Learning in Spatial Branching: Limitations of Strong Branching Imitation

TL;DR

This paper investigates the limitations of using learning-based methods, specifically imitation of strong branching and rule selection, to improve nonlinear programming algorithms, highlighting potential bounds on their effectiveness.

Contribution

It provides an analysis of the fundamental limitations of learning approaches for branching in nonlinear programming, extending prior work from linear to nonlinear contexts.

Findings

Limits on improvements from learning to select variables in nonlinear programming

Constraints on gains from learning to choose among predefined rules

Insights into the effectiveness bounds of imitation-based learning methods

Abstract

Over the last few years, there has been a surge in the use of learning techniques to improve the performance of optimization algorithms. In particular, the learning of branching rules in mixed integer linear programming has received a lot of attention, with most methodologies based on strong branching imitation. Recently, some advances have been made as well in the context of nonlinear programming, with some methodologies focusing on learning to select the best branching rule among a predefined set of rules leading to promising results. In this paper we explore, in the nonlinear setting, the limits on the improvements that might be achieved by the above two approaches: learning to select the best variable (strong branching) and learning to select the best rule (rule selection).