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This work investigates the formal policy synthesis of continuous-statestochastic dynamic systems given high-level specifications in linear temporallogic. To learn an optimal policy that maximizes the satisfaction probability,we take a product between a dynamic system and the translated automaton toconstruct a product system on which we solve an optimal planning problem. Sincethis product system has a hybrid product state space that results in rewardsparsity, we introduce a generalized optimal backup order, in reverse to thetopological order, to guide the value backups and accelerate the learningprocess. We provide the optimality proof for using the generalized optimalbackup order in this optimal planning problem. Further, this paper presents anactor-critic reinforcement learning algorithm when topological order applies.This algorithm leverages advanced mathematical techniques and enjoys theproperty of hyperparameter self-tuning. We provide proof of the optimality andconvergence of our proposed reinforcement learning algorithm. We use neuralnetworks to approximate the value function and policy function for hybridproduct state space. Furthermore, we observe that assigning integer numbers toautomaton states can rank the value or policy function approximated by neuralnetworks. To break the ordinal relationship, we use an individual neuralnetwork for each automaton state's value (policy) function, termed modularlearning. We conduct two experiments. First, to show the efficacy of ourreinforcement learning algorithm, we compare it with baselines on a classiccontrol task, CartPole. Second, we demonstrate the empirical performance of ourformal policy synthesis framework on motion planning of a Dubins car with atemporal specification.

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