# Tractable Reinforcement Learning for Full Class of Signal Temporal Logic Specifications Using Spatiotemporal Tube Reward

arXiv: https://arxiv.org/abs/2609.28396 · HTML: https://mlsanity.com/paper/2609.28396/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Safe and constrained RL, one of 15 directions in Deep reinforcement learning methods.
- Builds on 12 of its 19 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Placed in

- Deep reinforcement learning methods / [Safe and constrained RL](https://mlsanity.com/deeprl/safe-and-constrained-rl/)

## Builds on (most cited first, 12 of 12)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Q-Learning for Robust Satisfaction of Signal Temporal Logic Specifications](https://mlsanity.com/paper/1609.07409/) (2016)
- [Tractable Reinforcement Learning of Signal Temporal Logic Objectives](https://mlsanity.com/paper/2001.09467/) (2020)
- [Funnel-based Reward Shaping for Signal Temporal Logic Tasks in Reinforcement Learning](https://mlsanity.com/paper/2212.03181/) (2022)
- [Prescribed Performance Control for Signal Temporal Logic Specifications](https://mlsanity.com/paper/1703.07094/) (2017)
- [Does DQN Learn?](https://mlsanity.com/paper/2205.13617/) (2022)
- [Spatiotemporal Tubes for Temporal Reach-Avoid-Stay Tasks in Unknown Systems](https://mlsanity.com/paper/2411.13834/) (2024)
- [Approximation-free Control for Signal Temporal Logic Specifications using Spatiotemporal Tubes](https://mlsanity.com/paper/2505.05323/) (2025)
- [Prescribed Performance Control of Unknown Euler-Lagrange Systems Under Input Constraints](https://mlsanity.com/paper/2507.01426/) (2025)
- [Control Barrier Functions for the Full Class of Signal Temporal Logic Tasks using Spatiotemporal Tubes](https://mlsanity.com/paper/2510.19595/) (2025)
- [Temporal Reach-Avoid-Stay Control for Differential Drive Systems via Spatiotemporal Tubes](https://mlsanity.com/paper/2512.05495/) (2025)
- [Learning Spatiotemporal Tubes for Full Class of Signal Temporal Logic Tasks for Control of Unknown Systems under Input Constraints](https://mlsanity.com/paper/2607.07136/) (2026)

## Abstract (arXiv)

This paper addresses the control problem for robotic systems, including non-holonomic and underactuated platforms operating under unknown dynamics and strict actuator limits to satisfy complex high-level specifications. We denote these high-level specifications using Signal Temporal Logic (STL) and propose a novel time-aware Reinforcement Learning (RL) framework that leverages the geometric properties of Spatiotemporal Tubes (STTs). While traditional analytical STT controllers often struggle to enforce input constraints, and existing RL approaches rely on memory-intensive state history, our method natively overcomes both limitations. By mapping the logical and temporal complexities of the full class of STL into time-varying geometric boundaries, we directly constrain the multidimensional system state without relying on scalar robustness metrics. Augmenting the state space with time, we train a time-aware Soft Actor-Critic (SAC) agent using a continuous, geometry-aware reward function that eliminates the need to explicitly evaluate complex logical semantics during execution. The proposed framework offers a history-free, computationally efficient approach to learn continuous control policies that ensure robust satisfaction of specifications while strictly adhering to system input constraints.