Decision-driven Regularization



Joint prediction and optimization problems are common in many business applications ranging from customer relationship management and marketing to revenue and retail operations management. In this paper, we examine the predict-then-optimize framework, where in the first-stage learning model, outcomes are predicted from features, and in the second-stage decision process, optimal decisions are selected using these outcomes. We propose a novel model that solves both stages as a whole. Specifically, we introduce the notion of a regularizer that measures the value of a predictive model in terms of the cost incurred in the decision process. We term this decision-driven regularization, and it is centred on the premise that the bias-variance trade-off in the learning problem is not transformed linearly by the subsequent decision problem. We prove key properties of our model, namely, that it is consistent, robust to wrong estimation, and has bounded bias. We also examine special cases under which we draw links to existing models in the literature, propose hybrid models and are able to describe their effectiveness using our framework as a theoretical basis. In our numerical experiments, we illustrate the behaviour of our model, and its performance against other models in the literature.

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Meeting ID: 983 9748 4297