  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.
