GauOptX: Gaussian Process Optimization Framework

This repository is a collaborative effort of Eva Kaushik(kaushikeva0026@gmail.com) and Rohit Kaushik(kaushikrohit004@gmail.com)

Introduction

GauOptX is a high-performance, research-driven optimization framework that leverages Bayesian optimization with Gaussian processes (GPs) for efficient global optimization. Unlike traditional optimization techniques, which rely on gradient-based methods or brute-force search, GauOptX intelligently balances exploration and exploitation to find optima with minimal function evaluations.

Bayesian optimization is particularly useful for expensive-to-evaluate functions, such as:

• Hyperparameter tuning in deep learning and machine learning models.
• Experimental design in physical sciences and engineering.
• Automated decision-making in reinforcement learning.

GauOptX provides a modular, extensible, and scalable implementation that supports batch optimization, multi-fidelity optimization, and large-scale data handling.

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Why Bayesian Optimization? The Science Behind It

Optimization problems often involve black-box functions—functions where we lack an explicit mathematical formula, and evaluation is costly (e.g., computationally expensive simulations, real-world experiments). Traditional methods struggle in these scenarios due to:

• No Gradient Information: Many real-world functions are non-differentiable or noisy, making gradient-based methods ineffective.
• Computational Cost: Grid search and brute-force methods are infeasible in high-dimensional spaces.
• Local Minima Traps: Many heuristic methods (e.g., hill climbing, simulated annealing) may converge to suboptimal solutions.

Bayesian optimization (BO) mitigates these issues by using a probabilistic model (typically a Gaussian process) to approximate the function and guide sampling based on uncertainty.

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Gaussian Processes (GPs) as a Surrogate Model

A Gaussian process is a non-parametric probabilistic model that provides a distribution over possible functions that fit observed data. Given a set of observations, a GP can predict the mean and variance at unobserved points, allowing us to make informed decisions about where to evaluate next.

Mathematically, a Gaussian process is defined as: [ f(x) \sim \mathcal{GP} (m(x), k(x, x')) ] where:

• (m(x)) is the mean function (often set to zero for simplicity).
• (k(x, x')) is the covariance/kernel function (e.g., RBF kernel, Matern kernel), which determines the smoothness and complexity of the function approximation.

Using the GP model, we choose the next evaluation point using an acquisition function, which balances exploration (sampling in uncertain regions) and exploitation (sampling near promising points).

Acquisition Functions

GauOptX supports multiple acquisition functions, each with different trade-offs:

• Expected Improvement (EI): Prioritizes points that are likely to improve upon the current best solution.
• Upper Confidence Bound (UCB): Encourages exploration based on confidence intervals.
• Probability of Improvement (PI): Focuses on sampling points with a high probability of being better than the current optimum.
• Thompson Sampling: Uses random samples from the posterior to guide search.

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Key Features

• Global Optimization: Finds the global minimum of black-box functions efficiently.
• Batch Optimization: Supports parallel evaluations for faster convergence.
• Multi-fidelity Optimization: Integrates noisy and multi-resolution function evaluations.
• Machine Learning Applications: Optimize hyperparameters with fewer training iterations.
• Custom Kernel Support: Use built-in kernels or define your own covariance functions.
• Visualization Tools: Built-in plotting for convergence analysis.

Installation

Using pip

To install GauOptX, simply use:

pip install gauoptx

Installing from Source

1. Clone the repository:

   git clone https://github.com/YourUsername/GauOptX.git
   cd GauOptX

2. Install in development mode:

   python setup.py develop

3. Install dependencies:

   pip install -r requirements.txt

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Dependencies

GauOptX requires the following libraries:

• GPy (for Gaussian process modeling)
• numpy and scipy (for numerical computations)
• matplotlib (for visualization)

Optional dependencies:

• pyDOE (for experimental design strategies)
• sobol_seq (for quasi-random sequence sampling)
• cma (for evolutionary strategies)
• DIRECT (for derivative-free optimization)

Install all required dependencies using:

pip install -r requirements.txt

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Usage Example

from gauoptx import GauOptX
from gauoptx.benchmarks import synthetic_function

# Define the objective function
def objective_function(x):
    return synthetic_function(x)

# Initialize optimizer
optimizer = GauOptX(domain=[{'name': 'var_1', 'type': 'continuous', 'domain': (0, 1)}])

# Run optimization
results = optimizer.optimize(objective_function)

# Display results
print("Optimal value found: ", results.x)
print("Objective value at optimum: ", results.fx)
optimizer.plot_convergence()

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Real-World Applications

1. Hyperparameter Optimization: Bayesian optimization has been widely used in optimizing deep learning models (e.g., tuning CNN/LSTM architectures).
2. Drug Discovery: BO efficiently searches large chemical spaces for optimal molecular configurations.
3. Robotics: GauOptX can optimize control policies in reinforcement learning applications.
4. Engineering Design: Used for optimizing expensive simulation-based problems in aerospace, automotive, and energy sectors.

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Contributing

We welcome contributions! Whether you’re fixing a bug, adding new functionality, or improving documentation, your help is greatly appreciated.

How to Contribute:

1. Fork the repository.
2. Create a branch for your feature or bug fix:

   git checkout -b feature-or-bug

3. Make your changes and commit them.
4. Push to your branch:

   git push origin feature-or-bug

5. Submit a pull request.

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Citation

If you use GauOptX in your research, please cite:

@article{Kaushik2025,
  author = {Eva Kaushik and Rohit Kaushik},
  title = {GauOptX: A Gaussian Process Optimization Framework},
  journal = {Journal of Machine Learning Optimization},
  year = {2025},
}

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Contact

For support, contact the maintainer at `kaushikeva0026@gmail.com' or 'Kaushikrohit004@gmail.com' .