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#artificial intelligence Preprint Open access

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

Lening Li Zhentian Qian Jianan Xia Yawen Wang Zhongjing Li Qiren Geng Huasheng Zhang Liang Hu Qishuang Li Junqiang Lou
Sep 2026
Artificial Intelligence

Abstract

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%.

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