Lyapunov Exponent as Physics-Informed Dense Reward: RL Discovery of Stabilization Beyond the Kapitza Pendulum

TL;DR — This work proposes using the Lyapunov characteristic exponent (LCE) as a dense, physics-informed reward signal for a reinforcement learning agent tasked with stabilizing a vertically-driven inverted pendulum. It matters because LCE offers a principled, physics-grounded shaping signal that can guide RL toward stable dynamics rather than relying on hand-crafted sparse rewards.

• The core contribution is a reward-design idea: use the Lyapunov exponent (a measure of trajectory divergence/chaos) as a dense reward to steer RL toward stabilizing behavior.
• Applied to the classic inverted pendulum with vertical pivot motion, the agent rediscovered the known Kapitza oscillatory stabilization regime.
• Beyond replicating Kapitza, the LCE reward drove the agent to also damp the pendulum's pivoting, achieving a strictly upright equilibrium.
• Content is thin (abstract only): no details on the RL algorithm, training setup, baselines, or quantitative results are provided, so takeaways are inferred from the abstract.