Environment-Independent Task Specifications via GLTL

We propose a new task-specification language for Markov decision processes that is designed to be an improvement over reward functions by being environment independent. The language is a variant of Linear Temporal Logic (LTL) that is extended to probabilistic specifications in a way that permits approximations to be learned in finite time. We provide several small environments that demonstrate the advantages of our geometric LTL (GLTL) language and illustrate how it can be used to specify standard reinforcement-learning tasks straightforwardly.