Learning Linear Programs from Data Linear Programming lies at the core of mathematical modelling and optimization. Designing linear programs (LPs) is a difficult and expensive process, as it requires both mathematical programming and domain expertise, and it involves both designing an objective function and feasibility constraints. To support this design process, we propose INCALP, an algorithm for inducing linear programs from examples. Since the objective can often be learned with standard techniques (e.g. regression), INCALP learns the hard constraints only. It does so by encoding constraint learning as a mixed integer linear program. INCALP achieves significant efficiency gains by considering gradually larger subsets of examples, and terminating as soon as a suitable program is found. In addition, INCALP encourages both compactness and sparsity of the learned program. Our empirical analysis on synthetic data and textbook problems highlights the promise of the approach.

Constrained MultiObjective Optimization for Automated Machine Learning Automated machine learning has gained a lot of attention recently. Building and selecting the right machine learning models is often a multiobjective optimization problem. General purpose machine learning software that simultaneously supports multiple objectives and constraints is scant, though the potential benefits are great. In this work, we present a framework called Autotune that effectively handles multiple objectives and constraints that arise in machine learning problems. Autotune is built on a suite of derivativefree optimization methods, and utilizes multilevel parallelism in a distributed computing environment for automatically training, scoring, and selecting good models. Incorporation of multiple objectives and constraints in the model exploration and selection process provides the flexibility needed to satisfy tradeoffs necessary in practical machine learning applications. Experimental results from standard multiobjective optimization benchmark problems show that Autotune is very efficient in capturing Pareto fronts. These benchmark results also show how adding constraints can guide the search to more promising regions of the solution space, ultimately producing more desirable Pareto fronts. Results from two realworld case studies demonstrate the effectiveness of the constrained multiobjective optimization capability offered by Autotune.