BAYEX: Bayesian Optimization powered by JAX

Bayex is a high performance Bayesian global optimization library using Gaussian processes. In contrast to existing Bayesian optimization libraries, Bayex is designed to use JAX as its backend.

Instead of relaying on external libraries, Bayex only relies on JAX and its custom implementations, without requiring importing massive libraries such as sklearn.

What is Bayesian Optimization?

Bayesian Optimization (BO) methods are useful for optimizing functions that are expensive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the objective function, typically a Gaussian process (GP), upon which an acquisition function is built. The acquisition function guides the optimization process and measures the expected utility of performing an evaluation of the objective at a new point.

Why JAX?

Using JAX as a backend removes some of the limitations found on Python, as it gives us direct mapping to the XLA compiler.

XLA compiles and runs the JAX code into several architectures such as CPU, GPU and TPU without hassle. But the device agnostic approach is not the reason to back XLA for future scientific programs. XLA provides with optimizations under the hood such as Just-In-Time compilation and automatic parallelization that make Python (with a NumPy-like approach) a suitable candidate on some High Performance Computing scenarios.

Additionally, JAX provides Python code with automatic differentiation, which helps identify the conditions that maximize the acquisition function.

Installation

Bayex can be installed using PyPI via pip:

pip install bayex

or from GitHub directly

pip install git+git://github.com/alonfnt/bayex.git

For more advance instructions please refer to the installation guide.

Usage

Using Bayex is very straightforward:

import bayex

def f(x, y):
    return -y ** 2 - (x - y) ** 2 + 3 * x / y - 2

constrains = {'x': (-10, 10), 'y': (0, 10)}
optim_params = bayex.optim(f, constrains=constrains, seed=42, n=10)

showing the results can be done with

>> bayex.show_results(optim_params, min_len=13)
   #sample      target          x            y
      1        -9.84385      2.87875      3.22516
      2        -307.513     -6.13013      8.86493
      3        -19.2197      6.8417       1.9193
      4        -43.6495     -3.09738      2.52383
      5        -58.9488      2.63803      6.54768
      6        -64.8658      4.5109       7.47569
      7        -78.5649      6.91026      8.70257
      8        -9.49354      5.56705      1.43459
      9        -9.59955      5.60318      1.39322
     10        -15.4077      6.37659      1.5895
     11        -11.7703      5.83045      1.80338
     12        -11.4169      2.53303      3.32719
     13        -8.49429      2.67945      3.0094
     14        -9.17395      2.74325      3.11174
     15        -7.35265      2.86541      2.88627

we can then obtain the maximum value found using

>> optim_params.target
-7.352654457092285

as well as the input parameters that yield it

>> optim_params.params
{'x': 2.865405, 'y': 2.8862667}

Contributing

Everyone can contribute to Bayex and we welcome pull requests as well as raised issues. Please refer to this contribution guide on how to do it.

References

1. A Tutorial on Bayesian Optimization
2. BayesianOptimization Library
3. JAX: Autograd and XLA