Offline and Online Learning and Decision-Making in the Predict-then-Optimize Setting скачать в хорошем качестве

Offline and Online Learning and Decision-Making in the Predict-then-Optimize Setting

In the predict-then-optimize setting, the parameters of an optimization task are predicted based on contextual features, and it is desirable to leverage the structure of the underlying optimization task when training a machine learning model. A natural loss function in this setting is based on considering the cost of the decisions induced by the predicted parameters, in contrast to standard measures of prediction error. Since directly optimizing this loss function is computationally challenging, we propose the use of a novel convex surrogate loss function, called the “Smart Predict-then-Optimize+ (SPO+)” loss function. In the offline learning situation, we prove that the SPO+ loss function is statistically consistent and develop corresponding quantitative risk bounds under mild conditions. We then consider an online variant of our setting with resource constraints, where a decision-maker first predicts a reward vector and resource consumption matrix based on a given context vector and then makes a decision. We prove regret bounds that are sublinear with rate depending on the corresponding offline risk bounds of the surrogate loss used to learn the prediction model. We also conduct numerical experiments to empirically demonstrate the strength of our proposed SPO-type methods in the online setting. This talk is based on a series of papers jointly with Othman El Balghiti, Adam Elmachtoub, Ambuj Tewari, and Heyuan Liu.