# Equivariant Ensembles and Regularization for Reinforcement Learning in Map-based Path Planning

arXiv: https://arxiv.org/abs/2403.12856 · HTML: https://mlsanity.com/paper/2403.12856/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 14 of its 22 references that are in the map.
- First posted on arXiv 19 Mar 2024.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 14 of 14)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Image Augmentation Is All You Need: Regularizing Deep Reinforcement Learning from Pixels](https://mlsanity.com/paper/2004.13649/) (2020)
- [Reinforcement Learning with Augmented Data](https://mlsanity.com/paper/2004.14990/) (2020)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning](https://mlsanity.com/paper/2006.16908/) (2020)
- [SO(2)-Equivariant Reinforcement Learning](https://mlsanity.com/paper/2203.04439/) (2022)
- [Residual Pathway Priors for Soft Equivariance Constraints](https://mlsanity.com/paper/2112.01388/) (2021)
- [Equivariant Q Learning in Spatial Action Spaces](https://mlsanity.com/paper/2110.15443/) (2021)
- [The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetry](https://mlsanity.com/paper/2211.09231/) (2022)
- [UAV Coverage Path Planning under Varying Power Constraints using Deep Reinforcement Learning](https://mlsanity.com/paper/2003.02609/) (2020)
- [Symmetry-aware Reinforcement Learning for Robotic Assembly under Partial Observability with a Soft Wrist](https://mlsanity.com/paper/2402.18002/) (2024)
- [Learning to Recharge: UAV Coverage Path Planning through Deep Reinforcement Learning](https://mlsanity.com/paper/2309.03157/) (2023)

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

- [SE(3)-Equivariant Robot Learning and Control: A Tutorial Survey](https://mlsanity.com/paper/2503.09829/) (2025)
- [Coordinated Humanoid Robot Locomotion with Symmetry Equivariant Reinforcement Learning Policy](https://mlsanity.com/paper/2508.01247/) (2025)
- [Continuous World Coverage Path Planning for Fixed-Wing UAVs using Deep Reinforcement Learning](https://mlsanity.com/paper/2505.08382/) (2025)
- [Safe and Economical UAV Trajectory Planning in Low-Altitude Airspace: A Hybrid DRL-LLM Approach with Compliance Awareness](https://mlsanity.com/paper/2506.08532/) (2025)

## Abstract (arXiv)

In reinforcement learning (RL), exploiting environmental symmetries can significantly enhance efficiency, robustness, and performance. However, ensuring that the deep RL policy and value networks are respectively equivariant and invariant to exploit these symmetries is a substantial challenge. Related works try to design networks that are equivariant and invariant by construction, limiting them to a very restricted library of components, which in turn hampers the expressiveness of the networks. This paper proposes a method to construct equivariant policies and invariant value functions without specialized neural network components, which we term equivariant ensembles. We further add a regularization term for adding inductive bias during training. In a map-based path planning case study, we show how equivariant ensembles and regularization benefit sample efficiency and performance.