*SMPyBandits*Ā¶

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

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

A complete Sphinx-generated documentation is on SMPyBandits.GitHub.io.

You can also browse online the results of extensive benchmarks, powered by Airspeed Velocity, on this page (code on SMPyBandits-benchmarks).

## Quick presentationĀ¶

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.

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).Iām 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: SMPyBandits.GitHub.io. (I will use ReadTheDocs for this project, but I wonāt use any *continuous integration*, donāt even think of it!)

I (Lilian Besson) have started my PhD in October 2016, and this is a part of my

on goingresearch 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. / : /

## How to cite this work?Ā¶

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

```
@misc{SMPyBandits,
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 = {https://github.com/SMPyBandits/SMPyBandits/},
howpublished = {Online at: \url{github.com/SMPyBandits/SMPyBandits}},
note = {Code at https://github.com/SMPyBandits/SMPyBandits/, documentation at https://smpybandits.github.io/}
}
```

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.

## List of research publications using SMPyBanditsĀ¶

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

I designed and added the `Aggregator`

policy, in order to test its validity and performance.

It is a āsimpleā **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 āparallelā.

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

PDF : BKM_IEEEWCNC_2018.pdf | HAL notice : BKM_IEEEWCNC_2018 | BibTeX : BKM_IEEEWCNC_2018.bib | Source code and documentation

### 2nd article, about Multi-players Multi-Armed BanditsĀ¶

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: MultiPlayers.md and this research article.

PDF : BK__ALT_2018.pdf | HAL notice : BK__ALT_2018 | BibTeX : BK__ALT_2018.bib | Source code and documentation

### 3rd article, using Doubling Trick for Multi-Armed BanditsĀ¶

I studied what Doubling Trick can and canāt do to obtain efficient anytime version of non-anytime optimal Multi-Armed Bandits algorithms.

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

PDF : BK__DoublingTricks_2018.pdf | HAL notice : BK__DoublingTricks_2018 | BibTeX : BK__DoublingTricks_2018.bib | Source code and documentation

### 4th article, about Piece-Wise Stationary Multi-Armed BanditsĀ¶

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: NonStationaryBandits.md and this research article.

PDF : BK__COLT_2019.pdf | HAL notice : BK__COLT_2019 | BibTeX : BK__COLT_2019.bib | Source code and documentation

## Other interesting thingsĀ¶

### Single-player PoliciesĀ¶

More than 65 algorithms, including all known variants of the

`UCB`

, kl-UCB,`MOSS`

and Thompson Sampling algorithms, as well as other less known algorithms (`OCUCB`

,`BESA`

,`OSSB`

etc).For instance,

`SparseWrapper`

is a generalization of the SparseUCB from this article.Implementation of very recent Multi-Armed Bandits algorithms, e.g.,

`kl-UCB++`

(from this article),`UCB-dagger`

(from this article), or`MOSS-anytime`

(from this article).Experimental policies:

`BlackBoxOpt`

or`UnsupervisedLearning`

(using Gaussian processes to learn the arms distributions).

### Arms and problemsĀ¶

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 āBayesianā problems where the mean vector Āµ1,ā¦,ĀµK change*at every repetition*(see`MAB.DynamicMAB`

).There is also a good support for Markovian problems, see

`MAB.MarkovianMAB`

, even though I didnāt implement any policies tailored for Markovian problems.Iām 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 remarksĀ¶

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

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

G.Varoquauxās 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 ?Ā¶

See this document: How_to_run_the_code.md 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 https://GitHub.com/SMPyBandits/SMPyBandits.git
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 more
```

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+https://github.com/SMPyBandits/SMPyBandits.git#egg=SMPyBandits[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 kullback.py, 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.

### š„ WarningĀ¶

This work is still

**experimental**even if it is well tested and stable! Itās active research. It should be completely bug free and every single module/file should work perfectly (as this pylint log and this other one says), but bugs are sometimes hard to spot so if you encounter any issue, please fill a bug ticket.Whenever I add a new feature, I run experiments to check that nothing is broken (and Travis CI helps too). But

*there is no unittest*(I donāt have time). You would have to trust me š!This project is NOT meant to be a library that you can use elsewhere, but a research tool.

## Contributing?Ā¶

I donāt 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 CONTRIBUTING.md file, and if you want to be more seriously involved, read the CODE_OF_CONDUCT.md file.

You are welcome to submit an issue, if it was not previously answered,

If you have interesting example of use of SMPyBandits, please share it! (Jupyter Notebooks are preferred). And fill a pull request to add it to the notebooks examples.

## š„ TODOĀ¶

See this file TODO.md, and the issues on GitHub.

## š License ? Ā¶

MIT Licensed (file LICENSE).

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