We consider the problem of aggregating models learned from sequestered, possibly heterogeneous datasets.

Personalized federated learning with differential privacy has been considered a feasible solution to address non-IID distribution of data and privacy leakage risks. However, current personalized federated learning methods suffer from inflexible personalization and convergence difficulties due to two main factors: 1) Firstly, we observe that the prevailing personalization methods mainly achieve this by personalizing a fixed portion of the model, which lacks flexibility.

We propose Federated Preconditioned Mixing (FedPM), a novel Federated Learning (FL) method that leverages second-order optimization. Prior methods--such as LocalNewton, LTDA, and FedSophia--have incorporated second-order optimization in FL by performing iterative local updates on clients and applying simple mixing of local parameters on the server. However, these methods often suffer from drift in local preconditioners, which significantly disrupts the convergence of parameter training, particularly in heterogeneous data settings. To overcome this issue, we refine the update rules by decomposing the ideal second-order update--computed using globally preconditioned global gradients--into parameter mixing on the server and local parameter updates on clients. As a result, our FedPM introduces preconditioned mixing of local parameters on the server, effectively mitigating drift in local preconditioners. We provide a theoretical convergence analysis demonstrating a superlinear rate for strongly convex objectives in scenarios involving a single local update. To demonstrate the practical benefits of FedPM, we conducted extensive experiments. The results showed significant improvements with FedPM in the test accuracy compared to conventional methods incorporating simple mixing, fully leveraging the potential of second-order optimization.

We consider the problem of aggregating models learned from sequestered, possibly heterogeneous datasets.

To address this, we explore partially local federated learning.

We propose Bayesian Hierarchical Invariant Prediction (BHIP) reframing Invariant Causal Prediction (ICP) through the lens of Hierarchical Bayes. We leverage the hierarchical structure to explicitly test invariance of causal mechanisms under heterogeneous data, resulting in improved computational scalability for a larger number of predictors compared to ICP. Moreover, given its Bayesian nature BHIP enables the use of prior information. In this paper, we test two sparsity inducing priors: horseshoe and spike-and-slab, both of which allow us a more reliable identification of causal features. We test BHIP in synthetic and real-world data showing its potential as an alternative inference method to ICP.

Federated Learning (FL) aims to train models across decentralized clients or devices holding local data without the need for centralized data collection, thus enhancing data privacy and security. However, achieving both generalization and personalization in heterogeneous settings remains a significant challenge. To address this, we introduce FedOT, a novel approach that leverages black-box foundation models. FedOT shares only a global task-dependent classifier across clients while locally adapting features through orthogonal transformations. By enforcing orthogonality, FedOT mitigates gradient conflicts across diverse clients, preserves semantic integrity, and achieves robust performance even in the presence of substantial data heterogeneity. The strategy of combining global and local parameters enables a more balanced approach for both generalization and personalization, outperforming baseline FL methods across multiple benchmarks. Furthermore, our extensive analysis confirms that joint optimization of global classifiers and local orthogonal transformations yields superior performance and suggests broader applicability.