解决多方协作优化中目标与约束差异问题,提升联邦学习决策效果。
Decision-Focused Federated Learning Under Heterogeneous Objectives and Constraints

- 基于SPO+损失,分离目标与可行集的异质性影响。
- 强凸可行域下模型更稳定,联邦训练优势明显。
- 验证插值法有效降低最差客户端损失,适合实际应用。
我们研究决策导向的联邦学习(DFFL),在不交换原始数据的前提下,多个客户端协同训练用于下游线性优化问题的预测模型。除标准联邦学习中的数据异质性外,客户端还可能存在不同的目标函数和可行域。基于SPO+代理损失,我们推导出异质性边界,将目标偏移(通过成本向量距离衡量)与可行集偏移(通过支撑函数和形状距离项衡量)区分开来。对于一般紧致可行集,微小的目标扰动仍可能导致不可忽略的决策损失差异;而强凸可行域则能带来更紧致的稳定性边界。进一步将这些逐点边界扩展至局部与联邦模型的过失风险比较,表明当数据聚合的统计优势超过客户端特异性异质性惩罚时,联邦学习更具优势。在多面体和强凸问题上的计算实验表明,强凸可行域下联邦学习表现显著更鲁棒。最后,我们评估了一种简单的局部与联邦DFFL模型间的验证基插值方法。该插值缓解了理论权衡,在合成实验和PJM能源定价案例研究中均降低了总遗憾和最差客户端损害。
原文摘要 · Abstract (English)
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.
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