Topological Guided Actor-Critic Modular Learning of Continuous Systems with Temporal Objectives

Abstract: This work investigates the formal policy synthesis of continuous-state stochastic dynamic systems given high-level specifications in linear temporal logic. To learn an optimal policy that maximizes the satisfaction probability, we take a product between a dynamic system and the translated automaton to construct a product system on which we solve an optimal planning problem. Since this product system has a hybrid product state space that results in reward sparsity, we introduce a generalized optimal backup order, in reverse to the topological order, to guide the value backups and accelerate the learning process. We provide the optimality proof for using the generalized optimal backup order in this optimal planning problem. Further, this paper presents an actor-critic reinforcement learning algorithm when topological order applies. This algorithm leverages advanced mathematical techniques and enjoys the property of hyperparameter self-tuning. We provide proof of the optimality and convergence of our proposed reinforcement learning algorithm. We use neural networks to approximate the value function and policy function for hybrid product state space. Furthermore, we observe that assigning integer numbers to automaton states can rank the value or policy function approximated by neural networks. To break the ordinal relationship, we use an individual neural network for each automaton state's value (policy) function, termed modular learning. We conduct two experiments. First, to show the efficacy of our reinforcement learning algorithm, we compare it with baselines on a classic control task, CartPole. Second, we demonstrate the empirical performance of our formal policy synthesis framework on motion planning of a Dubins car with a temporal specification.