Scaling Learning-based Policy Optimization for Temporal Logic Tasks by Controller Network Dropout

This article introduces a model-based approach for training feedback controllers for an autonomous agent operating in a highly non-linear (albeit deterministic) environment. We desire the trained policy to ensure that the agent satisfies specific task objectives and safety constraints, both expressed in Discrete-Time Signal Temporal Logic (DT-STL). One advantage for reformulation of a task via formal frameworks, like DT-STL, is that it permits quantitative satisfaction semantics. In other words, given a trajectory and a DT-STL formula, we can compute the robustness , which can be interpreted as an approximate signed distance between the trajectory and the set of trajectories satisfying the formula. We utilize feedback control, and we assume a feed forward neural network for learning the feedback controller. We show how this learning problem is similar to training recurrent neural networks (RNNs), where the number of recurrent units is proportional to the temporal horizon of the agent’s task objectives. This poses a challenge: RNNs are susceptible to vanishing and exploding gradients, and naïve gradient descent-based strategies to solve long-horizon task objectives thus suffer from the same problems. To address this challenge, we introduce a novel gradient approximation algorithm based on the idea of dropout or gradient sampling. One of the main contributions is the notion of controller network dropout , where we approximate the NN controller in several timesteps in the task horizon by the control input obtained using the controller in a previous training step. We show that our control synthesis methodology can be quite helpful for stochastic gradient descent to converge with less numerical issues, enabling scalable back-propagation over longer time horizons and trajectories over higher-dimensional state spaces. We demonstrate the efficacy of our approach on various motion planning applications requiring complex spatio-temporal and sequential tasks ranging over thousands of timesteps.