Safe Exploration in Finite Markov Decision Processes with Gaussian Processes

TL;DR

This paper introduces a safe exploration algorithm for finite Markov decision processes that uses Gaussian process priors to ensure safety constraints are met during exploration, demonstrated on rover terrain mapping.

Contribution

It presents a novel algorithm that guarantees safe exploration of the reachable MDP regions under unknown safety constraints using Gaussian processes.

Findings

Successfully explores safe regions without violating safety constraints.

Guarantees complete exploration of safely reachable states.

Validated on digital terrain models for rover exploration.

Abstract

In classical reinforcement learning, when exploring an environment, agents accept arbitrary short term loss for long term gain. This is infeasible for safety critical applications, such as robotics, where even a single unsafe action may cause system failure. In this paper, we address the problem of safely exploring finite Markov decision processes (MDP). We define safety in terms of an, a priori unknown, safety constraint that depends on states and actions. We aim to explore the MDP under this constraint, assuming that the unknown function satisfies regularity conditions expressed via a Gaussian process prior. We develop a novel algorithm for this task and prove that it is able to completely explore the safely reachable part of the MDP without violating the safety constraint. To achieve this, it cautiously explores safe states and actions in order to gain statistical confidence about the safety of unvisited state-action pairs from noisy observations collected while navigating the environment. Moreover, the algorithm explicitly considers reachability when exploring the MDP, ensuring that it does not get stuck in any state with no safe way out. We demonstrate our method on digital terrain models for the task of exploring an unknown map with a rover.