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Entropy Measurement Impacts Policy Geometry in Bounded PPO

Yiyang He, Zhichun Zhou, Ziwei Wang, Tao Xue, Haolin Fei· August 26, 2026 View original

Key takeaways

  • The location of entropy measurement in PPO significantly affects learned policy geometry.
  • Measuring entropy in the executed action space can lead to more centered policies.
  • Latent entropy measurement often results in actions clustering near boundaries.
  • Policy geometry is a coupled mean-variance design choice, not solely determined by task return.

Who benefits

RoboticsAutonomous VehiclesIndustrial AutomationGamingSimulation

Summary

This research demonstrates that the choice of where entropy is measured significantly alters the policy geometry learned by Proximal Policy Optimization (PPO) in continuous-control tasks with bounded actions. It shows that measuring entropy in the executed action space, rather than the latent Gaussian space, can lead to more centered and less boundary-prone policies.

This paper investigates the critical impact of entropy measurement location on the policy geometry learned by Proximal Policy Optimization (PPO) algorithms, particularly in continuous-control environments where actions are bounded. Many such policies are initially optimized as unbounded Gaussians and then mapped into a constrained action space. The researchers reveal that whether entropy is calculated in the latent Gaussian space or the final executed action space profoundly influences the resulting policy. Through experiments on complex tasks like MyoLeg and Dog-Stand, the study illustrates that measuring entropy in the latent space often results in policies where a significant proportion of actions cluster near the boundaries. In contrast, measuring entropy in the executed action space introduces an inward gradient on the mean, leading to more centered policy means and reduced boundary occupancy. This finding highlights that entropy measurement is a crucial design choice affecting both mean and variance, and task return alone does not fully characterize the learned policy geometry.

Why it matters

For professionals developing reinforcement learning agents for robotics, autonomous systems, or other continuous control applications, understanding this nuance can lead to more stable, predictable, and performant policies by avoiding undesirable boundary-seeking behaviors.

How to implement this in your domain

  1. 1Review existing PPO implementations for continuous control to identify where entropy is currently being measured.
  2. 2Experiment with measuring entropy in the executed action space instead of the latent Gaussian space for bounded control tasks.
  3. 3Analyze the impact of different entropy measurement strategies on policy behavior, stability, and task performance.
  4. 4Consider direct mean penalties as an alternative or complementary approach to encourage interior policy means.
  5. 5Document and share findings within the team to establish best practices for PPO configuration in bounded environments.

Original post by Yiyang He, Zhichun Zhou, Ziwei Wang, Tao Xue, Haolin Fei

"arXiv:2608.24488v1 Announce Type: new Abstract: Many continuous-control policies are optimized as unbounded Gaussians and then mapped into bounded actions. We show that where entropy is measured changes the policy geometry learned by proximal policy optimization (PPO). In an 80-m…"

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Originally posted by Yiyang He, Zhichun Zhou, Ziwei Wang, Tao Xue, Haolin Fei on X · view source

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