Bayesian Optimization of Noisy Log-Likelihoods Evaluated by Particle Filters -- One Parameter Case --

2026-01-10

AI Summary

This work addresses the challenge of optimizing noisy, computationally expensive, and non-differentiable log-likelihood functions in particle filtering. To overcome this, the authors propose integrating Bayesian optimization into the framework, employing a Gaussian process as a surrogate model to approximate the noisy likelihood surface. By leveraging an acquisition function that balances exploration and exploitation, the method efficiently identifies maximum-likelihood parameters within a limited number of evaluations. This approach provides a stable and reliable optimization framework for non-differentiable, high-noise objective functions, enabling robust parameter estimation under observational noise. Empirical results demonstrate that the mean squared error of the estimated parameters closely approaches that of the exact maximum-likelihood solution obtained via Kalman filtering, thereby validating the effectiveness and practicality of the proposed method.

Technology Category

Machine Learning: OptimizationReasoning under Uncertainty: Stochastic OptimizationIntelligent Robots: State Estimation

Application Category

User Modeling, Personalization and Recommendation: ML for personalized search and recommendationsGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsEconomics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Likelihood functions evaluated using particle filters are typically noisy, computationally expensive, and non-differentiable due to Monte Carlo variability. These characteristics make conventional optimization methods difficult to apply directly or potentially unreliable. This paper investigates the use of Bayesian optimization for maximizing log-likelihood functions estimated by particle filters. By modeling the noisy log-likelihood surface with a Gaussian process surrogate and employing an acquisition function that balances exploration and exploitation, the proposed approach identifies the maximizer using a limited number of likelihood evaluations. Through numerical experiments, we demonstrate that Bayesian optimization provides robust and stable estimation in the presence of observation noise. The results suggest that Bayesian optimization is a promising alternative for likelihood maximization problems where exhaustive search or gradient-based methods are impractical. The estimation accuracy is quantitatively assessed using mean squared error metrics by comparison with the exact maximum likelihood solution obtained via the Kalman filter.

Problem

• Bayesian optimization
• particle filter
• noisy log-likelihood
• maximum likelihood estimation
• non-differentiable optimization

Innovation

• Bayesian Optimization
• Particle Filter
• Noisy Log-Likelihood
• Gaussian Process
• Maximum Likelihood Estimation