Improved Approximate Regret for Decentralized Online Continuous Submodular Maximization via Reductions

2026-02-10

AI Summary

This work addresses the significant gap in approximation regret bounds between decentralized online continuous submodular maximization (D-OCSM) and decentralized online convex optimization (D-OCO), as well as the difficulty of projection-free algorithms in matching centralized performance. To bridge this gap, the paper proposes two novel reduction techniques that transform D-OCSM into a D-OCO problem. These reductions achieve, for the first time, simultaneous improvement in regret bounds relative to convex optimization and a breakthrough in the performance of projection-free algorithms over general convex decision sets. Furthermore, when the feasible set is down-closed, the proposed methods closely approach the performance of centralized algorithms, substantially tightening the existing approximation regret bounds.

Technology Category

• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Online Learning & Bandits

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Decentralized Web and Fediverse systems

Abstract

To expand the applicability of decentralized online learning, previous studies have proposed several algorithms for decentralized online continuous submodular maximization (D-OCSM) -- a non-convex/non-concave setting with continuous DR-submodular reward functions. However, there exist large gaps between their approximate regret bounds and the regret bounds achieved in the convex setting. Moreover, if focusing on projection-free algorithms, which can efficiently handle complex decision sets, they cannot even recover the approximate regret bounds achieved in the centralized setting. In this paper, we first demonstrate that for D-OCSM over general convex decision sets, these two issues can be addressed simultaneously. Furthermore, for D-OCSM over downward-closed decision sets, we show that the second issue can be addressed while significantly alleviating the first issue. Our key techniques are two reductions from D-OCSM to decentralized online convex optimization (D-OCO), which can exploit D-OCO algorithms to improve the approximate regret of D-OCSM in these two cases, respectively.

Problem

• decentralized online learning
• continuous submodular maximization
• approximate regret
• projection-free algorithms
• decision sets

Innovation

• decentralized online learning
• continuous submodular maximization
• approximate regret
• reduction techniques
• projection-free algorithms