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Examining Policy Entropy of Reinforcement Learning Agents for Personalization Tasks

Anton Dereventsov, Andrew Starnes, Clayton G. Webster

TL;DR

This work investigates how the choice between Policy Optimization and Q-Learning shapes policy entropy in personalization tasks framed as contextual bandits. It formalizes and demonstrates that Policy Optimization tends to produce low-entropy policies during training, while Q-Learning maintains higher entropy, supported by extensive numerical experiments across image classification, music recommendation, online advertising, and behavioral personalization, plus theoretical analysis. The update-rule insights reveal that PO's dependence on action-probability $\pi(a|s)$ drives entropy collapse, whereas Q-Learning updates are confined to the chosen action and thus preserve diversity. These findings highlight entropy dynamics as a critical consideration for deploying RL in personalization and suggest entropy-regularization as a potential remedy. The results provide practical guidance for algorithm selection in recommender and personalization systems.

Abstract

This effort is focused on examining the behavior of reinforcement learning systems in personalization environments and detailing the differences in policy entropy associated with the type of learning algorithm utilized. We demonstrate that Policy Optimization agents often possess low-entropy policies during training, which in practice results in agents prioritizing certain actions and avoiding others. Conversely, we also show that Q-Learning agents are far less susceptible to such behavior and generally maintain high-entropy policies throughout training, which is often preferable in real-world applications. We provide a wide range of numerical experiments as well as theoretical justification to show that these differences in entropy are due to the type of learning being employed.

Examining Policy Entropy of Reinforcement Learning Agents for Personalization Tasks

TL;DR

This work investigates how the choice between Policy Optimization and Q-Learning shapes policy entropy in personalization tasks framed as contextual bandits. It formalizes and demonstrates that Policy Optimization tends to produce low-entropy policies during training, while Q-Learning maintains higher entropy, supported by extensive numerical experiments across image classification, music recommendation, online advertising, and behavioral personalization, plus theoretical analysis. The update-rule insights reveal that PO's dependence on action-probability drives entropy collapse, whereas Q-Learning updates are confined to the chosen action and thus preserve diversity. These findings highlight entropy dynamics as a critical consideration for deploying RL in personalization and suggest entropy-regularization as a potential remedy. The results provide practical guidance for algorithm selection in recommender and personalization systems.

Abstract

This effort is focused on examining the behavior of reinforcement learning systems in personalization environments and detailing the differences in policy entropy associated with the type of learning algorithm utilized. We demonstrate that Policy Optimization agents often possess low-entropy policies during training, which in practice results in agents prioritizing certain actions and avoiding others. Conversely, we also show that Q-Learning agents are far less susceptible to such behavior and generally maintain high-entropy policies throughout training, which is often preferable in real-world applications. We provide a wide range of numerical experiments as well as theoretical justification to show that these differences in entropy are due to the type of learning being employed.
Paper Structure (15 sections, 3 theorems, 48 equations, 14 figures, 8 tables)

This paper contains 15 sections, 3 theorems, 48 equations, 14 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Sample Experiment
  5. Numerical Experiments
  6. Image Classification Experiment
  7. Music Recommendation Experiment
  8. Online Advertisement Experiment
  9. Behavioral Preference Experiment
  10. Theoretical Analysis
  11. Conclusion
  12. Restrictions and Limitations
  13. Future Work
  14. Numerical Experiments
  15. Theoretical Analysis

Key Result

Theorem 1

Let a PG or QL agent with a linear network be trained on a contextual bandit task $\{\mathcal{S,A},r\}$ with the gradient descend algorithm with a batch size $N$ and a learning rate $\lambda$. Then with each update of the trainable weights $W \leftarrow W^\prime$ the policy output mappings $\mathcal where and $\{(s_n,a_n,r_n)\}_{n=1}^N$ is the batch of agent-environment interactions on which the

Figures (14)

  • Figure 1: Results of the Sample Experiment.
  • Figure 2: Action selection histograms in the Sample Experiment.
  • Figure 3: Results of the Image Classification Experiment on MNIST dataset.
  • Figure 4: Results of the Image Classification Experiment on CIFAR10 dataset.
  • Figure 5: Audio features of the musical genres used in the Music Recommendation Experiment.
  • ...and 9 more figures

Theorems & Definitions (6)

  • Theorem 1
  • Theorem 2
  • Lemma 1
  • proof : Proof of Lemma \ref{['thm:grad_pi']}
  • proof : Proof of Theorem \ref{['thm:outputs_linear']}
  • proof : Proof of Theorem \ref{['thm:outputs']}