How to visualize optimizer histories

optimagic’s criterion_plot can visualize the history of function values for one or multiple optimizations. optimagic’s params_plot can visualize the history of parameter values for one optimization.

This can help you to understand whether your optimization actually converged and if not, which parameters are problematic.

It can also help you to find the fastest optimizer for a given optimization problem.

import numpy as np
import plotly.io as pio

pio.renderers.default = "notebook_connected"

import optimagic as om

Run two optimization to get example results

def sphere(x):
    return x @ x


results = {}
for algo in ["scipy_lbfgsb", "scipy_neldermead"]:
    results[algo] = om.minimize(sphere, params=np.arange(5), algorithm=algo)

Make a single criterion plot

fig = om.criterion_plot(results["scipy_neldermead"])
fig.show()

Note

For details on using other plotting backends, see How to change the plotting backend.

Compare two optimizations in a criterion plot

fig = om.criterion_plot(results)
fig.show()

Use some advanced options of criterion plot

fig = om.criterion_plot(
    results,
    # cut off after 180 evaluations
    max_evaluations=180,
    # show only the current best function value
    monotone=True,
)
fig.show()

Make a params plot

fig = om.params_plot(results["scipy_neldermead"])
fig.show()

Use advanced options of params plot

fig = om.params_plot(
    results["scipy_neldermead"],
    # cut off after 180 evaluations
    max_evaluations=180,
    # select only the last three parameters
    selector=lambda x: x[2:],
)
fig.show()

Criterion plot with multistart optimization

def alpine(x):
    return np.sum(np.abs(x * np.sin(x) + 0.1 * x))


res = om.minimize(
    alpine,
    params=np.arange(7),
    bounds=om.Bounds(soft_lower=np.full(7, -3), soft_upper=np.full(7, 10)),
    algorithm="scipy_neldermead",
    multistart=om.MultistartOptions(n_samples=100, convergence_max_discoveries=3),
)

fig = om.criterion_plot(res, max_evaluations=1000, monotone=True)
fig.show()