Aggregation and garbage collection for online optimization

Online optimization approaches are popular for solving optimization problems where not all data is considered at once, because it is computationally prohibitive, or because new data arrives in an ongoing fashion. Online approaches solve the problem iteratively, with the amount of data growing in each iteration. Over time, many problem variables progressively become realized, i.e., their values were fixed in the past iterations and they can no longer affect the solution. If the solving approach does not remove these realized variables and associated data and simplify the corresponding constraints, solving performance will slow down significantly over time. Unfortunately, simply removing realized variables can be incorrect, as they might affect unrealized decisions. This is why this complex task is currently performed manually in a problem-specific and time-consuming way. We propose a problem-independent framework to identify realized data and decisions, and remove them by summarizing their effect on future iterations in a compact way. The result is a substantially improved model performance.