Addressing misspecification in contextual optimization

We study a linear contextual optimization problem where a decision maker has access to historical data and contextual features to learn a cost prediction model aimed at minimizing decision error. We adopt the predict-then-optimize framework for this analysis. Given that perfect model alignment with reality is often unrealistic in practice, we focus on scenarios where the chosen hypothesis set is misspecified. In this context, it remains unclear whether current contextual optimization approaches can effectively address such model misspecification. In this paper, we present a novel integrated learning and optimization approach designed to tackle model misspecification in contextual optimization. This approach offers theoretical generalizability, tractability, and optimality guarantees, along with strong practical performance. Our method involves minimizing a tractable surrogate loss that aligns with the performance value from cost vector predictions, regardless of whether the model misspecified or not, and can be optimized in reasonable time. To our knowledge, no previous work has provided an approach with such guarantees in the context of model misspecification.