Hyperparameter optimization

Replacing a hyperparameter problem with a hyperhyperparameter problem, which feels like progress

September 25, 2020 — January 22, 2024

functional analysis
how do science
model selection
Figure 1: Grad student and devops engineer meet at a local optimum.

This notebook was originally split off autoML, although neither topic is a strict subset of the other; they are overlapping clusters of concepts.

The art of choosing the best hyperparameters for a ML model’s algorithms, of which there may be many.

Should one bother getting fancy about this? Ben Recht argues that often random search is competitive with highly tuned Bayesian methods in hyperparameter tuning. Kevin Jamieson argues you can be cleverer than that though. Let’s inhale some hype.

1 Tracking and choosing hyperparameters

In practice this hyperparameter thing is integrated with the problem both of configuring ML and of tracking progress; See also those pages for practical implementation notes.

2 Bayesian/surrogate optimisation

Loosely, we think of interpolating between observations of a loss surface and guessing where the optimal point is. See Bayesian optimisation. This is generic. Not as popular in practice as I might have assumed because it turns out to be fairly greedy with data and does not exploit problem-specific ideas, such as early stopping, which is saves time and is in any case a useful type of neural net regularisation.

3 Multiple hyperparameters require multi-objective optimisations

This leads to difficulty. See multi-objective optimisation.

4 Differentiable hyperparameter optimisation

See differentiable model selection.

7 Implementations

A synoptic overview of the trendiest strategies can be found in Peter Cotton’s microprediction/humpday: Elo ratings for global black box derivative-free optimizers:

Behold! Fifty strategies assigned Elo ratings depending on dimension of the problem and number of function evaluations allowed.

Hello and welcome to HumpDay, a package that helps you choose a Python global optimizer package, and strategy therein, from Ax-Platform, bayesian-optimization, DLib, HyperOpt, NeverGrad, Optuna, Platypus, PyMoo, PySOT, Scipy classic and shgo, Skopt, nlopt, Py-Bobyaq, UltraOpt and maybe others by the time you read this. It also presents some of their functionality in a common calling syntax.

The introductory blog posts are enlightening:

Most of the implementations use, explicitly or implicitly, a surrogate model for parameter tuning, but wrap it with some tools to control and launch experiments in parallel, early termination etc.

Arranged so that the top few are hyped and popular and after that are less renowed hipster options.

Not yet filed:

7.1 Nevergrad

Meta’s Nevergrad seems fine. Its special feature is that is runs in HPC hell, via submitit. There is also a hydra plugin, see here.

7.2 Ax

Ax · Adaptive Experimentation Platform

Ax is a platform for optimizing any kind of experiment, including machine learning experiments, A/B tests, and simulations. Ax can optimize discrete configurations (e.g., variants of an A/B test) using multi-armed bandit optimization, and continuous (e.g., integer or floating point)-valued configurations using Bayesian optimization. This makes it suitable for a wide range of applications.

Also supported via Hydra plugin, which may mean that it is supported on clusters; This walthrough notebook seems to indicate it is.

7.3 Determined

determined includes hyperparameter tuning which is not in fact a surrogate surface, but an early stopping pruning of crappy models in a random search, i.e. fancy random search.

7.4 Ray

Ray includes Ray.Tune

Tune is a Python library for experiment execution and hyperparameter tuning at any scale. Core features:

7.5 Optuna

optuna (Akiba et al. 2019) supports fancy neural net training; similar to hyperopt AFAICT except that is supports Covariance Matrix Adaptation, whatever that is ? (see Hansen (2016)).

Optuna is an automatic hyperparameter optimization software framework, particularly designed for machine learning. It features an imperative, define-by-run style user API. Thanks to our define-by-run API, the code written with Optuna enjoys high modularity, and the user of Optuna can dynamically construct the search spaces for the hyperparameters.

7.6 hyperopt.py

hyperopt J. Bergstra, Yamins, and Cox (2013)

is a Python library for optimizing over awkward search spaces with real-valued, discrete, and conditional dimensions.

Currently two algorithms are implemented in hyperopt:

  • Random Search
  • Tree of Parzen Estimators (TPE)

Hyperopt has been designed to accommodate Bayesian optimization algorithms based on Gaussian processes and regression trees, but these are not currently implemented.

All algorithms can be run either serially, or in parallel by communicating via MongoDB or Apache Spark

7.7 Hyperopt.jl

7.8 auto-sklearn

auto-sklearn has recently been upgraded. Details TBD (Feurer et al. 2020).

7.9 skopt

skopt (aka scikit-optimize)

[…] is a simple and efficient library to minimize (very) expensive and noisy black-box functions. It implements several methods for sequential model-based optimization.

7.10 spearmint


Spearmint is a package to perform Bayesian optimization according to the algorithms outlined in the paper (Snoek, Larochelle, and Adams 2012).

The code consists of several parts. It is designed to be modular to allow swapping out various ‘driver’ and ‘chooser’ modules. The ‘chooser’ modules are implementations of acquisition functions such as expected improvement, UCB or random. The drivers determine how experiments are distributed and run on the system. As the code is designed to run experiments in parallel (spawning a new experiment as soon a result comes in), this requires some engineering.

Spearmint2 is similar, but more recently updated and fancier; however it has a restrictive license prohibiting wide redistribution without the payment of fees. You may or may not wish to trust the implied level of development and support of 4 Harvard Professors, depending on your application.

Both of the Spearmint options (especially the latter) have opinionated choices of technology stack in order to do their optimizations, which means they can do more work for you, but require more setup, than a simple little thing like skopt. Depending on your computing environment this might be an overall plus or a minus.

7.11 SMAC


(sequential model-based algorithm configuration) is a versatile tool for optimizing algorithm parameters (or the parameters of some other process we can run automatically, or a function we can evaluate, such as a simulation).

SMAC has helped us speed up both local search and tree search algorithms by orders of magnitude on certain instance distributions. Recently, we have also found it to be very effective for the hyperparameter optimization of machine learning algorithms, scaling better to high dimensions and discrete input dimensions than other algorithms. Finally, the predictive models SMAC is based on can also capture and exploit important information about the model domain, such as which input variables are most important.

We hope you find SMAC similarly useful. Ultimately, we hope that it helps algorithm designers focus on tasks that are more scientifically valuable than parameter tuning.

Python interface through pysmac.

7.12 AutoML


Won the land-grab for the name automl but is now unmaintained.

A quick overview of buzzwords, this project automates:

  • Analytics (pass in data, and auto_ml will tell you the relationship of each variable to what it is you’re trying to predict).
  • Feature Engineering (particularly around dates, and soon, NLP).
  • Robust Scaling (turning all values into their scaled versions between the range of 0 and 1, in a way that is robust to outliers, and works with sparse matrices).
  • Feature Selection (picking only the features that actually prove useful).
  • Data formatting (turning a list of dictionaries into a sparse matrix, one-hot encoding categorical variables, taking the natural log of y for regression problems).
  • Model Selection (which model works best for your problem).
  • Hyperparameter Optimization (what hyperparameters work best for that model).
  • Ensembling Subpredictors (automatically training up models to predict smaller problems within the meta problem).
  • Ensembling Weak Estimators (automatically training up weak models on the larger problem itself, to inform the meta-estimator’s decision).

8 References

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Bengio. 2000. Gradient-Based Optimization of Hyperparameters.” Neural Computation.
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Bergstra, James, and Bengio. 2012. Random Search for Hyper-Parameter Optimization.” Journal of Machine Learning Research.
Bergstra, J, Yamins, and Cox. 2013. “Making a Science of Model Search: Hyperparameter Optimization in Hundreds of Dimensions for Vision Architectures.” In ICML.
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