{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": "true" }, "source": [ "# Table of Contents\n", "

1  Easily creating MAB problems
1.1  Constant arms
1.2  Bernoulli arms
1.3  Gaussian arms
1.3.1  Wrong means for Gaussian arms ?
1.3.2  Closed form formula
1.3.3  With a larger variance ?
1.4  Exponential arms
1.5  Uniform arms
1.6  Arms with rewards outside of [0,1]
1.7  Gamma arms
1.8  Non-truncated Gaussian and Gamma arms
1.9  Conclusion
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "# Easily creating MAB problems\n", "First, be sure to be in the main folder, or to have installed [`SMPyBandits`](https://github.com/SMPyBandits/SMPyBandits), and import `MAB` from `Environment` package:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Requirement already satisfied: SMPyBandits in ./venv3/lib/python3.6/site-packages (0.9.4)\n", "Requirement already satisfied: watermark in ./venv3/lib/python3.6/site-packages (1.7.0)\n", "Requirement already satisfied: scikit-learn in ./venv3/lib/python3.6/site-packages (from SMPyBandits) (0.20.0)\n", "Requirement already satisfied: scikit-optimize in ./venv3/lib/python3.6/site-packages (from SMPyBandits) (0.5.2)\n", "Requirement already satisfied: scipy>0.9 in ./venv3/lib/python3.6/site-packages (from SMPyBandits) (1.1.0)\n", "Requirement already satisfied: numpy in ./venv3/lib/python3.6/site-packages (from SMPyBandits) (1.15.4)\n", "Requirement already satisfied: matplotlib>=2 in ./venv3/lib/python3.6/site-packages (from SMPyBandits) (3.0.2)\n", "Requirement already satisfied: seaborn in ./venv3/lib/python3.6/site-packages (from SMPyBandits) (0.9.0)\n", "Requirement already satisfied: joblib in ./venv3/lib/python3.6/site-packages (from SMPyBandits) (0.13.0)\n", "Requirement already satisfied: ipython in ./venv3/lib/python3.6/site-packages (from watermark) (7.1.1)\n", "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in ./venv3/lib/python3.6/site-packages (from matplotlib>=2->SMPyBandits) (2.3.0)\n", "Requirement already satisfied: kiwisolver>=1.0.1 in ./venv3/lib/python3.6/site-packages (from matplotlib>=2->SMPyBandits) (1.0.1)\n", "Requirement already satisfied: python-dateutil>=2.1 in ./venv3/lib/python3.6/site-packages (from matplotlib>=2->SMPyBandits) (2.7.5)\n", "Requirement already satisfied: cycler>=0.10 in ./venv3/lib/python3.6/site-packages (from matplotlib>=2->SMPyBandits) (0.10.0)\n", "Requirement already satisfied: pandas>=0.15.2 in ./venv3/lib/python3.6/site-packages (from seaborn->SMPyBandits) (0.23.4)\n", "Requirement already satisfied: setuptools>=18.5 in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (40.6.2)\n", "Requirement already satisfied: pexpect; sys_platform != \"win32\" in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (4.6.0)\n", "Requirement already satisfied: jedi>=0.10 in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (0.13.1)\n", "Requirement already satisfied: backcall in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (0.1.0)\n", "Requirement already satisfied: traitlets>=4.2 in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (4.3.2)\n", "Requirement already satisfied: pickleshare in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (0.7.5)\n", "Requirement already satisfied: pygments in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (2.2.0)\n", "Requirement already satisfied: prompt-toolkit<2.1.0,>=2.0.0 in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (2.0.7)\n", "Requirement already satisfied: decorator in ./venv3/lib/python3.6/site-packages (from ipython->watermark) (4.3.0)\n", "Requirement already satisfied: six>=1.5 in ./venv3/lib/python3.6/site-packages (from python-dateutil>=2.1->matplotlib>=2->SMPyBandits) (1.11.0)\n", "Requirement already satisfied: pytz>=2011k in ./venv3/lib/python3.6/site-packages (from pandas>=0.15.2->seaborn->SMPyBandits) (2018.7)\n", "Requirement already satisfied: ptyprocess>=0.5 in ./venv3/lib/python3.6/site-packages (from pexpect; sys_platform != \"win32\"->ipython->watermark) (0.6.0)\n", "Requirement already satisfied: parso>=0.3.0 in ./venv3/lib/python3.6/site-packages (from jedi>=0.10->ipython->watermark) (0.3.1)\n", "Requirement already satisfied: ipython-genutils in ./venv3/lib/python3.6/site-packages (from traitlets>=4.2->ipython->watermark) (0.2.0)\n", "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)\n", "Info: Using the Jupyter notebook version of the tqdm() decorator, tqdm_notebook() ...\n", "Lilian Besson \n", "\n", "CPython 3.6.6\n", "IPython 7.1.1\n", "\n", "SMPyBandits 0.9.4\n", "\n", "compiler : GCC 8.0.1 20180414 (experimental) [trunk revision 259383\n", "system : Linux\n", "release : 4.15.0-38-generic\n", "machine : x86_64\n", "processor : x86_64\n", "CPU cores : 4\n", "interpreter: 64bit\n" ] } ], "source": [ "!pip install SMPyBandits watermark\n", "%load_ext watermark\n", "%watermark -v -m -p SMPyBandits -a \"Lilian Besson\"" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from SMPyBandits.Environment import MAB" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And also, import all the types of arms." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "(SMPyBandits.Arms.Constant.Constant,\n", " SMPyBandits.Arms.Bernoulli.Bernoulli,\n", " SMPyBandits.Arms.Gaussian.Gaussian,\n", " SMPyBandits.Arms.Exponential.Exponential,\n", " SMPyBandits.Arms.Exponential.ExponentialFromMean,\n", " SMPyBandits.Arms.Poisson.Poisson,\n", " SMPyBandits.Arms.UniformArm.UniformArm,\n", " SMPyBandits.Arms.Gamma.Gamma,\n", " SMPyBandits.Arms.Gamma.GammaFromMean)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from SMPyBandits.Arms import *\n", "# Check it exists:\n", "Constant, Bernoulli, Gaussian, Exponential, ExponentialFromMean, Poisson, UniformArm, Gamma, GammaFromMean" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import matplotlib as mpl\n", "mpl.rcParams['figure.figsize'] = (12.4, 7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Constant arms\n", "\n", "This is the simpler example of arms : rewards are constant, and not randomly drawn from a distribution.\n", "Let consider an example with $K = 3$ arms." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Creating a new MAB problem ...\n", " Taking arms of this MAB problem from a list of arms 'configuration' = [Constant(0.1), Constant(0.5), Constant(0.9)] ...\n", " - with 'arms' = [Constant(0.1), Constant(0.5), Constant(0.9)]\n", " - with 'means' = [0.1 0.5 0.9]\n", " - with 'nbArms' = 3\n", " - with 'maxArm' = 0.9\n", " - with 'minArm' = 0.1\n", "\n", "This MAB problem has: \n", " - a [Lai & Robbins] complexity constant C(mu) = 2 ... \n", " - a Optimal Arm Identification factor H_OI(mu) = 26.67% ...\n", " - with 'arms' represented as: $[Constant(0.1), Constant(0.5), Constant(0.9)^*]$\n" ] } ], "source": [ "M_C = MAB([Constant(mu) for mu in [0.1, 0.5, 0.9]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `plotHistogram()` method draws samples from each arm, and plot a histogram of their repartition.\n", "For constant arms, no need to take a lot of samples as they are constant." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Warning: forcing to use putatright = False because there is 3 items in the legend.\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_ = M_C.plotHistogram(10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bernoulli arms\n", "Then it's easy to create a Multi-Armed Bandit problem, instance of `MAB` class, either from a list of `Arm` objects:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Creating a new MAB problem ...\n", " Taking arms of this MAB problem from a list of arms 'configuration' = [B(0.1), B(0.5), B(0.9)] ...\n", " - with 'arms' = [B(0.1), B(0.5), B(0.9)]\n", " - with 'means' = [0.1 0.5 0.9]\n", " - with 'nbArms' = 3\n", " - with 'maxArm' = 0.9\n", " - with 'minArm' = 0.1\n", "\n", "This MAB problem has: \n", " - a [Lai & Robbins] complexity constant C(mu) = 1.24 ... \n", " - a Optimal Arm Identification factor H_OI(mu) = 26.67% ...\n", " - with 'arms' represented as: $[B(0.1), B(0.5), B(0.9)^*]$\n" ] } ], "source": [ "M_B = MAB([Bernoulli(mu) for mu in [0.1, 0.5, 0.9]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or from a dictionary, with keys `\"arm_type\"` and `\"params\"`:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Creating a new MAB problem ...\n", " Reading arms of this MAB problem from a dictionnary 'configuration' = {'arm_type': , 'params': [0.1, 0.5, 0.9]} ...\n", " - with 'arm_type' = \n", " - with 'params' = [0.1, 0.5, 0.9]\n", " - with 'arms' = [B(0.1), B(0.5), B(0.9)]\n", " - with 'means' = [0.1 0.5 0.9]\n", " - with 'nbArms' = 3\n", " - with 'maxArm' = 0.9\n", " - with 'minArm' = 0.1\n", "\n", "This MAB problem has: \n", " - a [Lai & Robbins] complexity constant C(mu) = 1.24 ... \n", " - a Optimal Arm Identification factor H_OI(mu) = 26.67% ...\n", " - with 'arms' represented as: $[B(0.1), B(0.5), B(0.9)^*]$\n" ] } ], "source": [ "M_B = MAB({\n", " \"arm_type\": Bernoulli,\n", " \"params\": [0.1, 0.5, 0.9]\n", "})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `plotHistogram()` method draws a lot of samples from each arm, and plot a histogram of their repartition:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Warning: forcing to use putatright = False because there is 3 items in the legend.\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_ = M_B.plotHistogram()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gaussian arms\n", "And with Gaussian arms, with a small variance of $\\sigma^2 = 0.05$, for rewards truncated into $[0, 1]$:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Creating a new MAB problem ...\n", " Taking arms of this MAB problem from a list of arms 'configuration' = [N(0.1, 0.05), N(0.5, 0.05), N(0.9, 0.05)] ...\n", " - with 'arms' = [N(0.1, 0.05), N(0.5, 0.05), N(0.9, 0.05)]\n", " - with 'means' = [0.1 0.5 0.9]\n", " - with 'nbArms' = 3\n", " - with 'maxArm' = 0.9\n", " - with 'minArm' = 0.1\n", "\n", "This MAB problem has: \n", " - a [Lai & Robbins] complexity constant C(mu) = 0.375 ... \n", " - a Optimal Arm Identification factor H_OI(mu) = 26.67% ...\n", " - with 'arms' represented as: $[N(0.1), N(0.5), N(0.9)^*], \\sigma^2=0.05$\n" ] } ], "source": [ "M_G = MAB([Gaussian(mu, sigma=0.05) for mu in [0.1, 0.5, 0.9]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The histogram clearly shows that low-variance Gaussian arms are easy to separate:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Warning: forcing to use putatright = False because there is 3 items in the legend.\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_ = M_G.plotHistogram(100000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Wrong means for Gaussian arms ?\n", "The truncation seems to change the means.\n", "\n", "> For instance, the first arm (in red) has a small mass on the special value $0$, so it probably reduces its mean.\n", "\n", "Let's estimate it empirically, and then check with the closed form solution." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "arm = Gaussian(0.1, sigma=0.05)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "mean = arm.mean\n", "estimated_mean = np.mean(arm.draw_nparray((10000000,)))" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.1, 0.10042691516597835)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mean, estimated_mean" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.004269151659783421" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def relative_error(x, y):\n", " return abs(x - y) / x\n", "\n", "relative_error(mean, estimated_mean)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\implies$ That's a relative difference of $0.4\\%$, really negligible!\n", "\n", "And for other values for $(\\mu, \\sigma)$:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "arm = Gaussian(0.7, sigma=3)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "mean = arm.mean\n", "estimated_mean = np.mean(arm.draw_nparray((10000000,)))" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.7, 0.5266068636711595)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mean, estimated_mean" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.2477044804697721" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "relative_error(mean, estimated_mean)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\implies$ That's a relative difference of $25\\%$!\n", "\n", "> Clearly, this effect cannot be neglected!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Closed form formula" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Apparently, the closed form formula for the mean of a Gaussian arm $\\mathcal{N}(\\mu, \\sigma)$, **truncated to $[a,b]$** is :\n", "$$\\mathbb{E} (X\\mid a" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "M_G = MAB([Gaussian(mu, sigma=0.10) for mu in [0.1, 0.5, 0.9]])\n", "_ = M_G.plotHistogram(100000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that due to the truncation, if mean of the Gaussian is too close to $0$ or $1$, then actual mean rewards is pushed to $0$ or $1$ (here the blue arm clearly has a mean higher than $0.9$).\n", "\n", "And for larger variances, it is even stronger:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Creating a new MAB problem ...\n", " Taking arms of this MAB problem from a list of arms 'configuration' = [N(0.1, 0.25), N(0.5, 0.25), N(0.9, 0.25)] ...\n", " - with 'arms' = [N(0.1, 0.25), N(0.5, 0.25), N(0.9, 0.25)]\n", " - with 'means' = [0.1 0.5 0.9]\n", " - with 'nbArms' = 3\n", " - with 'maxArm' = 0.9\n", " - with 'minArm' = 0.1\n", "\n", "This MAB problem has: \n", " - a [Lai & Robbins] complexity constant C(mu) = 1.87 ... \n", " - a Optimal Arm Identification factor H_OI(mu) = 26.67% ...\n", " - with 'arms' represented as: $[N(0.1), N(0.5), N(0.9)^*], \\sigma^2=0.25$\n", "Warning: forcing to use putatright = False because there is 3 items in the legend.\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "M_G = MAB([Gaussian(mu, sigma=0.25) for mu in [0.1, 0.5, 0.9]])\n", "_ = M_G.plotHistogram()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exponential arms\n", "We can do the same with (truncated) Exponential arms, and as a convenience I prefer to work with `ExponentialFromMean`, to use the mean and not the $\\lambda$ parameter to create the arm." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Creating a new MAB problem ...\n", " Reading arms of this MAB problem from a dictionnary 'configuration' = {'arm_type': , 'params': [0.1, 0.5, 0.9]} ...\n", " - with 'arm_type' = \n", " - with 'params' = [0.1, 0.5, 0.9]\n", " - with 'arms' = [\\mathrm{Exp}(10, 1), \\mathrm{Exp}(1.59, 1), \\mathrm{Exp}(0.215, 1)]\n", " - with 'means' = [0.1 0.5 0.9]\n", " - with 'nbArms' = 3\n", " - with 'maxArm' = 0.9000000032329611\n", " - with 'minArm' = 0.10000000005466392\n", "\n", "This MAB problem has: \n", " - a [Lai & Robbins] complexity constant C(mu) = 3.4 ... \n", " - a Optimal Arm Identification factor H_OI(mu) = 26.67% ...\n", " - with 'arms' represented as: $[\\mathrm{Exp}(10, 1), \\mathrm{Exp}(1.59, 1), \\mathrm{Exp}(0.215, 1)^*]$\n" ] } ], "source": [ "M_E = MAB({ \"arm_type\": ExponentialFromMean, \"params\": [0.1, 0.5, 0.9]})" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Warning: forcing to use putatright = False because there is 3 items in the legend.\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_ = M_E.plotHistogram()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Uniform arms\n", "Arms with rewards uniform in $[0,1]$, are continuous versions of Bernoulli$(0.5)$.\n", "They can also be uniform in other intervals." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0, 1)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "(0, 0.1)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "(0.4, 0.09999999999999998)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "(0.8, 0.09999999999999998)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "UniformArm(0, 1).lower_amplitude\n", "UniformArm(0, 0.1).lower_amplitude\n", "UniformArm(0.4, 0.5).lower_amplitude\n", "UniformArm(0.8, 0.9).lower_amplitude" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Creating a new MAB problem ...\n", " Taking arms of this MAB problem from a list of arms 'configuration' = [U(0, 1), U(0, 0.1), U(0.4, 0.5), U(0.8, 0.9)] ...\n", " - with 'arms' = [U(0, 1), U(0, 0.1), U(0.4, 0.5), U(0.8, 0.9)]\n", " - with 'means' = [0.5 0.05 0.45 0.85]\n", " - with 'nbArms' = 4\n", " - with 'maxArm' = 0.8500000000000001\n", " - with 'minArm' = 0.05\n", "\n", "This MAB problem has: \n", " - a [Lai & Robbins] complexity constant C(mu) = 2.47 ... \n", " - a Optimal Arm Identification factor H_OI(mu) = 36.25% ...\n", " - with 'arms' represented as: $[U(0, 1), U(0, 0.1), U(0.4, 0.5), U(0.8, 0.9)^*]$\n" ] } ], "source": [ "M_U = MAB([UniformArm(0, 1), UniformArm(0, 0.1), UniformArm(0.4, 0.5), UniformArm(0.8, 0.9)])" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Warning: forcing to use putatright = False because there is 4 items in the legend.\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_ = M_U.plotHistogram(100000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "## Arms with rewards outside of $[0, 1]$\n", "\n", "Of course, everything work similarly if rewards are not in $[0, 1]$ but in any interval $[a, b]$.\n", "\n", "Note that all my algorithms assume $a = \\text{lower} = 0$ and $b = 1$ (and use \n", "$\\text{amplitude} = b - a$ instead of $b$).\n", "They just need to be specified if we stop using the default choice $[0, 1]$.\n", "\n", "For example, Gaussian arms can be truncated into $[-10, 10]$ instead of $[0, 1]$.\n", "Let define some Gaussian arms, with means $-5, 0, 5$ and a variance of $\\sigma^2 = 2$." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Creating a new MAB problem ...\n", " Taking arms of this MAB problem from a list of arms 'configuration' = [N(-5, 2), N(0, 2), N(5, 2)] ...\n", " - with 'arms' = [N(-5, 2), N(0, 2), N(5, 2)]\n", " - with 'means' = [-5 0 5]\n", " - with 'nbArms' = 3\n", " - with 'maxArm' = 5\n", " - with 'minArm' = -5\n", "\n", "This MAB problem has: \n", " - a [Lai & Robbins] complexity constant C(mu) = 1.2 ... \n", " - a Optimal Arm Identification factor H_OI(mu) = 16.67% ...\n", " - with 'arms' represented as: $[N(-5), N(0), N(5)^*], \\sigma^2=2$\n" ] } ], "source": [ "M_G = MAB([Gaussian(mu, sigma=2, mini=-10, maxi=10) for mu in [-5, 0, 5]])" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Warning: forcing to use putatright = False because there is 3 items in the legend.\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_ = M_G.plotHistogram(100000)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Creating a new MAB problem ...\n", " Taking arms of this MAB problem from a list of arms 'configuration' = [N(-5, 0.1), N(0, 0.1), N(5, 0.1)] ...\n", " - with 'arms' = [N(-5, 0.1), N(0, 0.1), N(5, 0.1)]\n", " - with 'means' = [-5 0 5]\n", " - with 'nbArms' = 3\n", " - with 'maxArm' = 5\n", " - with 'minArm' = -5\n", "\n", "This MAB problem has: \n", " - a [Lai & Robbins] complexity constant C(mu) = 0.06 ... \n", " - a Optimal Arm Identification factor H_OI(mu) = 16.67% ...\n", " - with 'arms' represented as: $[N(-5), N(0), N(5)^*], \\sigma^2=0.1$\n" ] } ], "source": [ "M_G = MAB([Gaussian(mu, sigma=0.1, mini=-10, maxi=10) for mu in [-5, 0, 5]])" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Warning: forcing to use putatright = False because there is 3 items in the legend.\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_ = M_G.plotHistogram()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gamma arms\n", "\n", "We can do the same with (truncated) Gamma arms, and as a convenience I prefer to work with `GammaFromMean`, to use the mean and not the $k$ shape parameter to create the arm.\n", "The scale $\\theta$ is fixed to $1$ by default, and here the rewards will be in $[0, 10]$." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Creating a new MAB problem ...\n", " Taking arms of this MAB problem from a list of arms 'configuration' = [\\Gamma(1, 1), \\Gamma(2, 1), \\Gamma(3, 1), \\Gamma(4, 1), \\Gamma(5, 1)] ...\n", " - with 'arms' = [\\Gamma(1, 1), \\Gamma(2, 1), \\Gamma(3, 1), \\Gamma(4, 1), \\Gamma(5, 1)]\n", " - with 'means' = [1. 2. 3. 4. 5.]\n", " - with 'nbArms' = 5\n", " - with 'maxArm' = 5.0\n", " - with 'minArm' = 1.0\n", "\n", "This MAB problem has: \n", " - a [Lai & Robbins] complexity constant C(mu) = 75.7 ... \n", " - a Optimal Arm Identification factor H_OI(mu) = 60.00% ...\n", " - with 'arms' represented as: $[\\Gamma(1, 1), \\Gamma(2, 1), \\Gamma(3, 1), \\Gamma(4, 1), \\Gamma(5, 1)^*]$\n" ] } ], "source": [ "M_Gamma = MAB([GammaFromMean(shape, scale=1, mini=0, maxi=10) for shape in [1, 2, 3, 4, 5]])" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Warning: forcing to use putatright = False because there is 5 items in the legend.\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_ = M_Gamma.plotHistogram(100000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As for Gaussian arms, the truncation is strongly changing the means of the arm rewards.\n", "Here the arm with mean parameter $5$ has an empirical mean close to $10$ due to truncation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Non-truncated Gaussian and Gamma arms\n", "\n", "Let try with non-truncated rewards." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Creating a new MAB problem ...\n", " Taking arms of this MAB problem from a list of arms 'configuration' = [N(-10, 3), N(0, 3), N(10, 3)] ...\n", " - with 'arms' = [N(-10, 3), N(0, 3), N(10, 3)]\n", " - with 'means' = [-10 0 10]\n", " - with 'nbArms' = 3\n", " - with 'maxArm' = 10\n", " - with 'minArm' = -10\n", "\n", "This MAB problem has: \n", " - a [Lai & Robbins] complexity constant C(mu) = 0.9 ... \n", " - a Optimal Arm Identification factor H_OI(mu) = 66.67% ...\n", " - with 'arms' represented as: $[N(-10), N(0), N(10)^*], \\sigma^2=3$\n" ] } ], "source": [ "M_G = MAB([Gaussian(mu, sigma=3, mini=float('-inf'), maxi=float('+inf')) for mu in [-10, 0, 10]])" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Warning: forcing to use putatright = False because there is 3 items in the legend.\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_ = M_G.plotHistogram(100000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And with non-truncated Gamma arms ?" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Creating a new MAB problem ...\n", " Taking arms of this MAB problem from a list of arms 'configuration' = [\\Gamma(1, 1), \\Gamma(2, 1), \\Gamma(3, 1), \\Gamma(4, 1), \\Gamma(5, 1)] ...\n", " - with 'arms' = [\\Gamma(1, 1), \\Gamma(2, 1), \\Gamma(3, 1), \\Gamma(4, 1), \\Gamma(5, 1)]\n", " - with 'means' = [1. 2. 3. 4. 5.]\n", " - with 'nbArms' = 5\n", " - with 'maxArm' = 5.0\n", " - with 'minArm' = 1.0\n", "\n", "This MAB problem has: \n", " - a [Lai & Robbins] complexity constant C(mu) = 75.7 ... \n", " - a Optimal Arm Identification factor H_OI(mu) = 80.00% ...\n", " - with 'arms' represented as: $[\\Gamma(1, 1), \\Gamma(2, 1), \\Gamma(3, 1), \\Gamma(4, 1), \\Gamma(5, 1)^*]$\n", "Warning: forcing to use putatright = False because there is 5 items in the legend.\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "M_Gamma = MAB([GammaFromMean(shape, scale=1, mini=float('-inf'), maxi=float('+inf')) for shape in [1, 2, 3, 4, 5]])\n", "_ = M_Gamma.plotHistogram(100000)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Creating a new MAB problem ...\n", " Taking arms of this MAB problem from a list of arms 'configuration' = [\\Gamma(10, 1), \\Gamma(20, 1), \\Gamma(30, 1), \\Gamma(40, 1), \\Gamma(50, 1)] ...\n", " - with 'arms' = [\\Gamma(10, 1), \\Gamma(20, 1), \\Gamma(30, 1), \\Gamma(40, 1), \\Gamma(50, 1)]\n", " - with 'means' = [10. 20. 30. 40. 50.]\n", " - with 'nbArms' = 5\n", " - with 'maxArm' = 50.0\n", " - with 'minArm' = 10.0\n", "\n", "This MAB problem has: \n", " - a [Lai & Robbins] complexity constant C(mu) = 757 ... \n", " - a Optimal Arm Identification factor H_OI(mu) = 80.00% ...\n", " - with 'arms' represented as: $[\\Gamma(10, 1), \\Gamma(20, 1), \\Gamma(30, 1), \\Gamma(40, 1), \\Gamma(50, 1)^*]$\n", "Warning: forcing to use putatright = False because there is 5 items in the legend.\n" ] }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "M_Gamma = MAB([GammaFromMean(shape, scale=1, mini=float('-inf'), maxi=float('+inf')) for shape in [10, 20, 30, 40, 50]])\n", "_ = M_Gamma.plotHistogram(1000000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----\n", "## Conclusion\n", "\n", "This small notebook demonstrated how to define arms and Multi-Armed Bandit problems in my framework, [SMPyBandits](https://github.com/SMPyBandits/SMPyBandits)." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.6" }, "toc": { "colors": { "hover_highlight": "#DAA520", "running_highlight": "#FF0000", "selected_highlight": "#FFD700" }, "moveMenuLeft": true, "nav_menu": { "height": "119px", "width": "251px" }, "navigate_menu": true, "number_sections": true, "sideBar": true, "threshold": 4, "toc_cell": true, "toc_position": { "height": "570px", "left": "0px", "right": "1164px", "top": "117px", "width": "212px" }, "toc_section_display": "block", "toc_window_display": true }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 1 }