# Cost-Driven Representation Learning for Linear Quadratic Gaussian Control: Part II

arXiv: https://arxiv.org/abs/2603.07437 · HTML: https://mlsanity.com/paper/2603.07437/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 38 references that are in the map.
- First posted on arXiv 8 Mar 2026.

## Builds on (most cited first, 26 of 26)

- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [Learning Invariant Representations for Reinforcement Learning without Reconstruction](https://mlsanity.com/paper/2006.10742/) (2020)
- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [Mastering Atari Games with Limited Data](https://mlsanity.com/paper/2111.00210/) (2021)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Value Prediction Network](https://mlsanity.com/paper/1707.03497/) (2017)
- [Low-rank Solutions of Linear Matrix Equations via Procrustes Flow](https://mlsanity.com/paper/1507.03566/) (2015)
- [Non-asymptotic Identification of LTI Systems from a Single Trajectory](https://mlsanity.com/paper/1806.05722/) (2018)
- [Approximate information state for approximate planning and reinforcement learning in partially observed systems](https://mlsanity.com/paper/2010.08843/) (2020)
- [Learning Linear Dynamical Systems with Semi-Parametric Least Squares](https://mlsanity.com/paper/1902.00768/) (2019)
- [Learning Task Informed Abstractions](https://mlsanity.com/paper/2106.15612/) (2021)
- [Statistical Learning Theory for Control: A Finite Sample Perspective](https://mlsanity.com/paper/2209.05423/) (2022)
- [Learning without Concentration](https://mlsanity.com/paper/1401.0304/) (2014)
- [Logarithmic Regret Bound in Partially Observable Linear Dynamical Systems](https://mlsanity.com/paper/2003.11227/) (2020)
- [Bootstrapping Upper Confidence Bound](https://mlsanity.com/paper/1906.05247/) (2019)
- [Learning the Linear Quadratic Regulator from Nonlinear Observations](https://mlsanity.com/paper/2010.03799/) (2020)
- [Sharper Sub-Weibull Concentrations](https://mlsanity.com/paper/2102.02450/) (2021)
- [Time varying regression with hidden linear dynamics](https://mlsanity.com/paper/2112.14862/) (2021)
- [Cost-Driven Representation Learning for Linear Quadratic Gaussian Control: Part I](https://mlsanity.com/paper/2212.14511/) (2022)

## Abstract (arXiv)

We study the problem of state representation learning for control from partial and potentially high-dimensional observations. We approach this problem via cost-driven state representation learning, in which we learn a dynamical model in a latent state space by predicting cumulative costs. In particular, we establish finite-sample guarantees on finding a near-optimal representation function and a near-optimal controller using the learned latent model for infinite-horizon time-invariant Linear Quadratic Gaussian (LQG) control. We study two approaches to cost-driven representation learning, which differ in whether the transition function of the latent state is learned explicitly or implicitly. The first approach has also been investigated in Part I of this work, for finite-horizon time-varying LQG control. The second approach closely resembles MuZero, a recent breakthrough in empirical reinforcement learning, in that it learns latent dynamics implicitly by predicting cumulative costs. A key technical contribution of this Part II is to prove persistency of excitation for a new stochastic process that arises from the analysis of quadratic regression in our approach, and may be of independent interest.