Safety Certificate against Latent Variables with Partially Unidentifiable Dynamics

TL;DR

This paper introduces a novel probabilistic safety certification method for systems with latent variables and unidentifiable dynamics, integrating causal reinforcement learning to ensure long-term safety despite distribution shifts.

Contribution

It proposes a new safety certificate framework based on invariance conditions in probability space, incorporating causal reinforcement learning for systems with latent variables and unidentifiable dynamics.

Findings

Effective safety certificates constructed using observed statistics.

Real-time control implementation demonstrated in simulations.

First integration of causal RL with safety certification for latent-variable systems.

Abstract

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.