Balancing Privacy and Robustness in Coded Computing Under Profiled Workers

TL;DR

This paper investigates how the placement of unreliable workers in coded computing affects privacy and robustness, deriving bounds and proposing a greedy strategy to balance these competing objectives.

Contribution

It introduces analytical bounds on privacy and robustness based on worker placement and proposes a greedy algorithm to optimize their trade-off.

Findings

Optimal index placements for privacy and robustness are fundamentally different.

Privacy-maximizing placements reduce error localization capabilities.

The proposed greedy strategy effectively balances privacy and robustness.

Abstract

In distributed computing with untrusted workers, the assignment of evaluation indices plays a critical role in determining both privacy and robustness. In this work, we study how the placement of unreliable workers within the Numerically Stable Lagrange Coded Computing (NS-LCC) framework influences privacy and the ability to localize Byzantine errors. We derive analytical bounds that quantify how different evaluation-index assignments affect privacy against colluding curious workers and robustness against Byzantine corruption under finite-precision arithmetic. Using these bounds, we formulate optimization problems that identify privacy-optimal and robustness-optimal index placements and show that the resulting assignments are fundamentally different. This exposes that index choices that maximizes privacy degrade error-localization, and vice versa. To jointly navigate this trade-off, we propose a low-complexity greedy assignment strategy that closely approximates the optimal balance between privacy and robustness.