Conformal Symplectic Optimization for Stable Reinforcement Learning

TL;DR

This paper introduces RAD, a physics-inspired optimization algorithm based on conformal symplectic integrators and relativistic principles, which enhances the stability and performance of deep reinforcement learning training.

Contribution

We propose RAD, a novel optimization method inspired by conformal Hamiltonian systems and special relativity, improving stability and convergence in deep RL training.

Findings

RAD outperforms nine baseline optimizers across multiple RL environments.

RAD achieves up to 155.1% performance improvement over ADAM in Atari games.

RAD demonstrates sublinear convergence under nonconvex settings.

Abstract

Training deep reinforcement learning (RL) agents necessitates overcoming the highly unstable nonconvex stochastic optimization inherent in the trial-and-error mechanism. To tackle this challenge, we propose a physics-inspired optimization algorithm called relativistic adaptive gradient descent (RAD), which enhances long-term training stability. By conceptualizing neural network (NN) training as the evolution of a conformal Hamiltonian system, we present a universal framework for transferring long-term stability from conformal symplectic integrators to iterative NN updating rules, where the choice of kinetic energy governs the dynamical properties of resulting optimization algorithms. By utilizing relativistic kinetic energy, RAD incorporates principles from special relativity and limits parameter updates below a finite speed, effectively mitigating abnormal gradient influences. Additionally, RAD models NN optimization as the evolution of a multi-particle system where each trainable parameter acts as an independent particle with an individual adaptive learning rate. We prove RAD's sublinear convergence under general nonconvex settings, where smaller gradient variance and larger batch sizes contribute to tighter convergence. Notably, RAD degrades to the well-known adaptive moment estimation (ADAM) algorithm when its speed coefficient is chosen as one and symplectic factor as a small positive value. Experimental results show RAD outperforming nine baseline optimizers with five RL algorithms across twelve environments, including standard benchmarks and challenging scenarios. Notably, RAD achieves up to a 155.1% performance improvement over ADAM in Atari games, showcasing its efficacy in stabilizing and accelerating RL training.