Sufficient Decision Proxies for Decision-Focused Learning
This work addresses a foundational gap in optimization under uncertainty for researchers and practitioners, though it is incremental in clarifying assumptions rather than introducing a new paradigm.
The paper tackles the problem of when to use single-scenario approximations versus distribution estimation in decision-focused learning, showing that effective decision proxies can be designed with minimal complexity increase, as demonstrated in experiments on continuous and discrete variable problems.
When solving optimization problems under uncertainty with contextual data, utilizing machine learning to predict the uncertain parameters is a popular and effective approach. Decision-focused learning (DFL) aims at learning a predictive model such that decision quality, instead of prediction accuracy, is maximized. Common practice here is to predict a single value for each uncertain parameter, implicitly assuming that there exists a (single-scenario) deterministic problem approximation (proxy) that is sufficient to obtain an optimal decision. Other work assumes the opposite, where the underlying distribution needs to be estimated. However, little is known about when either choice is valid. This paper investigates for the first time problem properties that justify using either assumption. Using this, we present effective decision proxies for DFL, with very limited compromise on the complexity of the learning task. We show the effectiveness of presented approaches in experiments on problems with continuous and discrete variables, as well as uncertainty in the objective function and in the constraints.