# Control Theoretic Analysis of Temporal Difference Learning

arXiv: https://arxiv.org/abs/2112.14417 · HTML: https://mlsanity.com/paper/2112.14417/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 39 references that are in the map.
- First posted on arXiv 29 Dec 2021.

## Builds on (most cited first, 6 of 6)

- [A Finite Time Analysis of Temporal Difference Learning With Linear Function Approximation](https://mlsanity.com/paper/1806.02450/) (2018)
- [Finite-Time Error Bounds For Linear Stochastic Approximation and TD Learning](https://mlsanity.com/paper/1902.00923/) (2019)
- [Target-Based Temporal Difference Learning](https://mlsanity.com/paper/1904.10945/) (2019)
- [Characterizing the Exact Behaviors of Temporal Difference Learning Algorithms Using Markov Jump Linear System Theory](https://mlsanity.com/paper/1906.06781/) (2019)
- [A Discrete-Time Switching System Analysis of Q-learning](https://mlsanity.com/paper/2102.08583/) (2021)
- [New Versions of Gradient Temporal Difference Learning](https://mlsanity.com/paper/2109.04033/) (2021)

## Abstract (arXiv)

The goal of this manuscript is to conduct a controltheoretic analysis of Temporal Difference (TD) learning algorithms. TD-learning serves as a cornerstone in the realm of reinforcement learning, offering a methodology for approximating the value function associated with a given policy in a Markov Decision Process. Despite several existing works that have contributed to the theoretical understanding of TD-learning, it is only in recent years that researchers have been able to establish concrete guarantees on its statistical efficiency. In this paper, we introduce a finite-time, control-theoretic framework for analyzing TD-learning, leveraging established concepts from the field of linear systems control. Consequently, this paper provides additional insights into the mechanics of TD learning and the broader landscape of reinforcement learning, all while employing straightforward analytical tools derived from control theory.