Learning Mixed-Integer Linear Programs from Contextual Examples
This addresses the challenge of reducing the need for domain and modeling expertise in designing MILPs for applications like scheduling and routing, representing a novel but incremental advancement in automated program learning.
The paper tackles the problem of automatically learning mixed-integer linear programs (MILPs) from contextual examples, which include solutions and non-solutions in specific contexts, and introduces the MISSLE algorithm that uses stochastic local search guided by gradient information to achieve faster and better performance than baseline methods on synthetic data.
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.