The Communication Complexity of Distributed Estimation

2025-12-17 · Source: Apple Machine Learning Research · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Cybersecurity & Data Privacy · Depth: Expert, quick

Summary

Researchers from UCLA, UC Berkeley, and IAS introduce the distributed estimation problem, an extension of the two-party communication model where Alice and Bob estimate $\mathbb{E}_{x \sim p, y \sim q}[f(x, y)]$ for distributions $p$ and $q$ and a known bounded function $f$. Their work aims to understand how communication scales with $f$'s communication complexity and the error parameter $\varepsilon$. They developed a new debiasing protocol that improves the dependence on $1/\varepsilon$ from quadratic to linear, outperforming the standard random sampling approach which requires $O(R(f)/\varepsilon^2)$ communication. The study also provides better upper bounds for specific function classes like Equality and Greater-than, and introduces lower bound techniques based on spectral methods and discrepancy, proving the optimality of their debiasing protocol for general functions and their protocols for Equality and Greater-than functions. They further demonstrate that Equality is among the easiest full-rank Boolean functions.

Key takeaway

For AI Researchers developing distributed algorithms, this work suggests that incorporating debiasing protocols can dramatically reduce communication overhead, particularly when aiming for high accuracy (small $\varepsilon$). You should evaluate whether your current distributed estimation tasks can benefit from a linear dependence on $1/\varepsilon$ rather than a quadratic one, potentially leading to more efficient systems.

Key insights

A new debiasing protocol significantly improves communication efficiency for distributed estimation problems.

Principles

• Debiasing can linearize error dependence.
• Spectral methods yield tight lower bounds.

Method

The debiasing protocol estimates $\mathbb{E}_{x \sim p, y \sim q}[f(x, y)]$ by averaging samples, then applies a debiasing step to reduce the $1/\varepsilon$ dependence from quadratic to linear.

In practice

• Apply debiasing for distributed mean estimation.
• Consider spectral methods for lower bound analysis.

Topics

• Distributed Estimation
• Communication Complexity
• Debiasing Protocols
• Lower Bounds
• Privacy

Best for: AI Researcher, AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Apple Machine Learning Research.