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# Async optimization Loop

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

Tim Head, February 2017. Reformatted by Holger Nahrstaedt 2020

They often follow a pattern a bit like this:

1. ask for a new set of parameters

2. walk to the experiment and program in the new parameters

3. observe the outcome of running the experiment

4. walk back to your laptop and tell the optimizer about the outcome

5. 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 notebook demonstrates how to use the ask and tell interface.

    print(__doc__)

    import numpy as np

    np.random.seed(1234)
    import matplotlib.pyplot as plt

    from skopt import Optimizer
    from skopt.plots import plot_gaussian_process

## 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.

    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

    def objective_wo_noise(x, noise_level=0):
        return objective(x, noise_level=0)

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

    # Plot f(x) + contours
    plt.set_cmap("viridis")
    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=0.2,
        fc="r",
        ec="None",
    )
    plt.legend()
    plt.grid()
    plt.show()

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)],
        "GP",
        acq_func="EI",
        acq_optimizer="sampling",
        initial_point_generator="lhs",
    )

    # 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)

    [-0.7315058981975282]

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: 0.20718649236432957
               x: [-0.7315058981975282]
       func_vals: [ 2.072e-01]
         x_iters: [[-0.7315058981975282]]
          models: []
           space: Space([Real(low=-2.0, high=2.0, prior='uniform', transform='normalize')])
    random_state: RandomState(MT19937)
           specs:     args:              dimensions: [(-2.0, 2.0)]
                                     base_estimator: GP
                                    n_random_starts: None
                                   n_initial_points: 10
                            initial_point_generator: lhs
                                             n_jobs: 1
                                           acq_func: EI
                                      acq_optimizer: sampling
                                       random_state: None
                                   model_queue_size: None
                                   space_constraint: None
                                    acq_func_kwargs: None
                               acq_optimizer_kwargs: None
                                   avoid_duplicates: True
                  function: Optimizer

Like *_minimize() the first few points are suggestions from the initial point generator 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)
        res = opt.tell(next_x, f_val)

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

    _ = plot_gaussian_process(
        res,
        objective=objective_wo_noise,
        noise_level=noise_level,
        show_next_point=False,
        show_acq_func=True,
    )
    plt.show()

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)
        res = opt.tell(next_x, f_val)

    _ = plot_gaussian_process(
        res,
        objective=objective_wo_noise,
        noise_level=noise_level,
        show_next_point=True,
        show_acq_func=True,
    )
    plt.show()

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)

Total running time of the script: (0 minutes 1.249 seconds)

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