News: The BADS paper [1] has been accepted for a poster presentation at NIPS 2017! (20.9% acceptance rate this year, for a total of 3240 submissions)

BADS is a novel, fast Bayesian optimization algorithm designed to solve difficult optimization problems, in particular related to fitting computational models (e.g., via maximum likelihood estimation).

BADS has been intensively tested for fitting behavioral, cognitive, and neural models and is currently being used in more than a dozen projects in the Ma lab. In our benchmark with real model-fitting problems, BADS performed on par or better than many other common and state-of-the-art MATLAB optimizers, such as fminsearch, fmincon, and cmaes [1].

BADS is recommended when no gradient information is available, and the objective function is non-analytical or noisy, for example evaluated through numerical approximation or via simulation.

BADS requires no specific tuning and runs off-the-shelf like other built-in MATLAB optimizers such as fminsearch.

Download the latest version of BADS as a ZIP file.

• To install BADS, clone or unpack the zipped repository where you want it and run the script install.m.
  • This will add the BADS base folder to the MATLAB search path.
• To see if everything works, run bads('test').

The BADS interface is similar to that of other MATLAB optimizers. The basic usage is:

[X,FVAL] = bads(FUN,X0,LB,UB,PLB,PUB);

with input parameters:

• FUN, a function handle to the objective function to minimize (typically, the negative log likelihood of a dataset and model, for a given input parameter vector);
• X0, the starting point of the optimization (a row vector);
• LB and UB, hard lower and upper bounds;
• PLB and PUB, plausible lower and upper bounds, that is a box where you would expect to find almost all solutions.

The output parameters are:

• X, the found optimum.
• FVAL, the (estimated) function value at the optimum.

For more usage examples, see bads_examples.m. You can also type help bads to display the documentation.

For practical recommendations, such as how to set LB and UB, and any other question, check out the FAQ on the BADS wiki.

BADS follows a mesh adaptive direct search (MADS) procedure for function minimization that alternates poll steps and search steps (see Fig 1).

• In the poll stage, points are evaluated on a mesh by taking steps in one direction at a time, until an improvement is found or all directions have been tried. The step size is doubled in case of success, halved otherwise.
• In the search stage, a Gaussian process (GP) is fit to a (local) subset of the points evaluated so far. Then, we iteratively choose points to evaluate according to a lower confidence bound strategy that trades off between exploration of uncertain regions (high GP uncertainty) and exploitation of promising solutions (low GP mean).

Fig 1: BADS procedure

See here for a visualization of several optimizers at work, including BADS.

See our paper for more details [1].

If you have trouble doing something with BADS:

• Check out the FAQ on the BADS wiki;
• Contact me at [email protected], putting 'BADS' in the subject of the email.

This project is under active development. If you find a bug, or anything that needs correction, please let me know.

1. Acerbi, L. & Ma, W. J. (2017). Practical Bayesian Optimization for Model Fitting with Bayesian Adaptive Direct Search. arXiv preprint, arXiv:1705.04405. (link)

Note: This is a temporary reference. The paper will eventually appear in the proceedings of the NIPS 2017 conference.

You can cite BADS in your work with something along the lines of

We optimized the log likelihoods of our models using Bayesian adaptive direct search (BADS; Acerbi and Ma, 2017). BADS alternates between a series of fast, local Bayesian optimization steps and a systematic, slower exploration of a mesh grid.

Besides formal citations, you can demonstrate your appreciation for BADS in the following ways:

• Star the BADS repository on GitHub;
• Follow me on Twitter for updates about BADS and other projects I am involved with;
• Tell me about your model-fitting problem and your experience with BADS (positive or negative) at [email protected] (putting 'BADS' in the subject of the email).

BADS is released under the terms of the GNU General Public License v3.0.