# A Locally Penalized Cross-Estimate Federated Method with Guarantees for Constrained Personalized Learning

arXiv: https://arxiv.org/abs/2603.19617 · HTML: https://mlsanity.com/paper/2603.19617/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 20 references that are in the map.
- First posted on arXiv 20 Mar 2026.

## Builds on (most cited first, 14 of 14)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Personalized Federated Learning using Hypernetworks](https://mlsanity.com/paper/2103.04628/) (2021)
- [Federated Composite Optimization](https://mlsanity.com/paper/2011.08474/) (2020)
- [Flow-FL: Data-Driven Federated Learning for Spatio-Temporal Predictions in Multi-Robot Systems](https://mlsanity.com/paper/2010.08595/) (2020)
- [Federated Learning with Convex Global and Local Constraints](https://mlsanity.com/paper/2310.10117/) (2023)
- [Geometric Convergence of Distributed Heavy-Ball Nash Equilibrium Algorithm over Time-Varying Digraphs with Unconstrained Actions](https://mlsanity.com/paper/2303.16385/) (2023)
- [Projected Push-Pull For Distributed Constrained Optimization Over Time-Varying Directed Graphs (extended version)](https://mlsanity.com/paper/2310.06223/) (2023)
- [Self-tuned Regularized Federated Methods with Guarantees for Optimal Solution Selection](https://mlsanity.com/paper/2503.08634/) (2025)

## Abstract (arXiv)

Federated learning (FL) is a communication-efficient framework for solving distributed optimization problems. Standard FL methods aggregate local updates into a single global model that is shared by all agents, effectively imposing consensus. Under heterogeneous local constraints, however, a common feasible model may be overly restrictive or may not exist. Existing constrained FL methods largely retain this shared-model structure and therefore do not directly address personalization under heterogeneous agent-specific feasible sets. We study a constrained personalized FL problem that assigns a distinct feasible model to each agent while coupling the models through a collaborative objective. We propose Locally Penalized Cross-Estimate Federated Averaging (PCE-FedAvg), where each agent maintains a multi-block vector containing its own model and estimates of the other agents' models while applying the feasibility penalty only locally to its own block. The server aggregates corresponding blocks separately, thereby preserving personalization without requiring agents to explicitly disclose their local constraint sets. For any ε>0, we establish finite-time upper and lower suboptimality bounds and agent-wise squared infeasibility bounds, yielding communication complexities of O(ε-2) and O(ε-1), respectively. Experiments on MNIST and CIFAR-10 support our theoretical results.