Online Decision-Focused Learning in Dynamic Environments

This paper introduces online decision-focused learning (DFL), a framework for training predictive models used in dynamic, sequential decision-making tasks where data distributions and objectives change over time. The authors propose a new algorithm, Decision-Focused Online Gradient Descent (DF-OGD), which handles the non-differentiable and non-convex nature of the decision objective by regularizing the problem and using an optimistic approach with perturbations. Theoretical dynamic regret bounds are provided for DF-OGD on both simplex and general convex polytope decision spaces, demonstrating its convergence guarantees. Empirical experiments on a knapsack problem show that DF-OGD outperforms a traditional prediction-focused approach in terms of downstream decision quality, particularly in the presence of model mispecification.