Online Combinatorial Optimization with Multiple Projections and Its Application to Scheduling Problem

We consider combinatorial online prediction problems and propose a new construction method of efficient algorithms for the problems. One of the previous approaches to the problem is to apply online prediction method, in which two external procedures the projection and the metarounding are assumed to be implemented. In this work, we generalize the projection to multiple projections. As an application of our framework, we show an algorithm for an online job scheduling problem with a single machine with precedence constraints.