Learning Mixed-Integer Linear Programs from Contextual Examples

TL;DR

This paper introduces a novel approach to learn mixed-integer linear programs (MILPs) from contextual examples, enabling automatic acquisition of decision models with improved efficiency.

Contribution

It proposes MISSLE, a stochastic local search algorithm guided by surrogate loss gradients, for learning MILPs from contextual data, a new problem setting.

Findings

MISSLE outperforms existing methods in speed and accuracy on synthetic data.

The approach effectively learns MILPs from limited and complex contextual examples.

Empirical results demonstrate the potential for automated MILP acquisition in AI and operations research.

Abstract

Mixed-integer linear programs (MILPs) are widely used in artificial intelligence and operations research to model complex decision problems like scheduling and routing. Designing such programs however requires both domain and modelling expertise. In this paper, we study the problem of acquiring MILPs from contextual examples, a novel and realistic setting in which examples capture solutions and non-solutions within a specific context. The resulting learning problem involves acquiring continuous parameters -- namely, a cost vector and a feasibility polytope -- but has a distinctly combinatorial flavor. To solve this complex problem, we also contribute MISSLE, an algorithm for learning MILPs from contextual examples. MISSLE uses a variant of stochastic local search that is guided by the gradient of a continuous surrogate loss function. Our empirical evaluation on synthetic data shows that MISSLE acquires better MILPs faster than alternatives based on stochastic local search and gradient descent.