# Topology-Guided Modular Actor-Critic Learning for Continuous Systems under Temporal Objectives

arXiv: https://arxiv.org/abs/2304.10041 · HTML: https://mlsanity.com/paper/2304.10041/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 20 Apr 2023.

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

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Bridging the Gap Between Value and Policy Based Reinforcement Learning](https://mlsanity.com/paper/1702.08892/) (2017)
- [Reinforcement Learning for Temporal Logic Control Synthesis with Probabilistic Satisfaction Guarantees](https://mlsanity.com/paper/1909.05304/) (2019)
- [Compositional Reinforcement Learning from Logical Specifications](https://mlsanity.com/paper/2106.13906/) (2021)
- [Probably Approximately Correct MDP Learning and Control With Temporal Logic Constraints](https://mlsanity.com/paper/1404.7073/) (2014)
- [Certified Reinforcement Learning with Logic Guidance](https://mlsanity.com/paper/1902.00778/) (2019)
- [Modular Deep Reinforcement Learning with Temporal Logic Specifications](https://mlsanity.com/paper/1909.11591/) (2019)
- [Formal Controller Synthesis for Continuous-Space MDPs via Model-Free Reinforcement Learning](https://mlsanity.com/paper/2003.00712/) (2020)
- [Topological Value Iteration Algorithms](https://mlsanity.com/paper/1401.3910/) (2014)

## Abstract (arXiv)

We study formal policy synthesis for continuous-state stochastic systems under linear temporal logic specifications. The product of the system with the automaton of the specification has a hybrid state space with sparse rewards. We introduce a generalized optimal backup order, defined in reverse to a topological order over automaton states, that guides value backups and provably preserves optimality. We further present a model-free actor-critic algorithm whose policy evaluation solves a constrained optimization problem by the augmented Lagrangian method, yielding hyperparameter self-tuning, and prove its optimality and convergence in the tabular case. Since integer encodings of automaton states impose a spurious ordinal relationship on functions learned by one network, we dedicate a value and a policy network to each automaton state (modular learning). The algorithm matches or outperforms PPO, DQN, and A2C on CartPole, and on a Dubins car under a temporal specification the topological order and modular learning raise the success rate from 26.0% to 71.5%.