# Adaptive Control and Regret Minimization in Linear Quadratic Gaussian (LQG) Setting

arXiv: https://arxiv.org/abs/2003.05999 · HTML: https://mlsanity.com/paper/2003.05999/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Mar 2020.

## Built on by (most cited first, 4 of 4)

- [A New Approach to Learning Linear Dynamical Systems](https://mlsanity.com/paper/2301.09519/) (2023)
- [Regret-optimal Estimation and Control](https://mlsanity.com/paper/2106.12097/) (2021)
- [Regret Analysis of Learning-Based MPC with Partially-Unknown Cost Function](https://mlsanity.com/paper/2108.02307/) (2021)
- [Finite-time System Identification and Adaptive Control in Autoregressive Exogenous Systems](https://mlsanity.com/paper/2108.11959/) (2021)

## Abstract (arXiv)

We study the problem of adaptive control in partially observable linear quadratic Gaussian control systems, where the model dynamics are unknown a priori. We propose LqgOpt, a novel reinforcement learning algorithm based on the principle of optimism in the face of uncertainty, to effectively minimize the overall control cost. We employ the predictor state evolution representation of the system dynamics and deploy a recently proposed closed-loop system identification method, estimation, and confidence bound construction. LqgOpt efficiently explores the system dynamics, estimates the model parameters up to their confidence interval, and deploys the controller of the most optimistic model for further exploration and exploitation. We provide stability guarantees for LqgOpt and prove the regret upper bound of tildeO(√T) for adaptive control of linear quadratic Gaussian (LQG) systems, where T is the time horizon of the problem.