Lyapunov Exponent as Physics-Informed Dense Reward: RL Discovery of Stabilization Beyond the Kapitza Pendulum
2026-07-15 • Machine Learning
Machine Learning
AI summaryⓘ
The authors propose using a measurement called the Lyapunov characteristic exponent (LCE) as a way to give feedback during reinforcement learning for balancing an inverted pendulum that moves vertically. By using LCE as a reward, their learning agent was able to discover a special oscillating movement called the Kapitza pendulum. Additionally, the agent managed to reduce the swinging of the pendulum's pivot, keeping it steady in an upright position. This shows that LCE can help guide learning for complex balancing tasks.
Lyapunov characteristic exponentreinforcement learninginverted pendulumKapitza pendulumoscillatory motionpivot dampingreward signalstabilization
Authors
Slava Andrejev
Abstract
We suggest using the Lyapunov characteristic exponent (LCE) as a dense reward signal for the reinforcement learning problem of stabilizing the inverted pendulum with vertical motion. With LCE, the agent not only successfully found the oscillatory motion known as the Kapitza pendulum but also damped the pendulum's pivoting, leaving it in a strictly upright position.