# Statistical Analysis of Policy Space Compression Problem

arXiv: https://arxiv.org/abs/2411.09900 · HTML: https://mlsanity.com/paper/2411.09900/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 0 of its 14 references that are in the map.
- First posted on arXiv 15 Nov 2024.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Abstract (arXiv)

Policy search methods are crucial in reinforcement learning, offering a framework to address continuous state-action and partially observable problems. However, the complexity of exploring vast policy spaces can lead to significant inefficiencies. Reducing the policy space through policy compression emerges as a powerful, reward-free approach to accelerate the learning process. This technique condenses the policy space into a smaller, representative set while maintaining most of the original effectiveness. Our research focuses on determining the necessary sample size to learn this compressed set accurately. We employ R'enyi divergence to measure the similarity between true and estimated policy distributions, establishing error bounds for good approximations. To simplify the analysis, we employ the l1 norm, determining sample size requirements for both model-based and model-free settings. Finally, we correlate the error bounds from the l1 norm with those from R'enyi divergence, distinguishing between policies near the vertices and those in the middle of the policy space, to determine the lower and upper bounds for the required sample sizes.