Water-Filling is Universally Minimax Optimal

ArXi:2603.26893v1 Announce Type: cross Allocation of dynamically-arriving (i.e., online) divisible resources among a set of offline agents is a fundamental problem, with applications to online marketplaces, scheduling, portfolio selection, signal processing, and many other areas. The water-filling algorithm, which allocates an incoming resource to maximize the minimum load of compatible agents, is ubiquitous in many of these applications whenever the underlying objectives prefer balanced solutions; however, the analysis and guarantees differ across settings.