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A Bayesian Optimization through Sequential Monte Carlo and Statistical Physics-Inspired Techniques

Anton Lebedev, Thomas Warford, M. Emre Şahin

TL;DR

The paper addresses the scalability and portability challenges of Bayesian optimization across computing platforms. It introduces a physics-inspired reformulation of Sequential Monte Carlo and Hamiltonian Monte Carlo using a temperature-based Boltzmann framework, implemented with NumPyro/JAX for CPU, GPU, and TPU execution. Through CT and IRT 2PL models, the authors demonstrate convergence properties and show favorable performance and scalability relative to Stan, supported by MPI-enabled parallelism. This approach yields a practical, cross-platform Bayesian optimization framework with potential extensions to maximum-entropy and quantum-inspired methods, enabling broader applicability in diverse optimization tasks.

Abstract

In this paper, we propose an approach for an application of Bayesian optimization using Sequential Monte Carlo (SMC) and concepts from the statistical physics of classical systems. Our method leverages the power of modern machine learning libraries such as NumPyro and JAX, allowing us to perform Bayesian optimization on multiple platforms, including CPUs, GPUs, TPUs, and in parallel. Our approach enables a low entry level for exploration of the methods while maintaining high performance. We present a promising direction for developing more efficient and effective techniques for a wide range of optimization problems in diverse fields.

A Bayesian Optimization through Sequential Monte Carlo and Statistical Physics-Inspired Techniques

TL;DR

The paper addresses the scalability and portability challenges of Bayesian optimization across computing platforms. It introduces a physics-inspired reformulation of Sequential Monte Carlo and Hamiltonian Monte Carlo using a temperature-based Boltzmann framework, implemented with NumPyro/JAX for CPU, GPU, and TPU execution. Through CT and IRT 2PL models, the authors demonstrate convergence properties and show favorable performance and scalability relative to Stan, supported by MPI-enabled parallelism. This approach yields a practical, cross-platform Bayesian optimization framework with potential extensions to maximum-entropy and quantum-inspired methods, enabling broader applicability in diverse optimization tasks.

Abstract

In this paper, we propose an approach for an application of Bayesian optimization using Sequential Monte Carlo (SMC) and concepts from the statistical physics of classical systems. Our method leverages the power of modern machine learning libraries such as NumPyro and JAX, allowing us to perform Bayesian optimization on multiple platforms, including CPUs, GPUs, TPUs, and in parallel. Our approach enables a low entry level for exploration of the methods while maintaining high performance. We present a promising direction for developing more efficient and effective techniques for a wide range of optimization problems in diverse fields.
Paper Structure (11 sections, 6 equations, 4 figures)

This paper contains 11 sections, 6 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Method Description
  3. Numerical Experiments
  4. Models
  5. CT model
  6. IRT 2PL
  7. Experimental Results
  8. Quality of Estimation
  9. Performance - HMC
  10. Conclusions and Future Work
  11. Acknowledgements

Figures (4)

  • Figure 1: Trajectories of our HMC implementation in the potential defined by \ref{['eq:PotentialDefinition']} for the CT model. Note the dense zig-zag trajectories that result if the momentum inversion proposed in homman2014 is implemented.
  • Figure 2: Parameter estimates obtained with SMC with physics-motivated moving averages. The dashed lines represent the true parameter values. The crosses refer to a reference implementation not available to the public.
  • Figure 3: Execution time and speed-up of our HMC implemetation when using mutliple CPU cores of a Ryzen 5 3600X to determine the coin biases of the CT model using HMC with 1000 Leap-Frog steps.
  • Figure 4: Execution time and speed-up of our HMC implementation when using mutliple CPU cores of a Ryzen 5 3600X as well as a RTX 3060 and GTX 1080 Ti to determine the coin biases of the IRT model for HMC with 1000 Leap-Frog steps.