Safety Certificate against Latent Variables with Partially Unidentifiable Dynamics

Many systems contain latent variables that make their dynamics partially unidentifiable or cause distribution shifts in the observed statistics between offline and online data. However, existing control techniques often assume access to complete dynamics or perfect simulators with fully observable states, which are necessary to verify whether the system remains within a safe set (forward invariance) or safe actions are consistently feasible at all times. To address this limitation, we propose a technique for designing probabilistic safety certificates for systems with latent variables. A key technical enabler is the formulation of invariance conditions in probability space, which can be constructed using observed statistics in the presence of distribution shifts due to latent variables. We use this invariance condition to construct a safety certificate that can be implemented efficiently in real-time control. The proposed safety certificate can continuously find feasible actions that control long-term risk to stay within tolerance. Stochastic safe control and (causal) reinforcement learning have been studied in isolation until now. To the best of our knowledge, the proposed work is the first to use causal reinforcement learning to quantify long-term risk for the design of safety certificates. This integration enables safety certificates to efficiently ensure long-term safety in the presence of latent variables. The effectiveness of the proposed safety certificate is demonstrated in numerical simulations.

Many real-world systems, like robots or self-driving cars, operate in environments where not everything can be seen or measured. This hidden information can make it hard to predict how the system will behave or to ensure it stays safe. Most existing safety methods assume we have complete knowledge or perfect simulations of these systems—which isn’t realistic. This paper introduces a new method to help systems stay safe even when some information is missing. This method can quickly compute safe actions while the system is running, helping it avoid risky situations in the long run. This is the first approach that combines safety techniques with a class of machine learning techniques—called causal reinforcement learning—to better understand and manage long-term risks when certain information in the environment is hidden.