  Learning-based approaches are emerging as an effective approach for safety
filters for black-box dynamical systems. Existing methods have relied on
certificate functions like Control Barrier Functions (CBFs) and Hamilton-Jacobi
(HJ) reachability value functions. The primary motivation for our work is the
recognition that ultimately, enforcing the safety constraint as a control input
constraint at each state is what matters. By focusing on this constraint, we
can eliminate dependence on any specific certificate function-based design. To
achieve this, we define a discriminating hyperplane that shapes the half-space
constraint on control input at each state, serving as a sufficient condition
for safety. This concept not only generalizes over traditional safety methods
but also simplifies safety filter design by eliminating dependence on specific
certificate functions. We present two strategies to learn the discriminating
hyperplane: (a) a supervised learning approach, using pre-verified control
invariant sets for labeling, and (b) a reinforcement learning (RL) approach,
which does not require such labels. The main advantage of our method, unlike
conventional safe RL approaches, is the separation of performance and safety.
This offers a reusable safety filter for learning new tasks, avoiding the need
to retrain from scratch. As such, we believe that the new notion of the
discriminating hyperplane offers a more generalizable direction towards
designing safety filters, encompassing and extending existing
certificate-function-based or safe RL methodologies.
