Learning safety critics via a non-contractive binary bellman operator

TL;DR

This paper introduces a novel binary Bellman equation for safety critics in reinforcement learning, addressing non-contractiveness and enabling the identification of maximal safe regions in state space.

Contribution

It formulates the binary safety critic with a new Bellman operator, characterizes its fixed points, and proposes an algorithm leveraging safe data to improve safety in RL.

Findings

Characterizes fixed points as maximal safe regions.

Provides an algorithm to avoid spurious solutions.

Addresses non-contractiveness of safety critic operators.

Abstract

The inability to naturally enforce safety in Reinforcement Learning (RL), with limited failures, is a core challenge impeding its use in real-world applications. One notion of safety of vast practical relevance is the ability to avoid (unsafe) regions of the state space. Though such a safety goal can be captured by an action-value-like function, a.k.a. safety critics, the associated operator lacks the desired contraction and uniqueness properties that the classical Bellman operator enjoys. In this work, we overcome the non-contractiveness of safety critic operators by leveraging that safety is a binary property. To that end, we study the properties of the binary safety critic associated with a deterministic dynamical system that seeks to avoid reaching an unsafe region. We formulate the corresponding binary Bellman equation (B2E) for safety and study its properties. While the resulting operator is still non-contractive, we fully characterize its fixed points representing--except for a spurious solution--maximal persistently safe regions of the state space that can always avoid failure. We provide an algorithm that, by design, leverages axiomatic knowledge of safe data to avoid spurious fixed points.