Decentralized Online Convex Optimization with Unknown Feedback Delays

2026-01-12

AI Summary

This work addresses the challenge of unknown and time-varying feedback delays in decentralized online convex optimization, where existing methods rely on prior knowledge of the total delay and yield suboptimal regret bounds. The authors propose a novel decentralized online learning algorithm that integrates adaptive learning rates with a gossip-based communication protocol, enabling agents to locally estimate delays and collaboratively optimize without requiring any prior information on the total delay. For the first time, the method achieves tight regret bounds under such agnostic conditions: $O(N\sqrt{d_{\text{tot}}} + N\sqrt{T}/(1-\sigma^2)^{1/4})$ for general convex functions and $O(N\delta_{\max} \ln T / \alpha)$ for strongly convex functions. The theoretical analysis leverages spectral graph theory, and empirical evaluations demonstrate superior performance over existing baselines.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Non-convex Optimization
• Multiagent Systems: Multiagent Learning

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Decentralized Web and Fediverse systems

Abstract

Decentralized online convex optimization (D-OCO), where multiple agents within a network collaboratively learn optimal decisions in real-time, arises naturally in applications such as federated learning, sensor networks, and multi-agent control. In this paper, we study D-OCO under unknown, time-and agent-varying feedback delays. While recent work has addressed this problem (Nguyen et al., 2024), existing algorithms assume prior knowledge of the total delay over agents and still suffer from suboptimal dependence on both the delay and network parameters. To overcome these limitations, we propose a novel algorithm that achieves an improved regret bound of O N $\sqrt$ d tot + N $\sqrt$ T (1-$\sigma$2) 1/4 , where T is the total horizon, d tot denotes the average total delay across agents, N is the number of agents, and 1 -$\sigma$ 2 is the spectral gap of the network. Our approach builds upon recent advances in D-OCO (Wan et al., 2024a), but crucially incorporates an adaptive learning rate mechanism via a decentralized communication protocol. This enables each agent to estimate delays locally using a gossip-based strategy without the prior knowledge of the total delay. We further extend our framework to the strongly convex setting and derive a sharper regret bound of O N $\delta$max ln T $\alpha$ , where $\alpha$ is the strong convexity parameter and $\delta$ max is the maximum number of missing observations averaged over agents. We also show that our upper bounds for both settings are tight up to logarithmic factors. Experimental results validate the effectiveness of our approach, showing improvements over existing benchmark algorithms.

Problem

• Decentralized Online Convex Optimization
• Unknown Feedback Delays
• Time-varying Delays
• Multi-agent Learning
• Regret Minimization

Innovation

• Decentralized Online Convex Optimization
• Unknown Feedback Delays
• Adaptive Learning Rate
• Gossip-based Communication
• Regret Bound