# Neural Reward Machines

arXiv: https://arxiv.org/abs/2408.08677 · HTML: https://mlsanity.com/paper/2408.08677/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Interpretable and logic-guided RL, one of 15 directions in Deep reinforcement learning methods.
- Builds on 23 of its 36 references that are in the map.
- First posted on arXiv 16 Aug 2024.

## Placed in

- Deep reinforcement learning methods / [Interpretable and logic-guided RL](https://mlsanity.com/deeprl/interpretable-and-logic-guided-rl/)

## Builds on (most cited first, 23 of 23)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Recurrent World Models Facilitate Policy Evolution](https://mlsanity.com/paper/1809.01999/) (2018)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Reward Machines: Exploiting Reward Function Structure in Reinforcement Learning](https://mlsanity.com/paper/2010.03950/) (2020)
- [LTL2Action: Generalizing LTL Instructions for Multi-Task RL](https://mlsanity.com/paper/2102.06858/) (2021)
- [Foundations for Restraining Bolts: Reinforcement Learning with LTLf/LDLf restraining specifications](https://mlsanity.com/paper/1807.06333/) (2018)
- [Environment-Independent Task Specifications via GLTL](https://mlsanity.com/paper/1704.04341/) (2017)
- [Reinforcement Learning with Non-Markovian Rewards](https://mlsanity.com/paper/1912.02552/) (2019)
- [Neural-Symbolic Integration: A Compositional Perspective](https://mlsanity.com/paper/2010.11926/) (2020)
- [Modular Deep Reinforcement Learning for Continuous Motion Planning with Temporal Logic](https://mlsanity.com/paper/2102.12855/) (2021)
- [Encoding formulas as deep networks: Reinforcement learning for zero-shot execution of LTL formulas](https://mlsanity.com/paper/2006.01110/) (2020)
- [Induction and Exploitation of Subgoal Automata for Reinforcement Learning](https://mlsanity.com/paper/2009.03855/) (2020)
- [Active Finite Reward Automaton Inference and Reinforcement Learning Using Queries and Counterexamples](https://mlsanity.com/paper/2006.15714/) (2020)
- [Reinforcement Learning Based Temporal Logic Control with Maximum Probabilistic Satisfaction](https://mlsanity.com/paper/2010.06797/) (2020)
- [Specification Patterns for Robotic Missions](https://mlsanity.com/paper/1901.02077/) (2019)
- [Joint Learning of Reward Machines and Policies in Environments with Partially Known Semantics](https://mlsanity.com/paper/2204.11833/) (2022)
- [Markov Abstractions for PAC Reinforcement Learning in Non-Markov Decision Processes](https://mlsanity.com/paper/2205.01053/) (2022)
- [Noisy Symbolic Abstractions for Deep RL: A case study with Reward Machines](https://mlsanity.com/paper/2211.10902/) (2022)
- [Differentiable Rule Induction with Learned Relational Features](https://mlsanity.com/paper/2201.06515/) (2022)
- [Learning Finite Linear Temporal Logic Specifications with a Specialized Neural Operator](https://mlsanity.com/paper/2111.04147/) (2021)

## Built on by (most cited first, 7 of 7)

- [Shortcuts and Identifiability in Concept-based Models from a Neuro-Symbolic Lens](https://mlsanity.com/paper/2502.11245/) (2025)
- [Neuro-Symbolic Predictive Process Monitoring](https://mlsanity.com/paper/2509.00834/) (2025)
- [Ground-Compose-Reinforce: Grounding Language in Agentic Behaviours using Limited Data](https://mlsanity.com/paper/2507.10741/) (2025)
- [Grounding LTL Tasks in Sub-Symbolic RL Environments for Zero-Shot Generalization](https://mlsanity.com/paper/2602.09761/) (2026)
- [DeepDFA: Injecting Temporal Logic in Deep Learning for Sequential Subsymbolic Applications](https://mlsanity.com/paper/2602.03486/) (2026)
- [Jaxolotl: A Unified High-Performance Benchmark Suite for LTL-Based Multi-Task RL](https://mlsanity.com/paper/2609.38065/) (2026)
- [Neurosymbolic Learning of Interpretable World Models](https://mlsanity.com/paper/2610.19955/) (2026)

## Abstract (arXiv)

Non-markovian Reinforcement Learning (RL) tasks are very hard to solve, because agents must consider the entire history of state-action pairs to act rationally in the environment. Most works use symbolic formalisms (as Linear Temporal Logic or automata) to specify the temporally-extended task. These approaches only work in finite and discrete state environments or continuous problems for which a mapping between the raw state and a symbolic interpretation is known as a symbol grounding (SG) function. Here, we define Neural Reward Machines (NRM), an automata-based neurosymbolic framework that can be used for both reasoning and learning in non-symbolic non-markovian RL domains, which is based on the probabilistic relaxation of Moore Machines. We combine RL with semisupervised symbol grounding (SSSG) and we show that NRMs can exploit high-level symbolic knowledge in non-symbolic environments without any knowledge of the SG function, outperforming Deep RL methods which cannot incorporate prior knowledge. Moreover, we advance the research in SSSG, proposing an algorithm for analysing the groundability of temporal specifications, which is more efficient than baseline techniques of a factor 103.