与DCT码联系实现错误定位和纠错，推导误差上界并制定优化问题，实验证明该框架能有效减轻相关问题并提高重建精度。
中文摘要 AI 辅助
编码计算是一种用于在分布式工作节点上执行大规模计算任务的可靠且容错的范式。在现有编码计算框架中，贝鲁特近似编码计算（BACC）通过有理插值实现任意非多项式函数的分布式计算。尽管BACC提供了可证明的近似保证和对掉队工作节点的弹性，但它对拜占庭工作节点的鲁棒性在很大程度上仍未得到探索。为填补这一研究空白，我们提出了鲁棒的贝鲁特近似编码计算（RBACC），它通过在存在拜占庭工作节点的情况下实现错误定位和纠错，为BACC建立了一个编码理论框架。特别是，RBACC引入了一种新的评估点选择，在贝鲁特插值和离散余弦变换（DCT）码之间建立了联系，从而在有限精度算法下实现错误定位和纠错。我们推导了RBACC在多种操作场景下的近似误差的解析上界，包括仅存在掉队者的系统和有限精度算法下存在拜占庭工作节点的系统。在此分析基础上，我们制定了几个优化问题，用于选择DCT码维度和为不可靠工作节点分配编码评估。我们表明，这些是以前未探索的设计参数，可以系统地优化以提高重建精度。实验结果表明，所提出的RBACC框架有效地减轻了掉队者和拜占庭工作节点的影响，同时比基线提供了更高的重建精度。
英文摘要
Coded computing is a reliable and fault-tolerant paradigm for executing large-scale computational tasks over distributed worker nodes. Among existing coded computing frameworks, Berrut Approximated Coded Computing (BACC) enables distributed computation of arbitrary non-polynomial functions through rational interpolation. Although BACC provides provable approximation guarantees and resilience against straggling workers, its robustness against Byzantine workers remains largely unexplored. To fill this research gap, we propose Robust Berrut Approximated Coded Computing (RBACC), which establishes a coding-theoretic framework for BACC by enabling error localization and error correction in the presence of Byzantine workers. In particular, RBACC introduces a new choice of evaluation points that establishes a connection between Berrut interpolation and Discrete Cosine Transform (DCT) codes, thereby enabling error localization and error correction under finite-precision arithmetic. We derive analytical upper bounds on the approximation error of RBACC under multiple operating scenarios, including straggler-only systems and systems with Byzantine workers under finite-precision arithmetic. Building upon this analysis, we formulate several optimization problems for selecting the DCT code dimension and for assigning encoded evaluations to unreliable workers. We show that these are previously unexplored design parameters that can be systematically optimized to improve the reconstruction accuracy. Experimental results demonstrate that the proposed RBACC framework effectively mitigates stragglers and Byzantine workers while offering improved reconstruction accuracy over the baselines.
