# Multitask LQG Control: Performance and Generalization Bounds

arXiv: https://arxiv.org/abs/2604.16730 · HTML: https://mlsanity.com/paper/2604.16730/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 23 of its 39 references that are in the map.
- First posted on arXiv 17 Apr 2026.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 23 of 23)

- [Deep Reinforcement Learning for Autonomous Driving: A Survey](https://mlsanity.com/paper/2002.00444/) (2020)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [Derivative-Free Methods for Policy Optimization: Guarantees for Linear Quadratic Systems](https://mlsanity.com/paper/1812.08305/) (2018)
- [Convergence and sample complexity of gradient methods for the model-free linear quadratic regulator problem](https://mlsanity.com/paper/1912.11899/) (2019)
- [Generalization Bounds for Meta-Learning via PAC-Bayes and Uniform Stability](https://mlsanity.com/paper/2102.06589/) (2021)
- [Analysis of the Optimization Landscape of Linear Quadratic Gaussian (LQG) Control](https://mlsanity.com/paper/2102.04393/) (2021)
- [Model-free Learning with Heterogeneous Dynamical Systems: A Federated LQR Approach](https://mlsanity.com/paper/2308.11743/) (2023)
- [Meta-Learning Linear Quadratic Regulators: A Policy Gradient MAML Approach for Model-free LQR](https://mlsanity.com/paper/2401.14534/) (2024)
- [Learning over All Stabilizing Nonlinear Controllers for a Partially-Observed Linear System](https://mlsanity.com/paper/2112.04219/) (2021)
- [A Theoretical Understanding of Gradient Bias in Meta-Reinforcement Learning](https://mlsanity.com/paper/2112.15400/) (2021)
- [Imitation and Transfer Learning for LQG Control](https://mlsanity.com/paper/2303.09002/) (2023)
- [Convergence and Sample Complexity of Policy Gradient Methods for Stabilizing Linear Systems](https://mlsanity.com/paper/2205.14335/) (2022)
- [Coreset-Based Task Selection for Sample-Efficient Meta-Reinforcement Learning](https://mlsanity.com/paper/2502.02332/) (2025)
- [Globally Convergent Policy Gradient Methods for Linear Quadratic Control of Partially Observed Systems](https://mlsanity.com/paper/2211.04051/) (2022)
- [Policy Gradient for LQR with Domain Randomization](https://mlsanity.com/paper/2503.24371/) (2025)
- [Asynchronous Heterogeneous Linear Quadratic Regulator Design](https://mlsanity.com/paper/2404.09061/) (2024)
- [Rate-Optimal Non-Asymptotics for the Quadratic Prediction Error Method](https://mlsanity.com/paper/2404.07937/) (2024)
- [Output-feedback Synthesis Orbit Geometry: Quotient Manifolds and LQG Direct Policy Optimization](https://mlsanity.com/paper/2403.17157/) (2024)
- [Layered Multirate Control of Constrained Linear Systems](https://mlsanity.com/paper/2504.10461/) (2025)
- [Policy Gradient Bounds in Multitask LQR](https://mlsanity.com/paper/2509.19266/) (2025)
- [Probabilistic Performance Guarantees for Multi-Task Reinforcement Learning](https://mlsanity.com/paper/2602.02098/) (2026)
- [Generalizable Optimal Control with Transformers: One Policy Across Diverse Systems](https://mlsanity.com/paper/2603.14910/) (2026)

## Built on by (most cited first, 1 of 1)

- [Why Does Agentic Safety Fail to Generalize Across Tasks?](https://mlsanity.com/paper/2605.06992/) (2026)

## Abstract (arXiv)

We study multitask learning for stochastic and partially observed control systems, focusing on the linear quadratic Gaussian (LQG) problem. Our goal is to learn a common stabilizing controller that generalizes across a distribution of systems and objectives. To this end, we leverage a history-dependent lifting that recasts the multitask LQG problem into an equivalent high-dimensional multitask LQR problem, allowing for the analysis of policy gradient methods. We show that learning a common lifted controller induces a heterogeneity bias which we characterize via a "bisimulation function". We establish performance and generalization guarantees that explicitly depend on such bisimulation-based heterogeneity measures. For model-free, we demonstrate that multitask learning reduces policy gradient estimation variance proportionally to the number of tasks in the training set.