# Scalar Federated Learning for Linear Quadratic Regulator

arXiv: https://arxiv.org/abs/2604.05088 · HTML: https://mlsanity.com/paper/2604.05088/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 29 references that are in the map.
- First posted on arXiv 6 Apr 2026.

## Builds on (most cited first, 20 of 20)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Challenges of Real-World Reinforcement Learning](https://mlsanity.com/paper/1904.12901/) (2019)
- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Federated Reinforcement Learning: Techniques, Applications, and Open Challenges](https://mlsanity.com/paper/2108.11887/) (2021)
- [Derivative-Free Methods for Policy Optimization: Guarantees for Linear Quadratic Systems](https://mlsanity.com/paper/1812.08305/) (2018)
- [LQR through the Lens of First Order Methods: Discrete-time Case](https://mlsanity.com/paper/1907.08921/) (2019)
- [Can Forward Gradient Match Backpropagation?](https://mlsanity.com/paper/2306.06968/) (2023)
- [Model-free Learning with Heterogeneous Dynamical Systems: A Federated LQR Approach](https://mlsanity.com/paper/2308.11743/) (2023)
- [Global Convergence of Policy Gradient Primal-dual Methods for Risk-constrained LQRs](https://mlsanity.com/paper/2104.04901/) (2021)
- [Federated Learning Using Variance Reduced Stochastic Gradient for Probabilistically Activated Agents](https://mlsanity.com/paper/2210.14362/) (2022)
- [Projected Forward Gradient-Guided Frank-Wolfe Algorithm via Variance Reduction](https://mlsanity.com/paper/2403.12511/) (2024)
- [Data-driven Optimal Filtering for Linear Systems with Unknown Noise Covariances](https://mlsanity.com/paper/2305.17836/) (2023)
- [Policy Optimization in Control: Geometry and Algorithmic Implications](https://mlsanity.com/paper/2406.04243/) (2024)
- [FedMPDD: Communication-Efficient Federated Learning with Privacy Preservation Attributes via Projected Directional Derivative](https://mlsanity.com/paper/2512.20814/) (2025)
- [Data-Driven Structured Policy Iteration for Homogeneous Distributed Systems](https://mlsanity.com/paper/2103.11572/) (2021)
- [Harnessing Data from Clustered LQR Systems: Personalized and Collaborative Policy Optimization](https://mlsanity.com/paper/2511.17489/) (2025)

## Abstract (arXiv)

We propose ScalarFedLQR, a communication-efficient federated algorithm for model-free learning of a common policy in linear quadratic regulator (LQR) control of cooperative agents. The method builds on a decomposed projected gradient mechanism, in which each agent communicates only a scalar projection of a local zeroth-order gradient estimate. The server aggregates these scalar messages to reconstruct a global descent direction, reducing per-agent uplink communication from O(d) to O(1), independent of the policy dimension. Crucially, the projection-induced approximation error diminishes as the number of participating agents increases, yielding a favorable scaling law: larger fleets enable more accurate gradient recovery, admit larger stepsizes, and achieve faster linear convergence despite high dimensionality. Under standard regularity conditions for homogeneous agents, all iterates remain stabilizing and the average LQR cost decreases linearly fast. Numerical results demonstrate performance comparable to full-gradient federated LQR with substantially reduced communication, even for heterogeneous (but similar) agents.