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

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.

Efficient Generation of Diverse Cooperative Agents with World Models

A major bottleneck in the training process for Zero-Shot Coordination (ZSC) agents is the generation of partner agents that are diverse in collaborative conventions. Current Cross-play Minimization (XPM) methods for population generation can be very computationally expensive and sample inefficient as the training objective requires sampling multiple types of trajectories. Each partner agent in the population is also trained from scratch, despite all of the partners in the population learning policies of the same coordination task. In this work, we propose that simulated trajectories from the dynamics model of an environment can drastically speed up the training process for XPM methods. We introduce XPM-WM, a framework for generating simulated trajectories for XPM via a learned World Model (WM). We show XPM with simulated trajectories removes the need to sample multiple trajectories. In addition, we show our proposed method can effectively generate partners with diverse conventions that match the performance of previous methods in terms of SP population training reward as well as training partners for ZSC agents. Our method is thus, significantly more sample efficient and scalable to a larger number of partners.