Open-Source Python package for Single- and Multi-Players multi-armed Bandits algorithms.

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This repository contains the code of Lilian Besson’s numerical environment, written in Python (2 or 3), for numerical simulations on 🎰 single-player and multi-players Multi-Armed Bandits (MAB) algorithms.

Quick presentation

It contains the most complete collection of single-player (classical) bandit algorithms on the Internet (over 65!), as well as implementation of all the state-of-the-art multi-player algorithms.

I follow very actively the latest publications related to Multi-Armed Bandits (MAB) research, and usually implement quite quickly the new algorithms (see for instance, Exp3++, CORRAL and SparseUCB were each introduced by articles (for Exp3++, for CORRAL, for SparseUCB) presented at COLT in July 2017, LearnExp comes from a NIPS 2017 paper, and kl-UCB++ from an ALT 2017 paper.). More recent examples are klUCBswitch from a paper from May 2018, and also MusicalChairNoSensing from a paper from August 2018.

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  • Classical MAB have a lot of applications, from clinical trials, A/B testing, game tree exploration, and online content recommendation (my framework does not implement contextual bandit - yet).

  • Multi-player MAB have applications in Cognitive Radio, and my framework implements all the collision models found in the literature, as well as all the algorithms from the last 10 years or so (rhoRand from 2009, MEGA from 2015, MusicalChair, and our state-of-the-art algorithms RandTopM and MCTopM, along with very recent algorithms SIC-MMAB from arXiv:1809.08151 and MusicalChairNoSensing from arXiv:1808.08416).

  • I’m working on adding a clean support for non-stationary MAB problem, and I will soon implement all state-of-the-art algorithms for these problems.

With this numerical framework, simulations can run on a single CPU or a multi-core machine, and summary plots are automatically saved as high-quality PNG, PDF and EPS (ready for being used in research article). Making new simulations is very easy, one only needs to write a configuration script and basically no code! See these examples (files named configuration_*.py).

A complete Sphinx documentation for each algorithms and every piece of code (included constants in the configurations!) is available here: (I will use ReadTheDocs for this project, but I won’t use any continuous integration, don’t even think of it!)

I (Lilian Besson) have started my PhD in October 2016, and this is a part of my on going research since December 2016.

I launched the documentation on March 2017, I wrote my first research articles using this framework in 2017 and decided to (finally) open-source my project in February 2018. Commits of / Date of last commit of Issues of : Open issues of / Closed issues of

How to cite this work?

If you use this package for your own work, please consider citing it with this piece of BibTeX:

    title =   {{SMPyBandits: an Open-Source Research Framework for Single and Multi-Players Multi-Arms Bandits (MAB) Algorithms in Python}},
    author =  {Lilian Besson},
    year =    {2018},
    url =     {},
    howpublished = {Online at: \url{}},
    note =    {Code at, documentation at}

I also wrote a small paper to present SMPyBandits, and I will send it to JMLR MLOSS. The paper can be consulted here on my website.

A DOI will arrive as soon as possible! I tried to publish a paper on both JOSS and MLOSS.

List of research publications using SMPyBandits

1st article, about policy aggregation algorithm (aka model selection)

I designed and added the Aggregator policy, in order to test its validity and performance.

It is a “simple” voting algorithm to combine multiple bandit algorithms into one. Basically, it behaves like a simple MAB bandit just based on empirical means (even simpler than UCB), where arms are the child algorithms A_1 .. A_N, each running in “parallel”.

For more details, refer to this file: and this research article.

2nd article, about Multi-players Multi-Armed Bandits

There is another point of view: instead of comparing different single-player policies on the same problem, we can make them play against each other, in a multi-player setting. The basic difference is about collisions : at each time t, if two or more user chose to sense the same channel, there is a collision. Collisions can be handled in different way from the base station point of view, and from each player point of view.

For more details, refer to this file: and this research article.

3rd article, using Doubling Trick for Multi-Armed Bandits

I studied what Doubling Trick can and can’t do to obtain efficient anytime version of non-anytime optimal Multi-Armed Bandits algorithms.

For more details, refer to this file: and this research article.

4th article, about Piece-Wise Stationary Multi-Armed Bandits

With Emilie Kaufmann, we studied the Generalized Likelihood Ratio Test (GLRT) for sub-Bernoulli distributions, and proposed the B-GLRT algorithm for change-point detection for piece-wise stationary one-armed bandit problems. We combined the B-GLRT with the kl-UCB multi-armed bandit algorithm and proposed the GLR-klUCB algorithm for piece-wise stationary multi-armed bandit problems. We prove finite-time guarantees for the B-GLRT and the GLR-klUCB algorithm, and we illustrate its performance with extensive numerical experiments.

For more details, refer to this file: and this research article.

Other interesting things

Single-player Policies

Arms and problems

  • My framework mainly targets stochastic bandits, with arms following Bernoulli, bounded (truncated) or unbounded Gaussian, Exponential, Gamma or Poisson distributions, and more.

  • The default configuration is to use a fixed problem for N repetitions (e.g. 1000 repetitions, use MAB.MAB), but there is also a perfect support for “Bayesian” problems where the mean vector µ1,…,µK change at every repetition (see MAB.DynamicMAB).

  • There is also a good support for Markovian problems, see MAB.MarkovianMAB, even though I didn’t implement any policies tailored for Markovian problems.

  • I’m actively working on adding a very clean support for non-stationary MAB problems, and MAB.PieceWiseStationaryMAB is already working well. Use it with policies designed for piece-wise stationary problems, like Discounted-Thompson, one of the CD-UCB algorithms, M-UCB, SlidingWindowUCB or Discounted-UCB, or SW-UCB#.

Other remarks

  • Everything here is done in an imperative, object oriented style. The API of the Arms, Policy and MultiPlayersPolicy classes is documented in this file (

  • The code is clean, valid for both Python 2 and Python 3.

  • Some piece of code come from the pymaBandits project, but most of them were refactored. Thanks to the initial project!

  • G.Varoquaux’s joblib is used for the Evaluator and EvaluatorMultiPlayers classes, so the simulations are easily parallelized on multi-core machines. (Put n_jobs = -1 or PARALLEL = True in the config file to use all your CPU cores, as it is by default).

How to run the experiments ?

See this document: for more details (or this documentation page).

TL;DR: this short bash snippet shows how to clone the code, install the requirements for Python 3 (in a virtualenv, and starts some simulation for N=100 repetitions of the default non-Bayesian Bernoulli-distributed problem, for K=9 arms, an horizon of T=10000 and on 4 CPUs (it should take about 20 minutes for each simulations):

cd /tmp/  # or wherever you want
git clone -c core.symlinks=true
cd SMPyBandits
# just be sure you have the latest virtualenv from Python 3
sudo pip3 install --upgrade --force-reinstall virtualenv
# create and active the virtualenv
virtualenv venv
. venv/bin/activate
type pip  # check it is /tmp/SMPyBandits/venv/bin/pip
type python  # check it is /tmp/SMPyBandits/venv/bin/python
# install the requirements in the virtualenv
pip install -r requirements_full.txt
# run a single-player simulation!
N=100 T=10000 K=9 N_JOBS=4 make single
# run a multi-player simulation!
N=100 T=10000 M=3 K=9 N_JOBS=4 make moremulti

You can also install it directly with pip and from GitHub:

cd /tmp/ ; mkdir SMPyBandits ; cd SMPyBandits/
virtualenv venv
. venv/bin/activate
type pip  # check it is /tmp/SMPyBandits/venv/bin/pip
type python  # check it is /tmp/SMPyBandits/venv/bin/python
pip install git+[full]
  • If speed matters to you and you want to use algorithms based on kl-UCB, you should take the time to build and install the fast C implementation of the utilities KL functions. Default is to use, but using the C version from Policies/C/ really speeds up the computations. Just follow the instructions, it should work well (you need gcc to be installed).

  • And if speed matters, be sure that you have a working version of Numba, it is used by many small functions to (try to automatically) speed up the computations.


A pinned Nix environment is available for this experimental setup in the nix/pkgs/ directory. From the root of the project:

$ nix-shell
nix-shell$ jupyter_notebook 
nix-shell$ N=100 T=10000 K=9 N_JOBS=4 make single

The following one-liner lets you explore one of the example notebooks from any Nix-enabled machine, without cloning the repository:

$ nix-shell --run 'jupyter-notebook $EXAMPLE_NOTEBOOKS/Example_of_a_small_Multi-Player_Simulation__with_Centralized_Algorithms.ipynb' 

💥 Warning


I don’t except issues or pull requests on this project, but you are welcome to.

Contributions (issues, questions, pull requests) are of course welcome, but this project is and will stay a personal environment designed for quick research experiments, and will never try to be an industry-ready module for applications of Multi-Armed Bandits algorithms. If you want to contribute, please have a look to the file, and if you want to be more seriously involved, read the file.


See this file, and the issues on GitHub.

📜 License ? GitHub license

MIT Licensed (file LICENSE).

© 2016-2018 Lilian Besson, with help from contributors.

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