Effective Policy Learning for Multi-Agent Online Coordination Beyond Submodular Objectives

The first one, MA-SPL, not only can achieve the optimal (1 ce)-approximation guarantee for the MA-OC problem with submodular objectives but also can handle the unexplored α-weakly DR-submodular and (γ,β)-weakly submodular scenarios, where c is the curvature of the investigated submodular functions, α denotes the diminishing-return(DR) ratio and the tuple (γ,β) represents the submodularity ratios. Subsequently, in order to reduce the reliance on the unknown parameters α,γ,β inherent in the MA-SPLalgorithm, we further introduce the second online algorithm named MA-MPL. This MA-MPL algorithm is entirely parameter-free and simultaneously can maintain the same approximation ratio as the first MA-SPL algorithm. The core of our MA-SPL and MA-MPL algorithms is a novel continuous-relaxation technique termed as policybased continuous extension. Compared with the well-established multi-linear extension, a notable advantage of this new policy-based continuous extension is its ability to provide a lossless rounding scheme for any set function, thereby enabling us to tackle the challenging weakly submodular objectives. Finally, extensive simulations are conducted to validate the effectiveness of our proposed algorithms.