Improved Approximate Regret for Decentralized Online Continuous Submodular Maximization via Reductions
🤖 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.
Application Category
📝 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
Research questions and friction points this paper is trying to address.
decentralized online learning
continuous submodular maximization
approximate regret
projection-free algorithms
decision sets
Innovation
Methods, ideas, or system contributions that make the work stand out.
decentralized online learning
continuous submodular maximization
approximate regret
reduction techniques
projection-free algorithms
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