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Merge pull request #383 from bwheelz36/update_simple_contraints_docs
Update simple contraints docs
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‎.github/workflows/run_tests.yml

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runs-on: ubuntu-latest
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strategy:
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matrix:
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python-version: ["3.6", "3.7", "3.8", "3.9", "3.10"]
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python-version: ["3.7", "3.8", "3.9", "3.10"]
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- uses: actions/checkout@v3

‎.gitignore

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venv/
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ENV/
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*temp*

‎examples/constraints.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Constrained Optimization\n",
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"\n",
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"Constrained optimization refers to situations in which you must for instance maximize `f`, a function of `x` and `y`, but the solution must lie in a region where for instance `x<y`.\n",
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"\n",
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"There are two distinct situations you may find yourself in:\n",
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"\n",
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"1. Simple, cheap contraints: in this case, you know whether or not a given solution violates your constraints **before** you even assess it. In this case, you can codify your constraints directly into the objective function and you should read **1** below.\n",
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"2. Expensive contraints - in other situations, you may not know whether or not a given solution violates your constraints until you have explicitly evaluate the objective function there - which is typically an expensive operation. In such situations, it is desirable to **learn** the constrained regions on the fly in order to avoid unnecessary expensive calls to the objective function. The way to handle these situations is descrived in **2. Advanced Constrained Optimization**\n",
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"\n",
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"\n",
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"# 1. Simple Constrained Optimization\n",
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"\n",
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"In situations where you know in advance whether or not a given point violates your constraints, you can normally simply code them directly into the objective function. To demonstrate this, let's start with a standart non-contrained optimziation:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"the best solution with no constraints is {'target': -3.0000001251185324, 'params': {'x': 2.0, 'y': 0.9996462790185919}}\n"
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]
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}
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],
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"source": [
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"from bayes_opt import BayesianOptimization\n",
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"\n",
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"def black_box_function_no_constraints(x, y):\n",
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" return -x ** 2 - (y - 1) ** 2 + 1\n",
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"\n",
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"# Bounded region of parameter space\n",
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"pbounds = {'x': (2, 4), 'y': (-3, 3)}\n",
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"\n",
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"optimizer = BayesianOptimization(\n",
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" f=black_box_function_no_constraints,\n",
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" pbounds=pbounds,\n",
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" random_state=0,\n",
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" verbose=0\n",
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")\n",
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"\n",
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"optimizer.maximize(\n",
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" init_points=2,\n",
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" n_iter=100\n",
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")\n",
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"\n",
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"print(f'the best solution with no constraints is {optimizer.max}')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Now, let's rerun this example, except with the constraint that y>x. To do this, we are simply going to return a 'bad' value from the objective function whenever this constrain is violated. What constitutes a 'bad' value is objective function specific - in general, it's a good idea for the 'bad' value you use to be similar in magnitude to the worst value that the objective function naturally has."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"the best solution with no constraints is {'target': -4.226389709162731, 'params': {'x': 2.0042130207949307, 'y': 2.099781740364328}}\n"
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]
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}
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],
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"source": [
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"def black_box_function_with_constraints(x, y):\n",
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" if y <= x:\n",
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" return -10\n",
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" else:\n",
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" return -x ** 2 - (y - 1) ** 2 + 1\n",
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" \n",
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"optimizer = BayesianOptimization(\n",
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" f=black_box_function_with_constraints,\n",
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" pbounds=pbounds,\n",
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" random_state=0,\n",
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" verbose=0\n",
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")\n",
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"\n",
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"optimizer.maximize(\n",
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" init_points=2,\n",
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" n_iter=100\n",
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")\n",
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"\n",
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"print(f'the best solution with no constraints is {optimizer.max}')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Ok, this seems to have worked pretty well; our constraints have been respected and the target value isn't even **that** much worse!\n",
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"\n",
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"In certain other cases, you may be able to reformulate your objective function such that the constraint is explicitly embedded. For instance, consider the constraint `x+y=4`. Since this implies that `y=4-x`, we could simply reformulate the objective function explicitly:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"the best solution with no constraints is {'target': -4.0, 'params': {'x': 2.0}}\n"
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]
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}
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],
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"source": [
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"def surrogate_objective(x):\n",
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" y=4-x\n",
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" return black_box_function_no_constraints(x,y)\n",
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"\n",
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"pbounds = {'x': (2, 4)}\n",
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"# note that in general, we would have to update pbounds such that the values that x were allowed to take on\n",
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"# respected the bounds of y. In this case (4-4=0)<=y<=(4-2=2) already respect our original bounds -3<=y<=3\n",
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"\n",
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"optimizer = BayesianOptimization(\n",
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" f=surrogate_objective,\n",
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" pbounds=pbounds,\n",
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" random_state=0,\n",
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" verbose=0\n",
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")\n",
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"\n",
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"optimizer.maximize(\n",
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" init_points=2,\n",
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" n_iter=100\n",
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")\n",
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"\n",
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"print(f'the best solution with no constraints is {optimizer.max}')"
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]
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},
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3.8.9 ('bopt')",
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"display_name": "Python 3 (ipykernel)",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.9"
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"version": "3.9.5"
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"vscode": {
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"interpreter": {

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