# Model-Based Reinforcement Learning Exploiting State-Action Equivalence

arXiv: https://arxiv.org/abs/1910.04077 · HTML: https://mlsanity.com/paper/1910.04077/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2019.

## Built on by (most cited first, 6 of 6)

- [Efficient Policy Iteration for Robust Markov Decision Processes via Regularization](https://mlsanity.com/paper/2205.14327/) (2022)
- [J4R: Learning to Judge with Equivalent Initial State Group Relative Policy Optimization](https://mlsanity.com/paper/2505.13346/) (2025)
- [An Efficient Solution to s-Rectangular Robust Markov Decision Processes](https://mlsanity.com/paper/2301.13642/) (2023)
- [Provably Efficient Exploration in Reward Machines with Low Regret](https://mlsanity.com/paper/2412.19194/) (2024)
- [Using Forwards-Backwards Models to Approximate MDP Homomorphisms](https://mlsanity.com/paper/2209.06356/) (2022)
- [How to Shrink Confidence Sets for Many Equivalent Discrete Distributions?](https://mlsanity.com/paper/2407.15662/) (2024)

## Abstract (arXiv)

Leveraging an equivalence property in the state-space of a Markov Decision Process (MDP) has been investigated in several studies. This paper studies equivalence structure in the reinforcement learning (RL) setup, where transition distributions are no longer assumed to be known. We present a notion of similarity between transition probabilities of various state-action pairs of an MDP, which naturally defines an equivalence structure in the state-action space. We present equivalence-aware confidence sets for the case where the learner knows the underlying structure in advance. These sets are provably smaller than their corresponding equivalence-oblivious counterparts. In the more challenging case of an unknown equivalence structure, we present an algorithm called ApproxEquivalence that seeks to find an (approximate) equivalence structure, and define confidence sets using the approximate equivalence. To illustrate the efficacy of the presented confidence sets, we present C-UCRL, as a natural modification of UCRL2 for RL in undiscounted MDPs. In the case of a known equivalence structure, we show that C-UCRL improves over UCRL2 in terms of regret by a factor of √SA/C, in any communicating MDP with S states, A actions, and C classes, which corresponds to a massive improvement when C ll SA. To the best of our knowledge, this is the first work providing regret bounds for RL when an equivalence structure in the MDP is efficiently exploited. In the case of an unknown equivalence structure, we show through numerical experiments that C-UCRL combined with ApproxEquivalence outperforms UCRL2 in ergodic MDPs.