GFN-SR: Symbolic Regression with Generative Flow Networks

Symbolic regression (SR) is an area of interpretable machine learning that aims to identify mathematical expressions, often composed of simple functions, that best fit in a given set of covariates $X$ and response $y$. In recent years, deep symbolic regression (DSR) has emerged as a popular method in the field by leveraging deep reinforcement learning to solve the complicated combinatorial search problem. In this work, we propose an alternative framework (GFN-SR) to approach SR with deep learning. We model the construction of an expression tree as traversing through a directed acyclic graph (DAG) so that GFlowNet can learn a stochastic policy to generate such trees sequentially. Enhanced with an adaptive reward baseline, our method is capable of generating a diverse set of best-fitting expressions. Notably, we observe that GFN-SR outperforms other SR algorithms in noisy data regimes, owing to its ability to learn a distribution of rewards over a space of candidate solutions.

Feedback Linearization of Car Dynamics for Racing via Reinforcement Learning

Through the method of Learning Feedback Linearization, we seek to learn a linearizing controller to simplify the process of controlling a car to race autonomously. A soft actor-critic approach is used to learn a decoupling matrix and drift vector that effectively correct for errors in a hand-designed linearizing controller. The result is an exactly linearizing controller that can be used to enable the well-developed theory of linear systems to design path planning and tracking schemes that are easy to implement and significantly less computationally demanding. To demonstrate the method of feedback linearization, it is first used to learn a simulated model whose exact structure is known, but varied from the initial controller, so as to introduce error. We further seek to apply this method to a system that introduces even more error in the form of a gym environment specifically designed for modeling the dynamics of car racing. To do so, we posit an extension to the method of learning feedback linearization; a neural network that is trained using supervised learning to convert the output of our linearizing controller to the required input for the racing environment. Our progress towards these goals is reported and the next steps in their accomplishment are discussed.