# Decision-Focused Federated Learning Under Heterogeneous Objectives and Constraints

arXiv: https://arxiv.org/abs/2604.20031 · HTML: https://mlsanity.com/paper/2604.20031/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 63 references that are in the map.
- First posted on arXiv 21 Apr 2026.

## Builds on (most cited first, 30 of 36)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Clustered Federated Learning: Model-Agnostic Distributed Multi-Task Optimization under Privacy Constraints](https://mlsanity.com/paper/1910.01991/) (2019)
- [Adaptive Personalized Federated Learning](https://mlsanity.com/paper/2003.13461/) (2020)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Three Approaches for Personalization with Applications to Federated Learning](https://mlsanity.com/paper/2002.10619/) (2020)
- [Tighter Theory for Local SGD on Identical and Heterogeneous Data](https://mlsanity.com/paper/1909.04746/) (2019)
- [Heterogeneous Federated Learning: State-of-the-art and Research Challenges](https://mlsanity.com/paper/2307.10616/) (2023)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems](https://mlsanity.com/paper/1911.10092/) (2019)
- [Generative Models for Effective ML on Private, Decentralized Datasets](https://mlsanity.com/paper/1911.06679/) (2019)
- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Generalization Bounds in the Predict-then-Optimize Framework](https://mlsanity.com/paper/1905.11488/) (2019)
- [Decision Trees for Decision-Making under the Predict-then-Optimize Framework](https://mlsanity.com/paper/2003.00360/) (2020)
- [A Survey on Heterogeneous Federated Learning](https://mlsanity.com/paper/2210.04505/) (2022)
- [Federated Learning with Domain Generalization](https://mlsanity.com/paper/2111.10487/) (2021)
- [Federated Deep Reinforcement Learning](https://mlsanity.com/paper/1901.08277/) (2019)
- [Risk Bounds and Calibration for a Smart Predict-then-Optimize Method](https://mlsanity.com/paper/2108.08887/) (2021)
- [Federated Multi-view Matrix Factorization for Personalized Recommendations](https://mlsanity.com/paper/2004.04256/) (2020)
- [Integrated Conditional Estimation-Optimization](https://mlsanity.com/paper/2110.12351/) (2021)

## Built on by (most cited first, 1 of 1)

- [FedRSPO+: A Heterogeneity-aware Algorithm for Decision-focused Federated Learning](https://mlsanity.com/paper/2610.09091/) (2026)

## Abstract (arXiv)

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.