Convex Optimization-based Policy Adaptation to Compensate for Distributional Shifts

Many real-world systems often involve physical components or operating environments with highly nonlinear and uncertain dynamics. A number of different control algorithms can be used to design optimal controllers for such systems, assuming a reasonably high-fidelity model of the actual system. However, the assumptions made on the stochastic dynamics of the model when designing the optimal controller may no longer be valid when the system is deployed in the real-world. The problem addressed by this paper is the following: Suppose we obtain an optimal trajectory by solving a control problem in the training environment, how do we ensure that the real-world system trajectory tracks this optimal trajectory with minimal amount of error in a deployment environment. In other words, we want to learn how we can adapt an optimal trained policy to distribution shifts in the environment. Distribution shifts are problematic in safety-critical systems, where a trained policy may lead to unsafe outcomes during deployment. We show that this problem can be cast as a nonlinear optimization problem that could be solved using heuristic method such as particle swarm optimization (PSO). However, if we instead consider a convex relaxation of this problem, we can learn policies that track the optimal trajectory with much better error performance, and faster computation times. We demonstrate the efficacy of our approach on tracking an optimal path using a Dubin's car model, and collision avoidance using both a linear and nonlinear model for adaptive cruise control

Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inference

We consider data-driven reachability analysis of discrete-time stochastic dynamical systems using conformal inference. We assume that we are not provided with a symbolic representation of the stochastic system, but instead have access to a dataset of $K$-step trajectories. The reachability problem is to construct a probabilistic flowpipe such that the probability that a $K$-step trajectory can violate the bounds of the flowpipe does not exceed a user-specified failure probability threshold. The key ideas in this paper are: (1) to learn a surrogate predictor model from data, (2) to perform reachability analysis using the surrogate model, and (3) to quantify the surrogate model's incurred error using conformal inference in order to give probabilistic reachability guarantees. We focus on learning-enabled control systems with complex closed-loop dynamics that are difficult to model symbolically, but where state transition pairs can be queried, e.g., using a simulator. We demonstrate the applicability of our method on examples from the domain of learning-enabled cyber-physical systems