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.
There are two categories of methods in Federated Learning (FL) for joint training across multiple clients: (i) parallel FL (PFL), where clients train models in a parallel manner; and (ii) sequential FL (SFL), where clients train models in a sequential manner. In contrast to that of PFL, the convergence theory of SFL on heterogeneous data is still lacking. In this paper, we establish the convergence guarantees of SFL for strongly/general/non-convex objectives on heterogeneous data. The convergence guarantees of SFL are better than that of PFL on heterogeneous data with both full and partial client participation. Experimental results validate the counterintuitive analysis result that SFL outperforms PFL on extremely heterogeneous data in cross-device settings.
Scheduling clients for model training is critical in federated learning due to both data and system heterogeneity. Most previous works focus on the quality of the scheduled clients to achieve faster convergence, shorter wall-clock convergence time, or better average model performance. They rarely consider the diversity of clients, which is important to counter heterogeneity and improve performance for the worst-off clients. In this work, we advocate the use of determinantal point processes (DPPs) to model and enhance the diversity in client scheduling. We first design the kernel matrices of DPPs using gradient information and quality scores, which inherently enables a flexible quality-diversity trade-off. Applying fast MAP inference over DPPs, we propose Adaptive Determinantal Client Scheduling (ADCS) in FL. We further quantify the gradient approximation error of ADCS and develop convergence analysis for general biased client selection in FL with non-convex loss functions. We conduct comparative numerical experiments showing that ADCS outperforms state-of-the-art client scheduling algorithms, including both quality-based and diversity-based ones.
Federated bilevel optimization is widely used for nested learning problems across distributed clients, such as federated hyperparameter tuning and meta-learning under privacy and communication constraints. Most existing formulations assume fixed client data distributions, which can be violated by performativity, where deployed decisions reshape client behavior and data collection, inducing client-specific, decision-dependent distribution shift. We study federated bilevel performative prediction, where both upper-level (UL) and lower-level (LL) objectives are evaluated under client-dependent, decision-dependent distributions. We formalize the federated bilevel performatively stable (FBPS) point under a decoupled-risk perspective and provide sufficient conditions for its existence and uniqueness. We then develop two federated methods to compute the FBPS solution: FBi-RRM, which converges linearly under a contraction condition, and FBi-SGD, a communication-efficient stochastic method based on federated hypergradient estimation with convergence guarantees under diminishing step sizes when sensitivities are sufficiently small. Experiments on strategic regression and meta strategic classification validate the predicted stability thresholds and demonstrate improved meta-generalization over non-performative baselines, and CNN-based classification further demonstrates the practical effectiveness of the proposed methods in nonconvex neural network settings.