Automatically Learning Compact Quality-aware Surrogates for Optimization Problems

Solving optimization problems with unknown parameters often requires learning\na predictive model to predict the values of the unknown parameters and then\nsolving the problem using these values. Recent work has shown that including\nthe optimization problem as a layer in the model training pipeline results in\npredictions of the unobserved parameters that lead to higher decision quality.\nUnfortunately, this process comes at a large computational cost because the\noptimization problem must be solved and differentiated through in each training\niteration; furthermore, it may also sometimes fail to improve solution quality\ndue to non-smoothness issues that arise when training through a complex\noptimization layer. To address these shortcomings, we learn a low-dimensional\nsurrogate model of a large optimization problem by representing the feasible\nspace in terms of meta-variables, each of which is a linear combination of the\noriginal variables. By training a low-dimensional surrogate model end-to-end,\nand jointly with the predictive model, we achieve: i) a large reduction in\ntraining and inference time; and ii) improved performance by focusing attention\non the more important variables in the optimization and learning in a smoother\nspace. Empirically, we demonstrate these improvements on a non-convex adversary\nmodeling task, a submodular recommendation task and a convex portfolio\noptimization task.\n