Programmatic Reinforcement Learning: Navigating Gridworlds
This work addresses foundational theoretical gaps in programmatic RL for researchers in machine learning and formal methods, though it is incremental as it focuses on gridworlds.
The paper tackles the lack of theoretical understanding in programmatic reinforcement learning by defining programmatic policies for gridworld environments, resulting in upper bounds on policy size and an algorithm for synthesis, with a prototype implementation.
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.