  Inferring unknown constraints is a challenging and crucial problem in many
robotics applications. When only expert demonstrations are available, it
becomes essential to infer the unknown domain constraints to deploy additional
agents effectively. In this work, we propose an approach to infer affine
constraints in control tasks after observing expert demonstrations. We
formulate the constraint inference problem as an inverse optimization problem,
and we propose an alternating optimization scheme that infers the unknown
constraints by minimizing a KKT residual objective. We demonstrate the
effectiveness of our method in a number of simulations, and show that our
method can infer less conservative constraints than a recent baseline method,
while maintaining comparable safety guarantees.
