# Expressive Temporal Specifications for Reward Monitoring

arXiv: https://arxiv.org/abs/2511.12808 · HTML: https://mlsanity.com/paper/2511.12808/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Interpretable and logic-guided RL, one of 15 directions in Deep reinforcement learning methods.
- Builds on 15 of its 53 references that are in the map.
- First posted on arXiv 16 Nov 2025.

## 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, 15 of 15)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (2017)
- [Revisiting the Arcade Learning Environment: Evaluation Protocols and Open Problems for General Agents](https://mlsanity.com/paper/1709.06009/) (2017)
- [Reward Machines: Exploiting Reward Function Structure in Reinforcement Learning](https://mlsanity.com/paper/2010.03950/) (2020)
- [Reinforcement Learning With Temporal Logic Rewards](https://mlsanity.com/paper/1612.03471/) (2016)
- [AI Safety Gridworlds](https://mlsanity.com/paper/1711.09883/) (2017)
- [Foundations for Restraining Bolts: Reinforcement Learning with LTLf/LDLf restraining specifications](https://mlsanity.com/paper/1807.06333/) (2018)
- [A Composable Specification Language for Reinforcement Learning Tasks](https://mlsanity.com/paper/2008.09293/) (2020)
- [A Learning Based Approach to Control Synthesis of Markov Decision Processes for Linear Temporal Logic Specifications](https://mlsanity.com/paper/1409.5486/) (2014)
- [Interpretable Reward Redistribution in Reinforcement Learning: A Causal Approach](https://mlsanity.com/paper/2305.18427/) (2023)
- [Learning Robust Reward Machines from Noisy Labels](https://mlsanity.com/paper/2408.14871/) (2024)
- [Counting Reward Automata: Sample Efficient Reinforcement Learning Through the Exploitation of Reward Function Structure](https://mlsanity.com/paper/2312.11364/) (2023)
- [FORM: Learning Expressive and Transferable First-Order Logic Reward Machines](https://mlsanity.com/paper/2501.00364/) (2024)
- [Being correct is not enough: efficient verification using robust linear temporal logic](https://mlsanity.com/paper/2102.11991/) (2021)

## Abstract (arXiv)

Specifying informative and dense reward functions remains a pivotal challenge in Reinforcement Learning, as it directly affects the efficiency of agent training. In this work, we harness the expressive power of quantitative Linear Temporal Logic on finite traces ((LTLf[F])) to synthesize reward monitors that generate a dense stream of rewards for runtime-observable state trajectories. By providing nuanced feedback during training, these monitors guide agents toward optimal behaviour and help mitigate the well-known issue of sparse rewards under long-horizon decision making, which arises under the Boolean semantics dominating the current literature. Our framework is algorithm-agnostic and only relies on a state labelling function, and naturally accommodates specifying non-Markovian properties. Empirical results show that our quantitative monitors consistently subsume and, depending on the environment, outperform Boolean monitors in maximizing a quantitative measure of task completion and in reducing convergence time.