SMPyBandits

https://smpybandits.github.io/
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SMPyBandits is an open-source Python research framework for numerical simulations on single-player...
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### Set up virtualenv and install requirements

Source: https://smpybandits.github.io/How_to_run_the_code.html

Shows the process of creating a virtualenv, activating it, checking pip, and installing requirements. The output shows the installation of packages.

```bash
$ virtualenv .
Using base prefix '/usr'
New python executable in /your/path/to/SMPyBandits/bin/python3
Also creating executable in /your/path/to/SMPyBandits/bin/python
Installing setuptools, pip, wheel...done.
$ source bin/activate  # in bash, use activate.csh or activate.fish if needed
$ type pip  # just to check
pip is /your/path/to/SMPyBandits/bin/pip
$ pip install -r requirements.txt
Collecting numpy (from -r requirements.txt (line 5))
...
Installing collected packages: numpy, scipy, cycler, pytz, python-dateutil, matplotlib, joblib, pandas, seaborn, tqdm, sphinx-rtd-theme, commonmark, docutils, recommonmark
Successfully installed commonmark-0.5.4 cycler-0.10.0 docutils-0.13.1 joblib-0.11 matplotlib-2.0.0 numpy-1.12.1 pandas-0.19.2 python-dateutil-2.6.0 pytz-2016.10 recommonmark-0.4.0 scipy-0.19.0 seaborn-0.7.1 sphinx-rtd-theme-0.2.4 tqdm-4.11.2

```

--------------------------------

### Instantiate MusicalChairNoSensing and configure multi-player setups

Source: https://smpybandits.github.io/_modules/Policies/MusicalChairNoSensing.html

Shows how to instantiate a single MusicalChairNoSensing player and how to configure multi-player setups using either the Selfish wrapper or a list comprehension. The examples are from the class docstring and assume nbPlayers, nbArms, and horizon are defined.

```python
>>> nbPlayers, nbArms, horizon = 3, 9, 10000
>>> player1 = MusicalChairNoSensing(nbPlayers, nbArms, horizon)
```

```python
>>> configuration["players"] = Selfish(NB_PLAYERS, MusicalChairNoSensing, nbArms, nbPlayers=nbPlayers, horizon=horizon).children
```

```python
>>> configuration["players"] = [ MusicalChairNoSensing(nbPlayers=nbPlayers, nbArms=nbArms, horizon=horizon) for _ in range(NB_PLAYERS) ]
```

--------------------------------

### Use Makefile to install and run

Source: https://smpybandits.github.io/How_to_run_the_code.html

Use the provided Makefile to install requirements and run the main.py script.

```bash
make install       # install the requirements
make multiplayers  # run and log the main.py script

```

--------------------------------

### Experiment Environment and Policy Initialization

Source: https://smpybandits.github.io/notebooks/Unsupervised_Learning_for_Bandit_problem.html

Logs showing the evaluation environment setup and the configuration of various bandit policies including UnsupervisedLearning, UCB, Thompson, and klUCB.

```text
Evaluating environment: MAB(nbArms: 9, arms: [G(0.3, 0.25), G(0.35, 0.25), G(0.4, 0.25), G(0.45, 0.25), G(0.5, 0.25), G(0.55, 0.25), G(0.6, 0.25), G(0.65, 0.25), G(0.7, 0.25)], minArm: 0.3, maxArm: 0.7)
- Adding policy #1 = {'archtype': <class '__main__.UnsupervisedLearning'>, 'params': {'bandwidth': 0.2, 'meanOf': 200, 'T_0': 100, 'kernel': 'gaussian', 'estimator': <class 'sklearn.neighbors.kde.KernelDensity'>, 'fit_every': 1000}} ...
  Creating this policy from a dictionnary 'self.cfg['policies'][0]' = {'archtype': <class '__main__.UnsupervisedLearning'>, 'params': {'bandwidth': 0.2, 'meanOf': 200, 'T_0': 100, 'kernel': 'gaussian', 'estimator': <class 'sklearn.neighbors.kde.KernelDensity'>, 'fit_every': 1000}} ...
- Adding policy #2 = {'archtype': <class '__main__.UnsupervisedLearning'>, 'params': {'estimator': <class '__main__.SimpleGaussianKernel'>, 'fit_every': 1000, 'meanOf': 200, 'T_0': 100}} ...
  Creating this policy from a dictionnary 'self.cfg['policies'][1]' = {'archtype': <class '__main__.UnsupervisedLearning'>, 'params': {'estimator': <class '__main__.SimpleGaussianKernel'>, 'fit_every': 1000, 'meanOf': 200, 'T_0': 100}} ...
- Adding policy #3 = {'archtype': <class 'Policies.UCB.UCB'>, 'params': {}} ...
  Creating this policy from a dictionnary 'self.cfg['policies'][2]' = {'archtype': <class 'Policies.UCB.UCB'>, 'params': {}} ...
- Adding policy #4 = {'archtype': <class 'Policies.Thompson.Thompson'>, 'params': {}} ...
  Creating this policy from a dictionnary 'self.cfg['policies'][3]' = {'archtype': <class 'Policies.Thompson.Thompson'>, 'params': {}} ...
- Adding policy #5 = {'archtype': <class 'Policies.klUCB.klUCB'>, 'params': {'klucb': <function klucbGauss at 0x7f835bfd9488>}} ...
  Creating this policy from a dictionnary 'self.cfg['policies'][4]' = {'archtype': <class 'Policies.klUCB.klUCB'>, 'params': {'klucb': <function klucbGauss at 0x7f835bfd9488>}} ...

- Evaluating policy #1/5: UnsupervisedLearning(KernelDensity, $T_0=100$, $T_1=1e+03$, $M=200$) ...
```

--------------------------------

### SimpleGaussianKernel Policy Evaluation

Source: https://smpybandits.github.io/notebooks/Unsupervised_Learning_for_Bandit_problem.html

Evaluation start log for the SimpleGaussianKernel policy.

```text
- Evaluating policy #2/5: UnsupervisedLearning(SimpleGaussianKernel, $T_0=100$, $T_1=1e+03$, $M=200$) ...
```

--------------------------------

### walk examples

Source: https://smpybandits.github.io/_modules/Environment/pykov.html

Examples for the walk method. The first call generates a 10-step random walk with default start and stop; the second call starts at 'B' and stops when 'B' is reached.

```python
>>> T = pykov.Chain({('A','B'): .3, ('A','A'): .7, ('B','A'): 1.})
>>> T.walk(10)
['B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'A', 'B', 'A']
>>> T.walk(10,'B','B')
['B', 'A', 'A', 'A', 'A', 'A', 'B']
```

--------------------------------

### Example: rhoRandSticky usage with UCB

Source: https://smpybandits.github.io/docs/PoliciesMultiPlayers.rhoRandSticky.html

Shows how to instantiate rhoRandSticky with UCB players, set a stickyTime, and get initial choices from the children. The example uses a fixed random seed for reproducibility.

```python
>>> from Policies import *
>>> import random; random.seed(0); import numpy as np; np.random.seed(0)
>>> nbArms = 17
>>> nbPlayers = 6
>>> stickyTime = 5
>>> s = rhoRandSticky(nbPlayers, nbArms, UCB, stickyTime=stickyTime)
>>> [ child.choice() for child in s.children ]
[12, 15, 0, 3, 3, 7]
>>> [ child.choice() for child in s.children ]
[9, 4, 6, 12, 1, 6]
```

--------------------------------

### Main Server Initialization

Source: https://smpybandits.github.io/_modules/policy_server.html

Constructs the learning policy from a JSON configuration and starts the server.

```python
[docs]def main(args):
    """
    Take args, construct the learning policy and starts the server.
    """
    host = str(args['--host'])
    port = int(args['--port'])
    try:
        means = str(args['--means'])
        means = means.replace('[', '').replace(']', '')
        means = [ float(m) for m in means.split(',') ]
        means = np.asarray(means, dtype=float)
    except ValueError:
        means = None

    json_configuration = args['<json_configuration>']
    configuration = read_configuration_policy(json_configuration)

    nbArms = int(configuration['nbArms'])
    # try to map strings in the dictionary to variables, e.g., policies
    params = configuration['params']
    transform_str(params)

    print("Params =", params)
    policy = globals()[configuration['archtype']](nbArms, **params)
    print("Using the policy", policy)

    return server(policy, host, port, means=means)



if __name__ == '__main__':
    arguments = docopt(__doc__, version=version)
    # print("arguments =", arguments)  # DEBUG
    main(arguments)
```

--------------------------------

### Import MAB environment

Source: https://smpybandits.github.io/_sources/notebooks/Easily_creating_MAB_problems.ipynb.txt

Initial setup to import the MAB class from the Environment package after ensuring SMPyBandits is installed.

```python
Requirement already satisfied: SMPyBandits in ./venv3/lib/python3.6/site-packages (0.9.4)
Requirement already satisfied: watermark in ./venv3/lib/python3.6/site-packages (1.7.0)
Requirement already satisfied: scikit-learn in ./venv3/lib/python3.6/site-packages (from SMPyBandits) (0.20.0)
Requirement already satisfied: scikit-optimize in ./venv3/lib/python3.6/site-packages (from SMPyBandits) (0.5.2)
Requirement already satisfied: scipy>0.9 in ./venv3/lib/python3.6/site-packages (from SMPyBandits) (1.1.0)
Requirement already satisfied: numpy in ./venv3/lib/python3.6/site-packages (from SMPyBandits) (1.15.4)
Requirement already satisfied: matplotlib>=2 in ./venv3/lib/python3.6/site-packages (from SMPyBandits) (3.0.2)
Requirement already satisfied: seaborn in ./venv3/lib/python3.6/site-packages (from SMPyBandits) (0.9.0)
Requirement already satisfied: joblib in ./venv3/lib/python3.6/site-packages (from SMPyBandits) (0.13.0)
Requirement already satisfied: ipython in ./venv3/lib/python3.6/site-packages (from watermark) (7.1.1)
```

--------------------------------

### Inspect kde.sample method

Source: https://smpybandits.github.io/notebooks/Unsupervised_Learning_for_Bandit_problem.html

Displays the signature and documentation for the kde.sample method.

```python
kde.sample?
```

```text
Signature: kde.sample(n_samples=1, random_state=None)
Docstring:
Generate random samples from the model.

Currently, this is implemented only for gaussian and tophat kernels.

Parameters
----------
n_samples : int, optional
    Number of samples to generate. Defaults to 1.

random_state : RandomState or an int seed (0 by default)
    A random number generator instance.

Returns
-------
X : array_like, shape (n_samples, n_features)
    List of samples.
File:      /usr/local/lib/python3.5/dist-packages/sklearn/neighbors/kde.py
Type:      method
```

--------------------------------

### Import and setup for performance comparison

Source: https://smpybandits.github.io/docs/Policies.kullback_cython.html

Illustrates the import of the C and Cython modules for performance comparison. The code is a placeholder for illustration purposes.

```python
>>> r = np.random.random
>>> import kullback_c; import kullback_cython  # fake, just for illustration
```

--------------------------------

### nrows_ncols usage example

Source: https://smpybandits.github.io/docs/Environment.plotsettings.html

Shows how to use nrows_ncols to get the number of rows and columns for subplots for N from 1 to 21, printing the result. The output demonstrates the grid sizes for each N.

```python
>>> for N in range(1, 22):
...     nrows, ncols = nrows_ncols(N)
...     print("For N = {:>2}, {} rows and {} cols are enough.".format(N, nrows, ncols))
For N =  1, 1 rows and 1 cols are enough.
For N =  2, 2 rows and 1 cols are enough.
For N =  3, 2 rows and 2 cols are enough.
For N =  4, 2 rows and 2 cols are enough.
For N =  5, 3 rows and 2 cols are enough.
For N =  6, 3 rows and 2 cols are enough.
For N =  7, 3 rows and 3 cols are enough.
For N =  8, 3 rows and 3 cols are enough.
For N =  9, 3 rows and 3 cols are enough.
For N = 10, 4 rows and 3 cols are enough.
For N = 11, 4 rows and 3 cols are enough.
For N = 12, 4 rows and 3 cols are enough.
For N = 13, 4 rows and 4 cols are enough.
For N = 14, 4 rows and 4 cols are enough.
For N = 15, 4 rows and 4 cols are enough.
For N = 16, 4 rows and 4 cols are enough.
For N = 17, 5 rows and 4 cols are enough.
For N = 18, 5 rows and 4 cols are enough.
For N = 19, 5 rows and 4 cols are enough.
For N = 20, 5 rows and 4 cols are enough.
For N = 21, 5 rows and 5 cols are enough.
```

--------------------------------

### Main execution function

Source: https://smpybandits.github.io/_modules/env_client.html

Constructs the learning policy and starts the server based on provided command-line arguments.

```python
[docs]def main(arguments):
    """
    Take arguments, construct the learning policy and starts the server.
    """
    host = arguments['--host']
    port = int(arguments['--port'])
    speed = float(arguments['--speed']) / 1000.0
    is_markovian = arguments['--markovian']
    is_dynamic = arguments['--dynamic']
    json_configuration = arguments['<json_configuration>']
    configuration = read_configuration_env(json_configuration)
    transform_str(configuration)
    if is_dynamic:
        env = ChangingAtEachRepMAB(configuration)
    elif is_markovian:
        env = MarkovianMAB(configuration)
    else:
        env = MAB(configuration)
    print("Using the environment: ", env)  # DEBUG
    print("Emitting regularly every", speed, "seconds.")  # DEBUG
    return client(env, host, port, speed)



if __name__ == '__main__':
    arguments = docopt(__doc__, version=version)
    # print("arguments =", arguments)  # DEBUG
    main(arguments)
```

--------------------------------

### Install and load watermark extension

Source: https://smpybandits.github.io/notebooks/Exploring_different_doubling_tricks_for_different_kinds_of_regret_bounds.html

Installs the watermark package and loads the IPython extension to display environment information. The output shows the installed versions and system details.

```python
!pip install watermark
%load_ext watermark
%watermark -v -m -p numpy,matplotlib,seaborn -a "Lilian Besson and Emilie Kaufmann"

```

```text
Requirement already satisfied: watermark in ./venv3/lib/python3.6/site-packages (1.7.0)
Requirement already satisfied: ipython in ./venv3/lib/python3.6/site-packages (from watermark) (7.1.1)
Requirement already satisfied: pexpect; sys_platform != "win32" in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (4.6.0)
Requirement already satisfied: prompt-toolkit<2.1.0,>=2.0.0 in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (2.0.7)
Requirement already satisfied: setuptools>=18.5 in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (40.6.2)
Requirement already satisfied: pygments in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (2.2.0)
Requirement already satisfied: pickleshare in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (0.7.5)
Requirement already satisfied: decorator in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (4.3.0)
Requirement already satisfied: jedi>=0.10 in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (0.13.1)
Requirement already satisfied: traitlets>=4.2 in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (4.3.2)
Requirement already satisfied: backcall in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (0.1.0)
Requirement already satisfied: ptyprocess>=0.5 in ./venv3/lib/python3.6/site-packages (from pexpect; sys_platform != "win32"->ipython->watermark) (0.6.0)
Requirement already satisfied: six>=1.9.0 in ./venv3/lib/python3.6/site-packages (from prompt-toolkit<2.1.0,>=2.0.0->ipython->watermark) (1.11.0)
Requirement already satisfied: wcwidth in ./venv3/lib/python3.6/site-packages (from prompt-toolkit<2.1.0,>=2.0.0->ipython->watermark) (0.1.7)
Requirement already satisfied: parso>=0.3.0 in ./venv3/lib/python3.6/site-packages (from jedi>=0.10->ipython->watermark) (0.3.1)
Requirement already satisfied: ipython-genutils in ./venv3/lib/python3.6/site-packages (from traitlets>=4.2->ipython->watermark) (0.2.0)
Lilian Besson and Emilie Kaufmann

CPython 3.6.6
IPython 7.1.1

numpy 1.15.4
matplotlib 3.0.2
seaborn 0.9.0

compiler   : GCC 8.0.1 20180414 (experimental) [trunk revision 259383
system     : Linux
release    : 4.15.0-38-generic
machine    : x86_64
processor  : x86_64
CPU cores  : 4
interpreter: 64bit

```

--------------------------------

### Build Cython extension

Source: https://smpybandits.github.io/docs/Policies.Experimentals.UCBcython.html

Run this command using the setup.py script to build the Cython extension in-place.

```bash
$ python setup.py build_ext --inplace
```

--------------------------------

### Install Jupyter Notebook and IPython with pip

Source: https://smpybandits.github.io/_sources/notebooks/README.md.txt

Installs Jupyter Notebook and IPython using pip. Requires sudo privileges. After installation, the jupyter-notebook or jupyter command should be available in your PATH.

```bash
sudo pip install jupyter ipython
```

--------------------------------

### Initialize MCTopMOld

Source: https://smpybandits.github.io/_modules/PoliciesMultiPlayers/RandTopM.html

Example usage of the MCTopMOld policy, demonstrating initialization and choice selection for multiple players.

```python
>>> from Policies import *
>>> import random; random.seed(0); import numpy as np; np.random.seed(0)
>>> nbArms = 17
>>> nbPlayers = 6
>>> s = MCTopMOld(nbPlayers, nbArms, UCB)
>>> [ child.choice() for child in s.children ]
[12, 15, 0, 3, 3, 7]
```

--------------------------------

### new_rank example with forceChange=True

Source: https://smpybandits.github.io/docs/PoliciesMultiPlayers.rhoRandALOHA.html

Example of the new_rank function with forceChange=True, ensuring the new rank is different from the current one. The output is deterministic due to the seed set in the previous example.

```python
>>> [ new_rank(1, 8, True) for _ in range(10) ]
[2, 2, 6, 8, 9, 2, 6, 7, 6, 4]
>>> [ new_rank(5, 8, True) for _ in range(10) ]
[9, 8, 8, 9, 1, 9, 1, 2, 7, 1]
```

--------------------------------

### Build Cython extension with setup.py

Source: https://smpybandits.github.io/docs/Policies.Experimentals.UCBoost_faster_cython.html

Compiles the Cython extension in-place using the setup.py script. Run this before importing the UCBoost_faster_cython module.

```bash
$ python setup.py build_ext --inplace

```

--------------------------------

### Install SMPyBandits dependencies

Source: https://smpybandits.github.io/NonStationaryBandits.html

Clone the repository and install the necessary requirements using the Makefile.

```bash
# if not already installed, otherwise update with 'git pull'
git clone https://github.com/SMPyBandits/SMPyBandits/
cd SMPyBandits
make install         # install the requirements ONLY ONCE
```

--------------------------------

### mean_fairness doctest examples

Source: https://smpybandits.github.io/_modules/Environment/fairnessMeasures.html

Doctest examples for the mean_fairness function. The examples use seeded random arrays and show the fairness index for the original, more spread out (squared), and less spread out (square root) versions of the data.

```python
>>> import numpy.random as rn; rn.seed(1)  # for reproductibility
>>> X = np.cumsum(rn.rand(10, 1000))
>>> mean_fairness(X)  # doctest: +ELLIPSIS
0.607...
>>> mean_fairness(X ** 2)  # More spreadout  # doctest: +ELLIPSIS
0.678...
>>> mean_fairness(np.sqrt(np.abs(X)))  # Less spreadout  # doctest: +ELLIPSIS
0.523...

>>> rn.seed(2)  # for reproductibility
>>> X = np.cumsum(rn.randint(0, 10, (10, 100)))
>>> mean_fairness(X)  # doctest: +ELLIPSIS
0.605...
>>> mean_fairness(X ** 2)  # More spreadout  # doctest: +ELLIPSIS
0.834...
>>> mean_fairness(np.sqrt(np.abs(X)))  # Less spreadout  # doctest: +ELLIPSIS
0.509...
```

--------------------------------

### klUCBPlusPlus.__init__(nbArms, horizon=None, tolerance=0.0001, klucb=CPUDispatcher(<function klucbBern>), c=1.0, lower=0.0, amplitude=1.0)

Source: https://smpybandits.github.io/docs/Policies.klUCBPlusPlus.html

Initializes the klUCBPlusPlus policy. This is a new generic index policy.

```APIDOC
## klUCBPlusPlus.__init__(nbArms, horizon=None, tolerance=0.0001, klucb=CPUDispatcher(<function klucbBern>), c=1.0, lower=0.0, amplitude=1.0)

### Description
Initializes the klUCBPlusPlus policy. This is a new generic index policy.

### Method
Constructor

### Signature
`klUCBPlusPlus.__init__(nbArms, horizon=None, tolerance=0.0001, klucb=CPUDispatcher(<function klucbBern>), c=1.0, lower=0.0, amplitude=1.0)`

### Parameters
- **nbArms** (int) - Required - The number of arms.
- **horizon** (int, optional) - Optional - Known horizon of the experiment. Default is None.
- **tolerance** (float, optional) - Optional - Tolerance parameter. Default is 0.0001.
- **klucb** (callable, optional) - Optional - Function for computing the KL upper confidence bound. Default is CPUDispatcher(<function klucbBern>).
- **c** (float, optional) - Optional - Exploration parameter. Default is 1.0.
- **lower** (float, optional) - Optional - Lower value of the rewards. Default is 0.0.
- **amplitude** (float, optional) - Optional - Known amplitude of the rewards. Default is 1.0.
```

--------------------------------

### rajjain_fairness doctest examples

Source: https://smpybandits.github.io/_modules/Environment/fairnessMeasures.html

Doctest examples for the rajjain_fairness function. The examples use a seeded random array and show the fairness index for the original, more spread out (squared), and less spread out (square root) versions of the data.

```python
>>> rn.seed(2)  # for reproductibility
>>> X = np.cumsum(rn.randint(0, 10, (10, 100)))
>>> rajjain_fairness(X)  # doctest: +ELLIPSIS
0.246...
>>> rajjain_fairness(X ** 2)  # More spreadout  # doctest: +ELLIPSIS
0.917...
>>> rajjain_fairness(np.sqrt(np.abs(X)))  # Less spreadout  # doctest: +ELLIPSIS
0.107...
```

--------------------------------

### TrekkingTSN __init__ method with doctest examples

Source: https://smpybandits.github.io/_modules/Policies/TrekkingTSN.html

Initializes the TrekkingTSN policy with parameters theta, epsilon, delta, lower, and amplitude. The docstring includes doctest examples for creating a single player and a multi-player configuration.

```python
def __init__(self, nbArms,
                theta=0.01, epsilon=0.1, delta=0.05,
                lower=0., amplitude=1.
        ):  # Named argument to give them in any order
        """
        - nbArms: number of arms,

        Example:

        >>> nbArms = 8
        >>> theta, epsilon, delta = 0.01, 0.1, 0.05
        >>> player1 = TrekkingTSN(nbArms, theta=theta, epsilon=epsilon, delta=delta)

        For multi-players use:

        >>> configuration["players"] = Selfish(NB_PLAYERS, TrekkingTSN, nbArms, theta=theta, epsilon=epsilon, delta=delta).children
        """
        super(TrekkingTSN, self).__init__(nbArms, lower=lower, amplitude=amplitude)
        self.state = State.NotStarted  #: Current state

        # compute times
        T_RH, T_SH, T_TR = special_times(nbArms=nbArms, theta=theta, epsilon=epsilon, delta=delta)

        self.theta = theta  #: Parameter :math:`\theta`.
        self.epsilon = epsilon  #: Parameter :math:`\epsilon`.
        self.delta = delta  #: Parameter :math:`\delta`.

        # Store parameters
        self.T_RH = T_RH  #: Parameter :math:`T_{RH}` computed from :func:`special_times`
        self.T_SH = T_SH  #: Parameter :math:`T_{SH}` computed from :func:`special_times`
        self.T_CC = T_RH + T_SH  #: Parameter :math:`T_{CC} = T_{RH} + T_{SH}`
        self.T_TR = T_TR  #: Parameter :math:`T_{TR}` computed from :func:`special_times`

        # Internal memory
        self.last_was_successful = False  #: That's the l of the paper
        self.last_choice = None  #: Keep memory of the last choice for CC phase
        self.cumulatedRewards = np.zeros(nbArms)  #: That's the V_n of the paper
        self.nbObservations = np.zeros(nbArms, dtype=int)  #: That's the S_n of the paper

        self.J = -1
        self.lock_channel = False  #: That's the L of the paper
        self.Y = np.zeros(nbArms, dtype=int)  # That's the Yi of the paper
        self.M = np.zeros(nbArms)  # That's the Mj of the paper
        self.index_sort = None

        # Implementation details
        self.t = -1  #: Internal times

```

--------------------------------

### Explore Notebooks with Nix

Source: https://smpybandits.github.io/README.html

Runs a specific example notebook directly from the master branch using a Nix-enabled machine.

```bash
$ nix-shell https://github.com/SMPYBandits/SMPyBandits/archive/master.tar.gz --run 'jupyter-notebook $EXAMPLE_NOTEBOOKS/Example_of_a_small_Multi-Player_Simulation__with_Centralized_Algorithms.ipynb' 
```

--------------------------------

### Install SMPyBandits via Pip

Source: https://smpybandits.github.io/README.html

Installs the package directly from the GitHub repository into a virtual environment.

```bash
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]
```
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