Safe Active Learning with Future Viability Guarantees in Time-Series Models

In time-series systems, safe active learning seeks to collect informative data while maintaining safety during data collection. A key challenge is that one-step safety does not guarantee future viability: an input can be immediately safe yet lead the system into a state from which no safe continuation exists. For example, in pressure regulation, an input may keep the current pressure below its limit but still drive the system toward an unsafe pressure spike over the next few steps. We study this problem in nonlinear time-series systems with unknown dynamics and safety constraints. We introduce the notion of $m$-step dead-end inputs and propose a future-aware safe active learning framework (FA-SAL) that enforces finite-horizon safety via margin-certified rollout constraints. Our approach constructs a conservative approximation of the true future-safe set by combining Gaussian process uncertainty with a recursive error bound over predicted trajectories. We show that FA-SAL provides high-probability safety guarantees, recovers interior future-safe inputs as uncertainty decreases, and provably excludes separated dead-end inputs. Experiments on synthetic and real-world benchmarks demonstrate that FA-SAL reduces safety violations and dead-end selections while maintaining competitive model learning performance.