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Async optimization Loop

Tim Head, February 2017.

import numpy as np
np.random.seed(1234)

%matplotlib inline
import matplotlib.pyplot as plt
plt.set_cmap("viridis")
<matplotlib.figure.Figure at 0x7fa260c509b0>

Bayesian optimization is used to tune parameters for walking robots or other experiments that are not a simple (expensive) function call.

They often follow a pattern a bit like this: 1. ask for a new set of parameters 1. walk to the experiment and program in the new parameters 1. observe the outcome of running the experiment 1. walk back to your laptop and tell the optimizer about the outcome 1. go to step 1

A setup like this is difficult to implement with the *_minimize() function interface. This is why scikit-optimize has a ask-and-tell interface that you can use when you want to control the execution of the optimization loop.

This notenook demonstrates how to use the ask and tell interface.

The Setup

We will use a simple 1D problem to illustrate the API. This is a little bit artificial as you normally would not use the ask-and-tell interface if you had a function you can call to evaluate the objective.

from skopt.learning import ExtraTreesRegressor
from skopt import Optimizer

noise_level = 0.1

# Our 1D toy problem, this is the function we are trying to
# minimize
def objective(x, noise_level=noise_level):
    return np.sin(5 * x[0]) * (1 - np.tanh(x[0] ** 2)) + np.random.randn() * noise_level

Here a quick plot to visualize what the function looks like:

# Plot f(x) + contours
x = np.linspace(-2, 2, 400).reshape(-1, 1)
fx = np.array([objective(x_i, noise_level=0.0) for x_i in x])
plt.plot(x, fx, "r--", label="True (unknown)")
plt.fill(np.concatenate([x, x[::-1]]),
         np.concatenate(([fx_i - 1.9600 * noise_level for fx_i in fx], 
                         [fx_i + 1.9600 * noise_level for fx_i in fx[::-1]])),
         alpha=.2, fc="r", ec="None")
plt.legend()
plt.grid()
plt.show()

png

Now we setup the Optimizer class. The arguments follow the meaning and naming of the *_minimize() functions. An important difference is that you do not pass the objective function to the optimizer.

opt = Optimizer([(-2.0, 2.0)], "ET", acq_optimizer="sampling")

To obtain a suggestion for the point at which to evaluate the objective you call the ask() method of opt:

next_x = opt.ask()
print(next_x)
[-1.7121321838148869]

In a real world use case you would probably go away and use this parameter in your experiment and come back a while later with the result. In this example we can simply evaluate the objective function and report the value back to the optimizer:

f_val = objective(next_x)
opt.tell(next_x, f_val)
          fun: -0.032758350111535384
    func_vals: array([-0.03275835])
       models: []
 random_state: <mtrand.RandomState object at 0x7fa24addbbd0>
        space: Space([Real(low=-2.0, high=2.0, prior=uniform, transform=identity)])
        specs: None
            x: [-1.7121321838148869]
      x_iters: [[-1.7121321838148869]]

Like *_minimize() the first few points are random suggestions as there is no data yet with which to fit a surrogate model.

for i in range(9):
    next_x = opt.ask()
    f_val = objective(next_x)
    opt.tell(next_x, f_val)

We can now plot the random suggestions and the first model that has been fit:

from skopt.acquisition import gaussian_ei

def plot_optimizer(opt, x, fx):
    model = opt.models[-1]
    x_model = opt.space.transform(x.tolist())

    # Plot true function.
    plt.plot(x, fx, "r--", label="True (unknown)")
    plt.fill(np.concatenate([x, x[::-1]]),
             np.concatenate([fx - 1.9600 * noise_level, 
                             fx[::-1] + 1.9600 * noise_level]),
             alpha=.2, fc="r", ec="None")

    # Plot Model(x) + contours
    y_pred, sigma = model.predict(x_model, return_std=True)
    plt.plot(x, y_pred, "g--", label=r"$\mu(x)$")
    plt.fill(np.concatenate([x, x[::-1]]),
             np.concatenate([y_pred - 1.9600 * sigma, 
                             (y_pred + 1.9600 * sigma)[::-1]]),
             alpha=.2, fc="g", ec="None")

    # Plot sampled points
    plt.plot(opt.Xi, opt.yi,
             "r.", markersize=8, label="Observations")

    acq = gaussian_ei(x_model, model, y_opt=np.min(opt.yi))
    # shift down to make a better plot
    acq = 4*acq - 2
    plt.plot(x, acq, "b", label="EI(x)")
    plt.fill_between(x.ravel(), -2.0, acq.ravel(), alpha=0.3, color='blue')

    # Adjust plot layout
    plt.grid()
    plt.legend(loc='best')

plot_optimizer(opt, x, fx)

png

Let us sample a few more points and plot the optimizer again:

for i in range(10):
    next_x = opt.ask()
    f_val = objective(next_x)
    opt.tell(next_x, f_val)

plot_optimizer(opt, x, fx)

png

By using the Optimizer class directly you get control over the optimization loop.

You can also pickle your Optimizer instance if you want to end the process running it and resume it later. This is handy if your experiment takes a very long time and you want to shutdown your computer in the meantime:

import pickle

with open('my-optimizer.pkl', 'wb') as f:
    pickle.dump(opt, f)

with open('my-optimizer.pkl', 'rb') as f:
    opt_restored = pickle.load(f)