Programmatic Reinforcement Learning: Navigating Gridworlds

TL;DR

This paper initiates a theoretical study of programmatic reinforcement learning in gridworlds, providing bounds on policy sizes and an algorithm for synthesis, bridging machine learning and formal methods.

Contribution

It introduces a formal framework for programmatic RL, establishes size bounds for optimal policies, and develops a synthesis algorithm with a prototype implementation.

Findings

Upper bounds on the size of optimal programmatic policies

An algorithm for synthesizing programmatic policies

Prototype implementation demonstrating the approach

Abstract

The field of reinforcement learning (RL) is concerned with algorithms for learning optimal policies in unknown stochastic environments. Programmatic RL studies representations of policies as programs, meaning involving higher order constructs such as control loops. Despite attracting a lot of attention at the intersection of the machine learning and formal methods communities, very little is known on the theoretical front about programmatic RL: what are good classes of programmatic policies? How large are optimal programmatic policies? How can we learn them? The goal of this paper is to give first answers to these questions, initiating a theoretical study of programmatic RL. Considering a class of gridworld environments, we define a class of programmatic policies. Our main contributions are to place upper bounds on the size of optimal programmatic policies, and to construct an algorithm for synthesizing them. These theoretical findings are complemented by a prototype implementation of the algorithm.