# Backup-Based Safety Filters: A Comparative Review of Backup CBF, Model Predictive Shielding, and gatekeeper

arXiv: https://arxiv.org/abs/2604.02401 · HTML: https://mlsanity.com/paper/2604.02401/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2026.

## Built on by (most cited first, 3 of 3)

- [DiffCVaR: Reinforcement Learning for Risk Adaptation via Differentiable CVaR Barrier Functions](https://mlsanity.com/paper/2605.21257/) (2026)
- [Provably Safe, Yet Scalable Reinforcement Learning](https://mlsanity.com/paper/2606.14536/) (2026)
- [Predictive Semantic Safety: From Visual Physical Reasoning to Safety-Critical Control](https://mlsanity.com/paper/2609.34356/) (2026)

## Abstract (arXiv)

This paper revisits three backup-based safety filters -- Backup Control Barrier Functions (Backup CBF), Model Predictive Shielding (MPS), and gatekeeper -- through a unified comparative framework. Using a common safety-filter abstraction and shared notation, we make explicit both their common backup-policy structure and their key algorithmic differences. We compare the three methods through their filter-inactive sets, i.e., the states where the nominal policy is left unchanged. In particular, we show that MPS is a special case of gatekeeper, and we further relate gatekeeper to the interior of the Backup CBF inactive set within the implicit safe set. This unified view also highlights a key source of conservatism in backup-based safety filters: safety is often evaluated through the feasibility of a backup maneuver, rather than through the nominal policy's continued safe execution. The paper is intended as a compact tutorial and review that clarifies the theoretical connections and differences among these methods.