arXiv AI
Sep 1

Dec-BFTRL: Squre-Root Regret for Decentralized Online Upper-Linearizable Optimization under Separation Access with Application to Continuous Submodular Maximization

The paper introduces Dec-BFTRL, a decentralized algorithm for online optimization of upper-linearizable payoffs with efficient separation access, targeting continuous diminishing-return submodular maximization. Each agent evaluates its action against the average of local objectives, projects via an approximate gauge, exchanges a cumulative surrogate-gradient dual state, and uses a local HybridNewton step to minimize its BFTRL potential. The method achieves an expected network-aggregate regret of “~O(√T)” while requiring T neighbor-mixing steps and ~O(T) separation-oracle calls per agent, and provides four wrapper instantiations for three DR-submodular problems.

By Yiyang Lu, Mohammad Pedramfar, Vaneet Aggarwal