# Automatic feature identification in least-squares policy iteration using the Koopman operator framework

arXiv: https://arxiv.org/abs/2603.26464 · HTML: https://mlsanity.com/paper/2603.26464/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 5 of its 13 references that are in the map.
- First posted on arXiv 27 Mar 2026.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 5 of 5)

- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Linearly-Recurrent Autoencoder Networks for Learning Dynamics](https://mlsanity.com/paper/1712.01378/) (2017)
- [Forecasting Sequential Data using Consistent Koopman Autoencoders](https://mlsanity.com/paper/2003.02236/) (2020)
- [Finite-data error bounds for Koopman-based prediction and control](https://mlsanity.com/paper/2108.07102/) (2021)
- [Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems](https://mlsanity.com/paper/2308.10697/) (2023)

## Abstract (arXiv)

In this paper, we present a Koopman autoencoder-based least-squares policy iteration (KAE-LSPI) algorithm in reinforcement learning (RL). The KAE-LSPI algorithm is based on reformulating the so-called least-squares fixed-point approximation method in terms of extended dynamic mode decomposition (EDMD), thereby enabling automatic feature learning via the Koopman autoencoder (KAE) framework. The approach is motivated by the lack of a systematic choice of features or kernels in linear RL techniques. We compare the KAE-LSPI algorithm with two previous works, the classical least-squares policy iteration (LSPI) and the kernel-based least-squares policy iteration (KLSPI), using stochastic chain walk and inverted pendulum control problems as examples. Unlike previous works, no features or kernels need to be fixed a priori in our approach. Empirical results show the number of features learned by the KAE technique remains reasonable compared to those fixed in the classical LSPI algorithm. The convergence to an optimal or a near-optimal policy is also comparable to the other two methods.