Safe Dynamic Programming

TL;DR

This paper introduces a formal framework for integrating safety constraints into dynamic programming for Markov decision processes, providing methods to compute safety functions and develop algorithms for safe decision-making.

Contribution

It presents a novel formalism based on evolution equations to incorporate safety into dynamic programming and develops algorithms for safe decision-making in MDPs.

Findings

Safety functions can be computed using the proposed dynamic programming methods.

New algorithms enable safe decision-making in Markov decision processes.

The formalism effectively incorporates safety constraints into dynamic programming.

Abstract

We incorporate safety specifications into dynamic programming. Explicitly, we address the minimization problem of a Markov decision process up to a stopping time with safety constraints. To incorporate safety into dynamic programming, we establish a formalism leaning upon the evolution equation. We show how to compute the safety function with the method of dynamic programming. In the last part of the paper, we develop several algorithms for safe dynamic programming.