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Reinforcement Learning Using known Invariances

arXiv 2511.03473 ↗First posted 5 Nov 2025cs.LGcited by 0

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Abstract (arXiv)

In many real-world reinforcement learning (RL) problems, the environment exhibits inherent symmetries that can be exploited to improve learning efficiency. This paper develops a theoretical and algorithmic framework for incorporating known group symmetries into kernel-based RL. We propose a symmetry-aware variant of optimistic least-squares value iteration (LSVI), which leverages invariant kernels to encode invariance in both rewards and transition dynamics. Our analysis establishes new bounds on the maximum information gain and covering numbers for invariant RKHSs, explicitly quantifying the sample efficiency gains from symmetry. Empirical results on a customized Frozen Lake environment and a 2D placement design problem confirm the theoretical improvements, demonstrating that symmetry-aware RL achieves significantly better performance than their standard kernel counterparts. These findings highlight the value of structural priors in designing more sample-efficient reinforcement learning algorithms.

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References · 40

  1. 2018QT-Opt: Scalable Deep Reinforcement Learning for Vision-Based Robotic Manipulationcited by 730
  2. 2020Image Augmentation Is All You Need: Regularizing Deep Reinforcement Learning from Pixelscited by 573
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  8. 2019Reinforcement Learning in Feature Space: Matrix Bandit, Kernels, and Regret Boundcited by 199
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  10. 2021High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspacescited by 139
  11. 2020MDP Homomorphic Networks: Group Symmetries in Reinforcement Learningcited by 133
  12. 2019Network Randomization: A Simple Technique for Generalization in Deep Reinforcement Learningcited by 102
28 more
  1. 2019Frequentist Regret Bounds for Randomized Least-Squares Value Iterationcited by 100
  2. 2021Learning with invariances in random features and kernel modelscited by 89
  3. 2017Uncertainty-Aware Reinforcement Learning for Collision Avoidancecited by 86
  4. 2021S4RL: Surprisingly Simple Self-Supervision for Offline Reinforcement Learningcited by 85
  5. 2022SO(2)-Equivariant Reinforcement Learningcited by 79
  6. 2020Meta-Learning Symmetries by Reparameterizationcited by 75
  7. 2019Worst-Case Regret Bounds for Exploration via Randomized Value Functionscited by 57
  8. 2020Symmetry-Aware Actor-Critic for 3D Molecular Designcited by 55
  9. 2018Learning Invariances using the Marginal Likelihoodcited by 51
  10. 2020A Unifying View of Optimism in Episodic Reinforcement Learningcited by 50
  11. 2019PIC: Permutation Invariant Critic for Multi-Agent Deep Reinforcement Learningcited by 46
  12. 2019On Online Learning in Kernelized Markov Decision Processescited by 32
  13. 2021Koopman Q-learning: Offline Reinforcement Learning via Symmetries of Dynamicscited by 27
  14. 2023The Exact Sample Complexity Gain from Invariances for Kernel Regressioncited by 27
  15. 2021Multi-Agent MDP Homomorphic Networkscited by 24
  16. 2020Kernel-Based Reinforcement Learning: A Finite-Time Analysiscited by 23
  17. 2023Kernelized Reinforcement Learning with Order Optimal Regret Boundscited by 20
  18. 2024Equivariant Reinforcement Learning under Partial Observabilitycited by 17
  19. 2022Equivariant Networks for Zero-Shot Coordinationcited by 16
  20. 2021On the Sample Complexity of Learning under Invariance and Geometric Stabilitycited by 13
  21. 2023On Robot Grasp Learning Using Equivariant Modelscited by 12
  22. 2023Leveraging Partial Symmetry for Multi-Agent Reinforcement Learningcited by 11
  23. 2023ESP: Exploiting Symmetry Prior for Multi-Agent Reinforcement Learningcited by 9
  24. 2024Boosting Sample Efficiency and Generalization in Multi-agent Reinforcement Learning via Equivariancecited by 9
  25. 2025Expected Return Symmetriescited by 5
  26. 2023rm E(3)-Equivariant Actor-Critic Methods for Cooperative Multi-Agent Reinforcement Learningcited by 4
  27. 2024Sample-efficient Bayesian Optimisation Using Known Invariancescited by 4
  28. 2024On Improved Regret Bounds In Bayesian Optimization with Gaussian Noisecited by 1

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