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Sparsifying Parametric Models with L0 Regularization

Nicolò Botteghi, Urban Fasel

TL;DR

This approach together with dictionary learning is utilized together with dictionary learning to learn sparse polynomial policies for deep reinforcement learning to control parametric partial differential equations.

Abstract

This document contains an educational introduction to the problem of sparsifying parametric models with L0 regularization. We utilize this approach together with dictionary learning to learn sparse polynomial policies for deep reinforcement learning to control parametric partial differential equations. The code and a tutorial are provided here: https://github.com/nicob15/Sparsifying-Parametric-Models-with-L0.

Sparsifying Parametric Models with L0 Regularization

TL;DR

This approach together with dictionary learning is utilized together with dictionary learning to learn sparse polynomial policies for deep reinforcement learning to control parametric partial differential equations.

Abstract

This document contains an educational introduction to the problem of sparsifying parametric models with L0 regularization. We utilize this approach together with dictionary learning to learn sparse polynomial policies for deep reinforcement learning to control parametric partial differential equations. The code and a tutorial are provided here: https://github.com/nicob15/Sparsifying-Parametric-Models-with-L0.
Paper Structure (14 sections, 41 equations, 5 figures)

This paper contains 14 sections, 41 equations, 5 figures.

Table of Contents

  1. Sparsifying Neural Network Layers with L$_0$ Regularization
  2. Problem Settings
  3. A General Framework for L$_0$ Regularization
  4. Spike and Slab Distribution and Relation to Variational Inference
  5. Efficient Gradient-based Optimization of the L$_0$ Norm
  6. The Hard-Concrete Distribution
  7. Deep Reinforcement Learning with L$_0$ Regularization
  8. Learning Transition and Reward Models
  9. Dataset Collection
  10. Transition and reward models
  11. Training the Models
  12. Results
  13. Learning Control Policies
  14. Results

Figures (5)

  • Figure 1: L$_0$, L$_1$, and L$_2$ norm penalties for a parameter $\xi$. Figure reproduced from loiseau2020data.
  • Figure 2: The spike and slab distribution.
  • Figure 3: Gate $z$ for the binary concrete and hard-concrete distributions. Figure recreated from louizos2018learning.
  • Figure 4: Prediction errors of the different transition and reward models
  • Figure 5: Cumulative reward over training and evaluation.