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feat(algorithms): add CMA-ME, fix CMA-ES and CMA-MEGA (#86)
Add emitters introduced in CMA-ME, add tests, notebook, update the documentation, fix CMA-ES and fix CMA-MEGA
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| # Covariance Matrix Adaptation MAP Elites (CMAME) | ||
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| To create an instance of CMAME, one need to use an instance of [MAP-Elites](map_elites.md) with the desired CMA Emitter - optimizing, random direction, improvement - detailed below.To use the pool of emitter mechanism, use the CMAPoolEmitter. | ||
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| Three emitter types: | ||
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| ::: qdax.core.emitters.cma_emitter.CMAEmitter | ||
| ::: qdax.core.emitters.cma_rnd_emitter.CMARndEmitter | ||
| ::: qdax.core.emitters.cma_opt_emitter.CMAOptimizingEmitter | ||
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| Pool of homogeneous emitters: | ||
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| ::: qdax.core.emitters.cma_pool_emitter.CMAPoolEmitter |
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| ../examples/ |
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| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "222bbe00", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "# Optimizing with CMA-ES in Jax\n", | ||
| "\n", | ||
| "This notebook shows how to use QDax to find performing parameters on Rastrigin and Sphere problems with [CMA-ES](https://arxiv.org/pdf/1604.00772.pdf). It can be run locally or on Google Colab. We recommand to use a GPU. This notebook will show:\n", | ||
| "\n", | ||
| "- how to define the problem\n", | ||
| "- how to create a CMA-ES optimizer\n", | ||
| "- how to launch a certain number of optimizing steps\n", | ||
| "- how to visualise the optimization process" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "d731f067", | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import jax\n", | ||
| "import jax.numpy as jnp\n", | ||
| "\n", | ||
| "import matplotlib.pyplot as plt\n", | ||
| "from matplotlib.patches import Ellipse\n", | ||
| "\n", | ||
| "from qdax.core.cmaes import CMAES" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "7b6e910b", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "## Set the hyperparameters" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "404fb0dc", | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "#@title Hyperparameters\n", | ||
| "#@markdown ---\n", | ||
| "num_iterations = 1000 #@param {type:\"integer\"}\n", | ||
| "num_dimensions = 100 #@param {type:\"integer\"}\n", | ||
| "batch_size = 36 #@param {type:\"integer\"}\n", | ||
| "num_best = 18 #@param {type:\"integer\"}\n", | ||
| "sigma_g = 0.5 # 0.5 #@param {type:\"number\"}\n", | ||
| "minval = -5.12 #@param {type:\"number\"}\n", | ||
| "optim_problem = \"sphere\" #@param[\"rastrigin\", \"sphere\"]\n", | ||
| "#@markdown ---" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "ccc7cbeb", | ||
| "metadata": { | ||
| "pycharm": { | ||
| "name": "#%% md\n" | ||
| } | ||
| }, | ||
| "source": [ | ||
| "## Define the fitness function - choose rastrigin or sphere" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "436dccbb", | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "def rastrigin_scoring(x: jnp.ndarray):\n", | ||
| " first_term = 10 * x.shape[-1]\n", | ||
| " second_term = jnp.sum((x + minval * 0.4) ** 2 - 10 * jnp.cos(2 * jnp.pi * (x + minval * 0.4)))\n", | ||
| " return -(first_term + second_term)\n", | ||
| "\n", | ||
| "def sphere_scoring(x: jnp.ndarray):\n", | ||
| " return -jnp.sum((x + minval * 0.4) * (x + minval * 0.4), axis=-1)\n", | ||
| "\n", | ||
| "if optim_problem == \"sphere\":\n", | ||
| " fitness_fn = sphere_scoring\n", | ||
| "elif optim_problem == \"rastrigin\":\n", | ||
| " fitness_fn = jax.vmap(rastrigin_scoring)\n", | ||
| "else:\n", | ||
| " raise Exception(\"Invalid opt function name given\")" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "62bdd2a4", | ||
| "metadata": { | ||
| "pycharm": { | ||
| "name": "#%% md\n" | ||
| } | ||
| }, | ||
| "source": [ | ||
| "## Define a CMA-ES optimizer instance" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "4cf03f55", | ||
| "metadata": { | ||
| "pycharm": { | ||
| "name": "#%%\n" | ||
| } | ||
| }, | ||
| "outputs": [], | ||
| "source": [ | ||
| "cmaes = CMAES(\n", | ||
| " population_size=batch_size,\n", | ||
| " num_best=num_best,\n", | ||
| " search_dim=num_dimensions,\n", | ||
| " fitness_function=fitness_fn,\n", | ||
| " mean_init=jnp.zeros((num_dimensions,)),\n", | ||
| " init_sigma=sigma_g,\n", | ||
| " delay_eigen_decomposition=True,\n", | ||
| ")" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "f1f69f50", | ||
| "metadata": { | ||
| "pycharm": { | ||
| "name": "#%% md\n" | ||
| } | ||
| }, | ||
| "source": [ | ||
| "## Init the CMA-ES optimizer state" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "1a95b74d", | ||
| "metadata": { | ||
| "pycharm": { | ||
| "name": "#%%\n" | ||
| } | ||
| }, | ||
| "outputs": [], | ||
| "source": [ | ||
| "state = cmaes.init()\n", | ||
| "random_key = jax.random.PRNGKey(0)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "ac2d5c0d", | ||
| "metadata": { | ||
| "pycharm": { | ||
| "name": "#%% md\n" | ||
| } | ||
| }, | ||
| "source": [ | ||
| "## Run optimization iterations" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "363198ca", | ||
| "metadata": { | ||
| "pycharm": { | ||
| "name": "#%%\n" | ||
| } | ||
| }, | ||
| "outputs": [], | ||
| "source": [ | ||
| "%%time\n", | ||
| "\n", | ||
| "means = [state.mean]\n", | ||
| "covs = [(state.sigma**2) * state.cov_matrix]\n", | ||
| "\n", | ||
| "iteration_count = 0\n", | ||
| "for _ in range(num_iterations):\n", | ||
| " iteration_count += 1\n", | ||
| " \n", | ||
| " # sample\n", | ||
| " samples, random_key = cmaes.sample(state, random_key)\n", | ||
| " \n", | ||
| " # udpate\n", | ||
| " state = cmaes.update(state, samples)\n", | ||
| " \n", | ||
| " # check stop condition\n", | ||
| " stop_condition = cmaes.stop_condition(state)\n", | ||
| "\n", | ||
| " if stop_condition:\n", | ||
| " break\n", | ||
| " \n", | ||
| " # store data for plotting\n", | ||
| " means.append(state.mean)\n", | ||
| " covs.append((state.sigma**2) * state.cov_matrix)\n", | ||
| " \n", | ||
| "print(\"Num iterations before stop condition: \", iteration_count)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "0e5820b8", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "## Check final fitnesses and distribution mean" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "1e4a2c7b", | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "# checking final fitness values\n", | ||
| "fitnesses = fitness_fn(samples)\n", | ||
| "\n", | ||
| "print(\"Min fitness in the final population: \", jnp.min(fitnesses))\n", | ||
| "print(\"Mean fitness in the final population: \", jnp.mean(fitnesses))\n", | ||
| "print(\"Max fitness in the final population: \", jnp.max(fitnesses))\n", | ||
| "\n", | ||
| "# checking mean of the final distribution\n", | ||
| "print(\"Final mean of the distribution: \\n\", means[-1])\n", | ||
| "# print(\"Final covariance matrix of the distribution: \", covs[-1])" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "f3bd2b0f", | ||
| "metadata": { | ||
| "pycharm": { | ||
| "name": "#%% md\n" | ||
| } | ||
| }, | ||
| "source": [ | ||
| "## Visualization of the optimization trajectory" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "ad85551c", | ||
| "metadata": { | ||
| "pycharm": { | ||
| "name": "#%%\n" | ||
| } | ||
| }, | ||
| "outputs": [], | ||
| "source": [ | ||
| "fig, ax = plt.subplots(figsize=(12, 6))\n", | ||
| "\n", | ||
| "# sample points to show fitness landscape\n", | ||
| "random_key, subkey = jax.random.split(random_key)\n", | ||
| "x = jax.random.uniform(subkey, minval=-4, maxval=8, shape=(100000, 2))\n", | ||
| "f_x = fitness_fn(x)\n", | ||
| "\n", | ||
| "# plot fitness landscape\n", | ||
| "points = ax.scatter(x[:, 0], x[:, 1], c=f_x, s=0.1)\n", | ||
| "fig.colorbar(points)\n", | ||
| "\n", | ||
| "# plot cma-es trajectory\n", | ||
| "traj_min = 0\n", | ||
| "traj_max = iteration_count\n", | ||
| "for mean, cov in zip(means[traj_min:traj_max], covs[traj_min:traj_max]):\n", | ||
| " ellipse = Ellipse((mean[0], mean[1]), cov[0, 0], cov[1, 1], fill=False, color='k', ls='--')\n", | ||
| " ax.add_patch(ellipse)\n", | ||
| " ax.plot(mean[0], mean[1], color='k', marker='x')\n", | ||
| " \n", | ||
| "ax.set_title(f\"Optimization trajectory of CMA-ES between step {traj_min} and step {traj_max}\")\n", | ||
| "plt.show()" | ||
| ] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "kernelspec": { | ||
| "display_name": "Python 3 (ipykernel)", | ||
| "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": "3.8.13" | ||
| }, | ||
| "vscode": { | ||
| "interpreter": { | ||
| "hash": "9ae46cf6a59eb5e192bc4f27fbb5c33d8a30eb9acb43edbb510eeaf7c819ab64" | ||
| } | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 5 | ||
| } |
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