Abstract: Mathematical optimization models can improve decision making in a wide variety of real-world applications. However, in many cases, it is difficult or impossible to model some of the constraints or objectives for such problems. Examples include complex physical and chemical processes in industrial manufacturing plants, as well as quantities which are difficult to formally define such as food palatability. One way to overcome this is to use the technique known as constraint learning, which utilizes historical data to learn the relevant parts of the optimization model. However, such constraint learning may result in inaccuracies very different from the ones in traditional machine learning settings, and which pose significant challenges in learning good optimization models.
In this work, we present a formal approach for addressing this gap, to improve the quality of the solutions produced by the learnt models. Our approach consists of: a) a formal definition of the measure of quality of the generated model; b) a Gaussian Process approach for estimating model; and c) methods to augment the generated optimization model with additional constraints so as to obtain high quality (as defined by our measure) optimization models. The talk will include detailed theoretical analysis of our framework, as well as empirical analysis.