nano-nudge

A lightweight Python library for surrogate-based Bayesian Optimization.

nano-nudge provides a simple, understandable implementation of Bayesian Optimization for finding the optimal parameters of expensive-to-evaluate functions.

Core Concepts

Bayesian Optimization works by building a probabilistic model (a "surrogate model") of the objective function. This model is then used to intelligently select the most promising points to evaluate next.

nano-nudge is built around a few key components:

• SurrogateBayesianOptimizer: The main class that orchestrates the optimization process using a surrogate model (random forest by fault) and acquisition functions like Expected Improvement (EI).
• SurrogateModel: A model that learns the shape of your objective function from past trials.
• ParzenOptimizer: An alternative optimizer that implements the Tree-Structured Parzen Estimator (TPE) approach (note that the parzen estimator in this implementation is simplified to not be tree-structured), building probability distributions (KDEs) for good and bad performing trials to guide sampling.
• Acquisition Function: A function (e.g., Expected Improvement) that uses the surrogate model's predictions to quantify how "promising" a candidate point is.
• Trial: An object that stores a parameter suggestion and its resulting value.

Demo

Optimizing a function with nano-nudge is straightforward. Here is a complete example of finding the maximum of a simple function.

import numpy as np
from nano_nudge.optimizer import SurrogateBayesianOptimizer

def objective(trial):
  x = trial.suggest_float(min=-10, max=10)
  return np.exp((-x**2)/2)/np.sqrt(2*np.pi)

optimizer = SurrogateBayesianOptimizer(objective=objective, n_trials=30, direction='maximize')
optimizer.optimize()

print("\n")
print("Best trial:")
print(optimizer.history.get_best_trial())

Trial number: 0 | Suggestion: 7.769077156726528 | Value: 3.120436310418126e-14
Trial number: 1 | Suggestion: 8.678406672808347 | Value: 1.764093319457085e-17
Trial number: 2 | Suggestion: 1.1376615768300837 | Value: 0.20886326722844653
(...)
Trial number: 27 | Suggestion: 0.6785836994168211 | Value: 0.31689764243866037
Trial number: 28 | Suggestion: -0.6012088625574608 | Value: 0.3329827535734924
Trial number: 29 | Suggestion: 0.43840897881871577 | Value: 0.3623880247819842


Best trial:
Trial number: 16 | Suggestion: 0.03761830347918682 | Value: 0.39866010130132035

Future Work

nano-nudge is in active development. Here are some of the planned features:

• Parallel Optimization: Implement q-Expected Improvement (q-EI) to allow for evaluating multiple trials in parallel.
• More Model: Allow the use of other surrogate models
• Better Handling of Search-Space Bounds and Sampling: Currently the solution to handle these syttems is inelegant and requires significant overhauling.
• Tree-Structured Parzen Estimation: Implement TPE as an alternative bayesian optimisation strategy
• Expanded Search Space: Add support for categorical and integer hyperparameters, in addition to continuous ones.