$\lambda$-Reachability: Geometric-Horizon Safety Bellman Equations for Humanoid Safety (opens in new tab)

We introduce $\lambda$-Reachability, a scalable approach to Hamilton--Jacobi safety analysis for high-dimensional robotic systems. Unlike prior discounted formulations that rely on fixed one-step Bellman updates, $\lambda$-Reachability employs a stochastic multi-step estimator of the safety value, using a geometrically distributed rollout horizon together with a randomly absorbed terminal. Conceptually analogous to TD($\lambda$), $\lambda$-Reach...