01_Bayesian_Meta-Optimization.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian Meta-Optimization\n",
    "\n",
    "by [Magnus Erik Hvass Pedersen](http://www.hvass-labs.org/)\n",
    "/ [GitHub](https://github.com/Hvass-Labs/MetaOps) / [Videos on YouTube](https://www.youtube.com/playlist?list=PL9Hr9sNUjfsl1877BS8m3yt8t_wq2IWji)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "Heuristic optimizers such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO) and Differential Evolution (DE) all have a number of parameters that may greatly influence their performance and ability to optimize any given problem. Setting these parameters is somewhat of a *black art* because the inner workings of these optimizers are still very poorly understood. Often the best parameters are counter-intuitive and a choice of parameters that is good for one problem may be almost useless for another problem.\n",
    "\n",
    "Here we present a new method for automatic tuning of the parameters of a heuristic optimizer. This is often called [Meta-Optimization](https://en.wikipedia.org/wiki/Meta-optimization) which is an idea that is closely related to [Hyper-Parameter Optimization](https://en.wikipedia.org/wiki/Hyperparameter_optimization). The method presented here is quite sophisticated and would take considerable effort to implement from scratch. Fortunately we can build the entire system very quickly with just a few lines of source-code by using two existing Python packages."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Flowchart\n",
    "\n",
    "We use a so-called [Gaussian Process](https://en.wikipedia.org/wiki/Gaussian_process) to approximate how different parameters affect the performance of the heuristic optimizer on a benchmark problem. We then use a form of so-called [Bayesian Optimization](https://en.wikipedia.org/wiki/Bayesian_optimization) to find the set of parameters that most likely improve upon the optimizer's performance. These parameters are then tried and the result is used to improve the accuracy of the Gaussian Process. This is repeated until a good set of parameters has been found for the optimizer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Flowchart](images/01_flowchart_bayesian_optimization.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/magnus/anaconda3/envs/metaops/lib/python3.6/site-packages/sklearn/ensemble/weight_boosting.py:29: DeprecationWarning: numpy.core.umath_tests is an internal NumPy module and should not be imported. It will be removed in a future NumPy release.\n",
      "  from numpy.core.umath_tests import inner1d\n"
     ]
    }
   ],
   "source": [
    "# Normal packages.\n",
    "import numpy as np\n",
    "\n",
    "# Heuristic optimizers such as DE and PSO.\n",
    "# This is actually implemented in C++ so it should run very fast.\n",
    "import pygmo as pg\n",
    "\n",
    "# Bayesian optimization.\n",
    "import skopt\n",
    "from skopt import gp_minimize\n",
    "from skopt.space import Real, Integer\n",
    "from skopt.utils import use_named_args\n",
    "from skopt.plots import plot_convergence, plot_objective"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'2.8'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pg.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0.5.2'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "skopt.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem\n",
    "\n",
    "In this example, the problem that we ultimately want to optimize is the [Rosenbrock](https://en.wikipedia.org/wiki/Rosenbrock_function) benchmark problem in 100 dimensions. You could replace this with your own problem, see the [pygmo manual](https://esa.github.io/pagmo2/docs/python/tutorials/python_tut.html) for instructions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create an instance of the problem we want to optimize.\n",
    "problem = pg.problem(pg.rosenbrock(dim=100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize the best-found solution and associated fitness.\n",
    "# This will be updated after each optimization run.\n",
    "best_x = None\n",
    "best_fitness = float('inf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Max number of problem evaluations allowed in a single\n",
    "# optimization run.\n",
    "num_fitness_evals = 100000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Number of optimization runs to perform for each new choice\n",
    "# of parameters for the optimizer. This should not be too low\n",
    "# because the optimizer is stochastic. Even though the Bayesian\n",
    "# Optimizer can handle this, it seems to be better to average\n",
    "# the performance over several runs. It should also not be too high.\n",
    "num_runs = 20"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimizer Parameters\n",
    "\n",
    "In this example, we will use [Differential Evolution (DE)](https://en.wikipedia.org/wiki/Differential_evolution) as the heuristic optimizer whose parameters we want to tune. We first need to setup the search-space dimensions for the parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Parameter-dimension for population size.\n",
    "dim_pop_size = Integer(name=\"pop_size\", low=5, high=200)\n",
    "\n",
    "# Parameter-dimension for F (differential weight).\n",
    "dim_F = Real(name=\"F\", low=0.0, high=1.0)\n",
    "\n",
    "# Parameter-dimension for CR (crossover probability).\n",
    "dim_CR = Real(name=\"CR\", low=0.0, high=1.0)\n",
    "\n",
    "# Parameter-dimension for DE optimizer variant.\n",
    "dim_variant = Integer(name=\"variant\", low=1, high=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# List of all parameter-dimensions.\n",
    "dimensions  = [dim_pop_size, dim_F, dim_CR, dim_variant]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Names for the parameters.\n",
    "# This is needed in the plotting functions because the API of\n",
    "# scikit-optimize is poorly designed in places.\n",
    "dimension_names = [\"pop_size\", \"F\", \"CR\", \"variant\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# A default choice of parameters.\n",
    "default_parameters = [100, 0.8, 0.9, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Names of the optimizer variants used for printing.\n",
    "variant_names = \\\n",
    "{\n",
    "     1: \"best/1/exp\",\n",
    "     2: \"rand/1/exp\",\n",
    "     3: \"rand-to-best/1/exp\",\n",
    "     4: \"best/2/exp\",\n",
    "     5: \"rand/2/exp\",\n",
    "     6: \"best/1/bin\",\n",
    "     7: \"rand/1/bin\",\n",
    "     8: \"rand-to-best/1/bin\",\n",
    "     9: \"best/2/bin\",\n",
    "     10: \"rand/2/bin\"    \n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Meta-Fitness\n",
    "\n",
    "This is the so-called Meta-Fitness function that takes a set of parameters for the heuristic optimizer and evaluates their performance on the benchmark problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "@use_named_args(dimensions=dimensions)\n",
    "def meta_fitness(pop_size, CR, F, variant):\n",
    "    \"\"\"\n",
    "    Meta-fitness for evaluating the performance of the\n",
    "    optimizer on one or more problems.\n",
    "\n",
    "    :param pop_size: Population size.\n",
    "    :param CR: Control-parameter CR (crossover probability).\n",
    "    :param F: Control-parameter F (differential weight).\n",
    "    :param variant: DE variant, integer between 1 and 10.\n",
    "    :return: Float to be minimized.\n",
    "    \"\"\"\n",
    "\n",
    "    # Type-cast from int64 to int because pygmo requires that.\n",
    "    pop_size = int(pop_size)\n",
    "    variant = int(variant)\n",
    "\n",
    "    # Print parameters.\n",
    "    print(\"pop_size:\", pop_size)\n",
    "    print(\"CR: {0:.2f}\".format(CR))\n",
    "    print(\"F: {0:.2f}\".format(F))\n",
    "    print(\"variant: {0} ({1})\".format(variant,\n",
    "                                      variant_names[variant]))\n",
    "    \n",
    "    # Number of iterations for the optimizer's population.\n",
    "    # This ensures that we perform the same number of\n",
    "    # evaluations of the problem's fitness function\n",
    "    # regardless of the population-size.\n",
    "    num_generations = num_fitness_evals // pop_size\n",
    "\n",
    "    def _run():\n",
    "        \"\"\"\n",
    "        Helper-function for performing a single optimization run.\n",
    "        \"\"\"\n",
    "\n",
    "        # Create a new instance of the optimizer using\n",
    "        # the given parameters.\n",
    "        uda = pg.de(gen=num_generations, CR=CR, F=F, variant=variant)\n",
    "        optimizer = pg.algorithm(uda=uda)\n",
    "\n",
    "        # Create a population of agents for the optimizer.\n",
    "        pop = pg.population(problem, size=pop_size)\n",
    "\n",
    "        # Evolve the optimizer's population.\n",
    "        pop = optimizer.evolve(pop)\n",
    "        \n",
    "        # Best fitness found in this optimization run.\n",
    "        fitness = pop.champion_f[0]\n",
    "        \n",
    "        # Update the global variables for best-found solution.\n",
    "        global best_fitness, best_x\n",
    "        if fitness < best_fitness:\n",
    "            best_fitness = fitness\n",
    "            best_x = np.copy(pop.champion_x)\n",
    "        \n",
    "        return fitness\n",
    "    \n",
    "    # Perform a number of optimization runs and get a list\n",
    "    # of the best fitness-values found in those runs.\n",
    "    fitnesses = np.array([_run() for i in range(num_runs)])\n",
    "\n",
    "    # The meta-fitness is the mean of those fitness-values.\n",
    "    meta_fitness = fitnesses.mean()\n",
    "    \n",
    "    # Print the meta-fitness.\n",
    "    print(\"meta_fitness: {0:.2e}\".format(meta_fitness))\n",
    "    print()\n",
    "    \n",
    "    return meta_fitness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pop_size: 100\n",
      "CR: 0.90\n",
      "F: 0.80\n",
      "variant: 2 (rand/1/exp)\n",
      "meta_fitness: 4.87e+03\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "4868.149167824088"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Test the function on the default parameters.\n",
    "meta_fitness(default_parameters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Meta-Optimization\n",
    "\n",
    "Now we can run the Meta-Optimization to find the best parameters for the heuristic optimizer, as well as the best solution for the actual problem we are interested in solving."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pop_size: 100\n",
      "CR: 0.90\n",
      "F: 0.80\n",
      "variant: 2 (rand/1/exp)\n",
      "meta_fitness: 4.66e+03\n",
      "\n",
      "pop_size: 196\n",
      "CR: 0.24\n",
      "F: 0.22\n",
      "variant: 9 (best/2/bin)\n",
      "meta_fitness: 4.71e+03\n",
      "\n",
      "pop_size: 37\n",
      "CR: 0.69\n",
      "F: 0.41\n",
      "variant: 3 (rand-to-best/1/exp)\n",
      "meta_fitness: 8.88e+01\n",
      "\n",
      "pop_size: 98\n",
      "CR: 0.27\n",
      "F: 0.20\n",
      "variant: 7 (rand/1/bin)\n",
      "meta_fitness: 1.89e+02\n",
      "\n",
      "pop_size: 46\n",
      "CR: 0.91\n",
      "F: 0.24\n",
      "variant: 6 (best/1/bin)\n",
      "meta_fitness: 2.71e+06\n",
      "\n",
      "pop_size: 156\n",
      "CR: 0.55\n",
      "F: 0.10\n",
      "variant: 5 (rand/2/exp)\n",
      "meta_fitness: 6.84e+02\n",
      "\n",
      "pop_size: 17\n",
      "CR: 0.50\n",
      "F: 0.85\n",
      "variant: 4 (best/2/exp)\n",
      "meta_fitness: 1.01e+02\n",
      "\n",
      "pop_size: 87\n",
      "CR: 0.87\n",
      "F: 0.43\n",
      "variant: 7 (rand/1/bin)\n",
      "meta_fitness: 2.86e+02\n",
      "\n",
      "pop_size: 34\n",
      "CR: 0.06\n",
      "F: 0.90\n",
      "variant: 4 (best/2/exp)\n",
      "meta_fitness: 4.22e+02\n",
      "\n",
      "pop_size: 145\n",
      "CR: 0.00\n",
      "F: 0.56\n",
      "variant: 1 (best/1/exp)\n",
      "meta_fitness: 4.64e+03\n",
      "\n",
      "pop_size: 123\n",
      "CR: 0.54\n",
      "F: 0.34\n",
      "variant: 6 (best/1/bin)\n",
      "meta_fitness: 2.39e+05\n",
      "\n",
      "pop_size: 11\n",
      "CR: 0.76\n",
      "F: 0.04\n",
      "variant: 5 (rand/2/exp)\n",
      "meta_fitness: 1.69e+05\n",
      "\n",
      "pop_size: 135\n",
      "CR: 0.35\n",
      "F: 0.97\n",
      "variant: 1 (best/1/exp)\n",
      "meta_fitness: 4.99e+03\n",
      "\n",
      "pop_size: 10\n",
      "CR: 0.00\n",
      "F: 0.69\n",
      "variant: 3 (rand-to-best/1/exp)\n",
      "meta_fitness: 2.31e+01\n",
      "\n",
      "pop_size: 35\n",
      "CR: 0.71\n",
      "F: 0.63\n",
      "variant: 4 (best/2/exp)\n",
      "meta_fitness: 9.44e+01\n",
      "\n",
      "pop_size: 174\n",
      "CR: 0.05\n",
      "F: 0.61\n",
      "variant: 2 (rand/1/exp)\n",
      "meta_fitness: 1.29e+04\n",
      "\n",
      "pop_size: 64\n",
      "CR: 0.63\n",
      "F: 0.28\n",
      "variant: 4 (best/2/exp)\n",
      "meta_fitness: 1.15e+02\n",
      "\n",
      "pop_size: 75\n",
      "CR: 0.81\n",
      "F: 0.03\n",
      "variant: 10 (rand/2/bin)\n",
      "meta_fitness: 1.41e+05\n",
      "\n",
      "pop_size: 188\n",
      "CR: 0.82\n",
      "F: 0.21\n",
      "variant: 2 (rand/1/exp)\n",
      "meta_fitness: 2.53e+02\n",
      "\n",
      "pop_size: 79\n",
      "CR: 0.51\n",
      "F: 0.05\n",
      "variant: 7 (rand/1/bin)\n",
      "meta_fitness: 6.51e+03\n",
      "\n",
      "pop_size: 25\n",
      "CR: 0.70\n",
      "F: 0.85\n",
      "variant: 9 (best/2/bin)\n",
      "meta_fitness: 1.65e+06\n",
      "\n",
      "pop_size: 150\n",
      "CR: 0.53\n",
      "F: 0.11\n",
      "variant: 2 (rand/1/exp)\n",
      "meta_fitness: 6.72e+02\n",
      "\n",
      "pop_size: 182\n",
      "CR: 0.93\n",
      "F: 0.68\n",
      "variant: 7 (rand/1/bin)\n",
      "meta_fitness: 1.01e+06\n",
      "\n",
      "pop_size: 153\n",
      "CR: 0.44\n",
      "F: 0.41\n",
      "variant: 4 (best/2/exp)\n",
      "meta_fitness: 1.53e+03\n",
      "\n",
      "pop_size: 183\n",
      "CR: 0.17\n",
      "F: 0.55\n",
      "variant: 6 (best/1/bin)\n",
      "meta_fitness: 4.77e+02\n",
      "\n",
      "pop_size: 128\n",
      "CR: 0.72\n",
      "F: 0.67\n",
      "variant: 10 (rand/2/bin)\n",
      "meta_fitness: 2.32e+06\n",
      "\n",
      "pop_size: 118\n",
      "CR: 0.39\n",
      "F: 0.17\n",
      "variant: 5 (rand/2/exp)\n",
      "meta_fitness: 6.48e+02\n",
      "\n",
      "pop_size: 196\n",
      "CR: 0.96\n",
      "F: 0.59\n",
      "variant: 1 (best/1/exp)\n",
      "meta_fitness: 1.69e+02\n",
      "\n",
      "pop_size: 88\n",
      "CR: 0.70\n",
      "F: 0.70\n",
      "variant: 3 (rand-to-best/1/exp)\n",
      "meta_fitness: 1.22e+02\n",
      "\n",
      "pop_size: 168\n",
      "CR: 0.98\n",
      "F: 0.38\n",
      "variant: 1 (best/1/exp)\n",
      "meta_fitness: 4.07e+04\n",
      "\n",
      "pop_size: 184\n",
      "CR: 0.29\n",
      "F: 0.18\n",
      "variant: 9 (best/2/bin)\n",
      "meta_fitness: 6.55e+04\n",
      "\n",
      "pop_size: 193\n",
      "CR: 0.78\n",
      "F: 0.38\n",
      "variant: 1 (best/1/exp)\n",
      "meta_fitness: 2.84e+02\n",
      "\n",
      "pop_size: 59\n",
      "CR: 0.54\n",
      "F: 0.94\n",
      "variant: 9 (best/2/bin)\n",
      "meta_fitness: 2.12e+06\n",
      "\n",
      "pop_size: 150\n",
      "CR: 0.63\n",
      "F: 0.15\n",
      "variant: 6 (best/1/bin)\n",
      "meta_fitness: 1.54e+06\n",
      "\n",
      "pop_size: 191\n",
      "CR: 0.46\n",
      "F: 0.95\n",
      "variant: 10 (rand/2/bin)\n",
      "meta_fitness: 2.26e+06\n",
      "\n",
      "pop_size: 20\n",
      "CR: 0.52\n",
      "F: 0.16\n",
      "variant: 6 (best/1/bin)\n",
      "meta_fitness: 2.37e+06\n",
      "\n",
      "pop_size: 154\n",
      "CR: 0.65\n",
      "F: 0.54\n",
      "variant: 2 (rand/1/exp)\n",
      "meta_fitness: 1.45e+03\n",
      "\n",
      "pop_size: 38\n",
      "CR: 0.65\n",
      "F: 0.41\n",
      "variant: 5 (rand/2/exp)\n",
      "meta_fitness: 9.46e+01\n",
      "\n",
      "pop_size: 24\n",
      "CR: 0.01\n",
      "F: 0.72\n",
      "variant: 7 (rand/1/bin)\n",
      "meta_fitness: 3.33e+02\n",
      "\n",
      "pop_size: 148\n",
      "CR: 0.83\n",
      "F: 0.60\n",
      "variant: 4 (best/2/exp)\n",
      "meta_fitness: 6.31e+03\n",
      "\n",
      "pop_size: 46\n",
      "CR: 0.21\n",
      "F: 0.76\n",
      "variant: 5 (rand/2/exp)\n",
      "meta_fitness: 4.84e+02\n",
      "\n",
      "pop_size: 101\n",
      "CR: 0.29\n",
      "F: 0.45\n",
      "variant: 2 (rand/1/exp)\n",
      "meta_fitness: 7.66e+02\n",
      "\n",
      "pop_size: 145\n",
      "CR: 0.22\n",
      "F: 0.65\n",
      "variant: 3 (rand-to-best/1/exp)\n",
      "meta_fitness: 3.19e+03\n",
      "\n",
      "pop_size: 172\n",
      "CR: 0.15\n",
      "F: 0.05\n",
      "variant: 8 (rand-to-best/1/bin)\n",
      "meta_fitness: 5.24e+04\n",
      "\n",
      "pop_size: 62\n",
      "CR: 0.79\n",
      "F: 0.47\n",
      "variant: 9 (best/2/bin)\n",
      "meta_fitness: 2.24e+02\n",
      "\n",
      "pop_size: 7\n",
      "CR: 0.28\n",
      "F: 0.78\n",
      "variant: 3 (rand-to-best/1/exp)\n",
      "meta_fitness: 1.48e+02\n",
      "\n",
      "pop_size: 15\n",
      "CR: 0.67\n",
      "F: 0.72\n",
      "variant: 4 (best/2/exp)\n",
      "meta_fitness: 9.18e+01\n",
      "\n",
      "pop_size: 194\n",
      "CR: 0.69\n",
      "F: 0.91\n",
      "variant: 2 (rand/1/exp)\n",
      "meta_fitness: 2.73e+04\n",
      "\n",
      "pop_size: 8\n",
      "CR: 0.11\n",
      "F: 0.93\n",
      "variant: 1 (best/1/exp)\n",
      "meta_fitness: 1.31e+02\n",
      "\n",
      "pop_size: 31\n",
      "CR: 0.30\n",
      "F: 0.98\n",
      "variant: 7 (rand/1/bin)\n",
      "meta_fitness: 4.68e+05\n",
      "\n",
      "CPU times: user 3min 9s, sys: 1min 1s, total: 4min 11s\n",
      "Wall time: 2min 51s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "search_result = gp_minimize(func=meta_fitness,\n",
    "                            dimensions=dimensions,\n",
    "                            n_calls=50,\n",
    "                            acq_func='EI', # Expected Improvement.\n",
    "                            x0=default_parameters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results\n",
    "\n",
    "We can now show several results of the Meta-Optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7157490455691291"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This is the best fitness value for the actual problem we\n",
    "# were trying to optimize, in this case the Rosenbrock problem.\n",
    "best_fitness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.9939679 , 0.99406711, 0.99407582, 0.99115199, 0.99275279,\n",
       "       0.9912751 , 0.99081977, 0.99145648, 0.99210012, 0.99319021,\n",
       "       0.99160839, 0.99397586, 0.99511176, 0.99382332, 0.99446491,\n",
       "       0.993103  , 0.9949504 , 0.99569109, 0.99428724, 0.99295317,\n",
       "       0.99407859, 0.99491388, 0.99511708, 0.99250253, 0.9921781 ,\n",
       "       0.99014079, 0.99293716, 0.99278222, 0.99522344, 0.99547432,\n",
       "       0.99691571, 0.99738423, 0.99694656, 0.99655378, 0.99716768,\n",
       "       0.99667813, 0.99742076, 0.99741898, 0.99604799, 0.99500783,\n",
       "       0.99707729, 0.99878386, 0.99983031, 1.00036703, 1.00026111,\n",
       "       1.00014392, 1.00009761, 0.99933234, 0.99840288, 0.99654709,\n",
       "       0.99657004, 0.99697644, 0.99735727, 0.99708081, 0.99659092,\n",
       "       0.99536468, 0.99713337, 0.99840613, 0.99804402, 0.99764227,\n",
       "       0.99572776, 0.99097023, 0.99213882, 0.98989369, 0.98783372,\n",
       "       0.99139423, 0.99012756, 0.98532272, 0.97923349, 0.9813734 ,\n",
       "       0.97491246, 0.9824034 , 0.99182786, 0.98992701, 0.98820122,\n",
       "       0.99214692, 0.99447964, 0.99388925, 0.99270652, 0.99423588,\n",
       "       0.99497001, 0.99313587, 0.99477533, 0.99549817, 0.99423582,\n",
       "       0.99499282, 0.99677415, 0.99637626, 0.99686555, 0.99833114,\n",
       "       0.99968132, 1.00051484, 1.00348209, 1.00922332, 1.01926109,\n",
       "       1.03742559, 1.07388717, 1.14704759, 1.31854344, 1.74724882])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Best solution for the Rosenbrock problem.\n",
    "best_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[10, 0.6924273767128258, 0.004773916775181576, 3]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Best parameters found for the heuristic optimizer.\n",
    "# These are useful if you want to run the optimizer again\n",
    "# on similar problems, without needing to tune it again.\n",
    "# You can also try and run the optimizer e.g. 100 times\n",
    "# using these parameters to see if you can improve upon\n",
    "# best_x and best_fitness for the actual problem.\n",
    "best_parameters = search_result.x\n",
    "best_parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Meta-fitness: 2.31e+01, Parameters: [10.0, 0.69, 0.0, 3.0]\n",
      "Meta-fitness: 8.88e+01, Parameters: [37.0, 0.41, 0.69, 3.0]\n",
      "Meta-fitness: 9.18e+01, Parameters: [15.0, 0.72, 0.67, 4.0]\n",
      "Meta-fitness: 9.44e+01, Parameters: [35.0, 0.63, 0.71, 4.0]\n",
      "Meta-fitness: 9.46e+01, Parameters: [38.0, 0.41, 0.65, 5.0]\n",
      "Meta-fitness: 1.01e+02, Parameters: [17.0, 0.85, 0.5, 4.0]\n",
      "Meta-fitness: 1.15e+02, Parameters: [64.0, 0.28, 0.63, 4.0]\n",
      "Meta-fitness: 1.22e+02, Parameters: [88.0, 0.7, 0.7, 3.0]\n",
      "Meta-fitness: 1.31e+02, Parameters: [8.0, 0.93, 0.11, 1.0]\n",
      "Meta-fitness: 1.48e+02, Parameters: [7.0, 0.78, 0.28, 3.0]\n",
      "Meta-fitness: 1.69e+02, Parameters: [196.0, 0.59, 0.96, 1.0]\n",
      "Meta-fitness: 1.89e+02, Parameters: [98.0, 0.2, 0.27, 7.0]\n",
      "Meta-fitness: 2.24e+02, Parameters: [62.0, 0.47, 0.79, 9.0]\n",
      "Meta-fitness: 2.53e+02, Parameters: [188.0, 0.21, 0.82, 2.0]\n",
      "Meta-fitness: 2.84e+02, Parameters: [193.0, 0.38, 0.78, 1.0]\n",
      "Meta-fitness: 2.86e+02, Parameters: [87.0, 0.43, 0.87, 7.0]\n",
      "Meta-fitness: 3.33e+02, Parameters: [24.0, 0.72, 0.01, 7.0]\n",
      "Meta-fitness: 4.22e+02, Parameters: [34.0, 0.9, 0.06, 4.0]\n",
      "Meta-fitness: 4.77e+02, Parameters: [183.0, 0.55, 0.17, 6.0]\n",
      "Meta-fitness: 4.84e+02, Parameters: [46.0, 0.76, 0.21, 5.0]\n",
      "Meta-fitness: 6.48e+02, Parameters: [118.0, 0.17, 0.39, 5.0]\n",
      "Meta-fitness: 6.72e+02, Parameters: [150.0, 0.11, 0.53, 2.0]\n",
      "Meta-fitness: 6.84e+02, Parameters: [156.0, 0.1, 0.55, 5.0]\n",
      "Meta-fitness: 7.66e+02, Parameters: [101.0, 0.45, 0.29, 2.0]\n",
      "Meta-fitness: 1.45e+03, Parameters: [154.0, 0.54, 0.65, 2.0]\n",
      "Meta-fitness: 1.53e+03, Parameters: [153.0, 0.41, 0.44, 4.0]\n",
      "Meta-fitness: 3.19e+03, Parameters: [145.0, 0.65, 0.22, 3.0]\n",
      "Meta-fitness: 4.64e+03, Parameters: [145.0, 0.56, 0.0, 1.0]\n",
      "Meta-fitness: 4.66e+03, Parameters: [100.0, 0.8, 0.9, 2.0]\n",
      "Meta-fitness: 4.71e+03, Parameters: [196.0, 0.22, 0.24, 9.0]\n",
      "Meta-fitness: 4.99e+03, Parameters: [135.0, 0.97, 0.35, 1.0]\n",
      "Meta-fitness: 6.31e+03, Parameters: [148.0, 0.6, 0.83, 4.0]\n",
      "Meta-fitness: 6.51e+03, Parameters: [79.0, 0.05, 0.51, 7.0]\n",
      "Meta-fitness: 1.29e+04, Parameters: [174.0, 0.61, 0.05, 2.0]\n",
      "Meta-fitness: 2.73e+04, Parameters: [194.0, 0.91, 0.69, 2.0]\n",
      "Meta-fitness: 4.07e+04, Parameters: [168.0, 0.38, 0.98, 1.0]\n",
      "Meta-fitness: 5.24e+04, Parameters: [172.0, 0.05, 0.15, 8.0]\n",
      "Meta-fitness: 6.55e+04, Parameters: [184.0, 0.18, 0.29, 9.0]\n",
      "Meta-fitness: 1.41e+05, Parameters: [75.0, 0.03, 0.81, 10.0]\n",
      "Meta-fitness: 1.69e+05, Parameters: [11.0, 0.04, 0.76, 5.0]\n",
      "Meta-fitness: 2.39e+05, Parameters: [123.0, 0.34, 0.54, 6.0]\n",
      "Meta-fitness: 4.68e+05, Parameters: [31.0, 0.98, 0.3, 7.0]\n",
      "Meta-fitness: 1.01e+06, Parameters: [182.0, 0.68, 0.93, 7.0]\n",
      "Meta-fitness: 1.54e+06, Parameters: [150.0, 0.15, 0.63, 6.0]\n",
      "Meta-fitness: 1.65e+06, Parameters: [25.0, 0.85, 0.7, 9.0]\n",
      "Meta-fitness: 2.12e+06, Parameters: [59.0, 0.94, 0.54, 9.0]\n",
      "Meta-fitness: 2.26e+06, Parameters: [191.0, 0.95, 0.46, 10.0]\n",
      "Meta-fitness: 2.32e+06, Parameters: [128.0, 0.67, 0.72, 10.0]\n",
      "Meta-fitness: 2.37e+06, Parameters: [20.0, 0.16, 0.52, 6.0]\n",
      "Meta-fitness: 2.71e+06, Parameters: [46.0, 0.24, 0.91, 6.0]\n"
     ]
    }
   ],
   "source": [
    "# Show all the parameters that were tried during meta-optimization.\n",
    "# Can you spot a trend here? Do some parameters generally work better?\n",
    "for meta_fit, params in sorted(zip(search_result.func_vals, search_result.x_iters)):\n",
    "    msg = \"Meta-fitness: {0:.2e}, Parameters: {1}\"\n",
    "    print(msg.format(meta_fit, list(np.around(params, 2))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plots\n",
    "\n",
    "We can also plot the progress of the Meta-Optimization by showing the best-found Meta-Fitness after each step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fe094d880b8>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_convergence(search_result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following plot is more complicated and requires some explanation.\n",
    "\n",
    "The Bayesian optimizer works by building a surrogate model of the search-space and then searching this model instead of the real search-space, because it is much faster. The following plot shows the last surrogate model built by the Bayesian optimizer where yellow regions are better and blue regions are worse. The black dots show where the optimizer has sampled the search-space and the red dot shows the best parameters found.\n",
    "\n",
    "Several things should be noted here. Firstly, this surrogate model of the search-space may not be accurate. It is built from only a small number of calls to the `meta_fitness()` function. The modelled meta-fitness landscape may differ significantly from its true values especially in regions of the search-space with few samples. Secondly, the plot may change each time the meta-optimization is run because of random noise. Thirdly, each sub-plot shows the effect of changing two parameters such as `pop_size` and `CR` when averaged over all other dimensions in the search-space, this is also called a Partial Dependence plot and is a way of visualizing high-dimensional spaces in only 2-dimensions.\n",
    "\n",
    "We now make a matrix-plot of all combinations of these dimensions. \n",
    "\n",
    "The diagonal shows the influence of a single dimension on the meta-fitness. This is a so-called Partial Dependence plot for that dimension. It shows how the approximated meta-fitness value changes with different values in that dimension.\n",
    "\n",
    "The plots below the diagonal show the Partial Dependence for two dimensions. This shows how the approximated meta-fitness value changes when we are varying two dimensions simultaneously.\n",
    "\n",
    "These Partial Dependence plots are only approximations of the modelled meta-fitness function - which in turn is only an approximation of the true meta-fitness function in `meta_fitness()`. This may be a bit difficult to understand. For example, in the first diagonal plot on the top, the Partial Dependence is calculated by fixing one value for the `pop_size` and then taking a large number of random samples for the remaining dimensions in the search-space. The estimated fitness for all these points is then averaged. This process is then repeated for other values of the `pop_size` to show how it affects the meta-fitness on average. A similar procedure is done for the plots that show the Partial Dependence plots for two dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plot_objective(result=search_result, dimensions=dimension_names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "We presented a method for automatically tuning the parameters of a heuristic optimizer. The method is fairly sophisticated but when combining existing Python libraries, it is very easy to implement.\n",
    "\n",
    "The method is mainly useful in two scenarios:\n",
    "\n",
    "1. If the default parameters for the heuristic optimizer do not work very well on your particular problem, and you can afford to run the optimizer many times to try different parameters. Then you can use this method to automatically find good parameters for the optimizer, as well as a better solution to the actual problem you are trying to optimize.\n",
    "\n",
    "2. If you need to run the heuristic optimizer many times on problems that are somewhat related, then you can use Meta-Optimization to find a good choice of parameters that makes the optimizer perform well on those problems."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises & Research Ideas\n",
    "\n",
    "There are plenty of opportunities for doing original research using these techniques. Here are some ideas to get you started:\n",
    "\n",
    "- Try using other benchmark problems as well as real-world problems. Record the results. Are there parameters that seem to work well for all problems?\n",
    "- Try using multiple problems inside the `meta_fitness()` function. First try and optimize each problem in turn and merely sum the results to an aggregate meta-fitness. What is the problem with that approach and can you find a better solution?\n",
    "- Try running more iterations of the meta-optimizer. Does that improve the results?\n",
    "- Use another Bayesian optimizer, see the [docs](https://scikit-optimize.github.io/#header-functions) for a list.\n",
    "- Use another acquisition function for the Bayesian optimizer.\n",
    "- Tune the parameters of another optimizer such as Particle Swarm Optimization (PSO) or Genetic Algorithm (GA).\n",
    "- Can you eliminate some of the optimizer's parameters if they are irrelevant? Can you simplify the algorithm as a result? How does it perform on a broad range of problems?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## License (MIT)\n",
    "\n",
    "Copyright (c) 2018 by [Magnus Erik Hvass Pedersen](http://www.hvass-labs.org/)\n",
    "\n",
    "Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the \"Software\"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:\n",
    "\n",
    "The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.\n",
    "\n",
    "THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE."
   ]
  }
 ],
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