Decentralized Parameter-Free Online Learning with Compressed Gossip

2026-05-26

AI Summary

This work addresses the challenge of error accumulation caused by communication compression in decentralized online convex optimization. The authors propose DECO-EF, the first parameter-free compressed learning algorithm that requires no prior knowledge of the learning rate, time horizon, or comparator norm. By integrating a coin-betting mechanism, error feedback, and a differential gossip protocol, each agent maintains a clean cumulative state and a compressed tracker, transmitting only the difference between states during communication. Theoretical analysis demonstrates that DECO-EF achieves a comparator-adaptive sublinear network regret bound under compressed communication, establishing it as the first decentralized online learning algorithm with such a guarantee.

Abstract

We study decentralized online convex optimization when agents communicate over a graph and messages may be compressed. Classical decentralized online methods typically require learning-rate choices that depend on the horizon, comparator scale, or other problem parameters, while compressed communication introduces additional disagreement that must be controlled. We propose DECO-EF (DEcentralized COin-betting with Error Feedback), a decentralized parameter-free online learning algorithm that combines coin-betting predictions with compressed difference-based gossip. Each agent maintains a clean accumulated state and a compressed tracker, and communicates only compressed state differences during gossip steps. The method is parameter-free in the online-learning sense: it does not tune to the horizon, the comparator norm, or the learning rate. We prove expected comparator-adaptive network-regret bounds for DECO-EF under compressed communication. To the best of our knowledge, this gives the first expected sublinear network-regret guarantees for parameter-free decentralized online learning under compressed communication.

Problem

• decentralized online learning
• parameter-free
• compressed communication
• network regret
• gossip

Innovation

• decentralized online learning
• parameter-free
• compressed communication
• coin-betting
• network regret