2024/01/17 by Mualem, Loay, Tukan, Murad, Fledman, Moran
#FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2401.09251
Optimization of DR-submodular functions has experienced a notable surge in significance in recent times, marking a pivotal development within the domain of non-convex optimization. Motivated by real-world scenarios, some recent works have delved into the maximization of non-monotone DR-submodular functions over general (not necessarily down-closed) convex set constraints. Up to this point, these works have all used the minimum ℓ_∞ norm of any feasible solution as a parameter. Unfortunately, a recent hardness result due to Mualem & Feldman~\citemualem2023resolving shows that this approach cannot yield a smooth interpolation between down-closed and non-down-closed constraints. In this work, we suggest novel offline and online algorithms that provably provide such an interpolation based on a natural decomposition of the convex body constraint into two distinct convex bodies: a down-closed convex body and a general convex body. We also empirically demonstrate the superiority of our proposed algorithms across three offline and two online applications.