[Paper Review] Safe Exploration in Finite Markov Decision Processes with Gaussian Processes

Matteo Turchetta, Felix Berkenkamp+1 more|arXiv (Cornell University)|Jun 1, 2016

Fault Detection and Control SystemsEngineering53 citations

TL;DR

This paper proposes SAFEMDP, a novel algorithm for safe exploration in finite Markov Decision Processes using Gaussian processes to model unknown safety constraints. By combining cautious exploration with reachability-aware planning, SAFEMDP ensures complete exploration of the safely reachable state space without violating safety constraints, even with noisy observations.

ABSTRACT

In classical reinforcement learning agents accept arbitrary short term loss for long term gain when exploring their environment. This is infeasible for safety critical applications such as robotics, where even a single unsafe action may cause system failure or harm the environment. 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 and satisfies certain regularity conditions expressed via a Gaussian process prior. We develop a novel algorithm, SAFEMDP, for this task and prove that it completely explores 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.

Motivation & Objective

• To enable safe exploration in finite MDPs where safety constraints are a priori unknown but regular and modeled via Gaussian processes.
• To develop an algorithm that completely explores all safely reachable states without violating safety constraints.
• To ensure the agent does not get trapped in states with no safe exit, by explicitly considering reachability during exploration.
• To build statistical confidence about the safety of unvisited state-action pairs through cautious, observation-driven learning.

Proposed method

• Modeling safety constraints as a Gaussian process prior over state-action pairs to encode prior beliefs about safety.
• Using noisy observations from environment interactions to update belief about safety, refining confidence in unvisited state-action pairs.
• Designing an exploration strategy that prioritizes safe states and actions while maintaining reachability to avoid dead ends.
• Integrating reachability analysis into the planning process to ensure all explored states can be exited safely.
• Employing a confidence-bound approach to balance exploration and safety, only expanding into unvisited regions when safety is statistically likely.

Experimental results

Research questions

• RQ1 How can we safely explore an unknown finite MDP when safety constraints are unknown but smooth and regular?
• RQ2 What algorithmic structure enables complete exploration of the safely reachable state space without violating safety?
• RQ3 How can we ensure that the agent does not become trapped in states with no safe exit during exploration?
• RQ4 To what extent can Gaussian process priors support reliable safety inference from limited, noisy observations?

Key findings

• SAFEMDP successfully explores the entire safely reachable region of the MDP without violating safety constraints.
• The algorithm maintains reachability by ensuring all explored states have a safe exit path, preventing entrapment.
• Statistical confidence in safety is incrementally built through cautious exploration and observation collection.
• The method demonstrates feasibility on digital terrain models, showing effective safe exploration with a rover in unknown environments.