Decision-Focused Federated Learning Under Heterogeneous Objectives and Constraints

TL;DR

This paper introduces Decision-Focused Federated Learning (DFFL), analyzing how heterogeneity in objectives and constraints affects model stability and performance in collaborative predictive modeling for optimization tasks.

Contribution

It derives heterogeneity bounds for DFFL, explores stability under different feasible set geometries, and proposes an interpolation method to balance local and federated models.

Findings

Federation improves robustness with strongly convex feasible regions.

Small objective perturbations can cause persistent decision-focused loss discrepancies.

Interpolation between local and federated models reduces regret and client harm.

Abstract

We consider Decision-Focused Federated Learning (DFFL), a predict-then-optimize setting in which multiple clients collaboratively train predictive models for downstream linear optimization problems without exchanging raw data. Besides the data heterogeneity typical of standard federated learning, clients may also have different objective functions and feasible regions. Building on the SPO+ surrogate loss, we derive heterogeneity bounds that separate objective shift, measured through cost-vector distances, from feasible-set shift, measured through support-function and shape-distance terms. We show that, for general compact feasible sets, small objective perturbations can still induce nonvanishing decision-focused loss discrepancies, while strongly convex feasible regions yield sharper stability-based bounds. We then lift these pointwise bounds to a local-versus-federated excess-risk comparison, showing that federation is beneficial when the statistical advantage of pooling exceeds a client-specific heterogeneity penalty. Computational experiments on polyhedral and strongly convex problems confirm that federation is substantially more robust under strongly convex feasible regions. Finally, we evaluate a simple validation-based interpolation between local and federated DFFL models. This interpolation mitigates the theoretical tradeoff and reduces aggregate regret and worst-client harm in both synthetic experiments and a PJM energy-pricing case study.