# Planning With Uncertain Specifications (PUnS)

## TL;DR

This paper introduces PUnS, a framework for planning with uncertain, belief-based non-Markovian task specifications expressed as LTL formulas, and demonstrates its effectiveness in a robotic dinner setting.

## Contribution

It formulates a novel approach to handle uncertain specifications in reinforcement learning by converting belief-based LTL formulas into an equivalent MDP.

## Key findings

- Existence of an equivalent MDP for PUnS instances.
- Four criteria capturing semantics of belief satisfaction.
- Successful real-world robot task execution.

## Abstract

Reward engineering is crucial to high performance in reinforcement learning systems. Prior research into reward design has largely focused on Markovian functions representing the reward. While there has been research into expressing non-Markov rewards as linear temporal logic (LTL) formulas, this has focused on task specifications directly defined by the user. However, in many real-world applications, task specifications are ambiguous, and can only be expressed as a belief over LTL formulas. In this paper, we introduce planning with uncertain specifications (PUnS), a novel formulation that addresses the challenge posed by non-Markovian specifications expressed as beliefs over LTL formulas. We present four criteria that capture the semantics of satisfying a belief over specifications for different applications, and analyze the qualitative implications of these criteria within a synthetic domain. We demonstrate the existence of an equivalent Markov decision process (MDP) for any instance of PUnS. Finally, we demonstrate our approach on the real-world task of setting a dinner table automatically with a robot that inferred task specifications from human demonstrations.