Feasibility modeling#
A more complicated example involves minimizing in two dimensions, where some parts of the parameter space are off-limits. Let’s minimize Himmelblau’s function, subject to the constraint that \(x_1^2 + x_2^2 < 50\)
[1]:
import numpy as np
import matplotlib as mpl
from matplotlib import pyplot as plt
from bloptools import test_functions
x1 = x2 = np.linspace(-8, 8, 256)
X1, X2 = np.meshgrid(x1, x2)
from bloptools.tasks import Task
task = Task(key="himmelblau", kind="min")
F = test_functions.constrained_himmelblau(X1, X2)
plt.pcolormesh(x1, x2, F, norm=mpl.colors.LogNorm(), shading="auto")
plt.colorbar()
plt.xlabel("x1")
plt.ylabel("x2")
[1]:
Text(0, 0.5, 'x2')
where everything outside our constraint is undefined. In our digestion function, we return a NaN when we violate the constraint:
[2]:
def digestion(db, uid):
products = db[uid].table()
for index, entry in products.iterrows():
products.loc[index, "himmelblau"] = test_functions.constrained_himmelblau(entry.x1, entry.x2)
return products
and create the agent in the usual way:
[3]:
%run -i ../../../examples/prepare_bluesky.py # prepare the bluesky environment
from bloptools import devices
from bloptools.bayesian import Agent
dofs = [
{"device": devices.DOF(name="x1"), "limits": (-8, 8), "kind": "active"},
{"device": devices.DOF(name="x2"), "limits": (-8, 8), "kind": "active"},
]
tasks = [
{"key": "himmelblau", "kind": "minimize"},
]
agent = Agent(
dofs=dofs,
tasks=tasks,
digestion=digestion,
db=db,
)
RE(agent.initialize("qr", n_init=64))
agent.plot_tasks()
Transient Scan ID: 1 Time: 2023-08-11 05:54:12
Persistent Unique Scan ID: '28a13d88-cb29-4b2f-9d50-8bcfab116275'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:12.7 | 4.615 | -6.168 |
| 2 | 05:54:12.7 | -4.988 | 3.077 |
| 3 | 05:54:12.7 | -3.109 | -0.170 |
| 4 | 05:54:12.7 | 3.490 | 5.077 |
| 5 | 05:54:12.7 | 1.262 | -3.447 |
| 6 | 05:54:12.7 | -1.134 | 6.292 |
| 7 | 05:54:12.7 | -6.761 | -5.446 |
| 8 | 05:54:12.7 | 6.640 | 0.292 |
| 9 | 05:54:12.8 | 7.733 | -1.903 |
| 10 | 05:54:12.8 | -7.855 | 4.874 |
| 11 | 05:54:12.8 | -0.227 | -7.904 |
| 12 | 05:54:12.8 | 0.356 | 2.874 |
| 13 | 05:54:12.8 | 2.395 | -4.744 |
| 14 | 05:54:12.8 | -2.017 | 1.526 |
| 15 | 05:54:12.8 | -5.893 | -2.743 |
| 16 | 05:54:12.8 | 5.523 | 7.527 |
| 17 | 05:54:12.8 | 5.045 | -2.382 |
| 18 | 05:54:12.8 | -5.418 | 7.349 |
| 19 | 05:54:12.8 | -2.539 | -4.382 |
| 20 | 05:54:12.8 | 2.919 | 1.348 |
| 21 | 05:54:12.8 | 0.833 | -7.222 |
| 22 | 05:54:12.8 | -0.704 | 2.000 |
| 23 | 05:54:12.8 | -7.331 | -1.222 |
| 24 | 05:54:12.8 | 7.210 | 4.002 |
| 25 | 05:54:12.8 | 6.178 | -5.678 |
| 26 | 05:54:12.8 | -6.300 | 0.584 |
| 27 | 05:54:12.8 | -1.672 | -3.679 |
| 28 | 05:54:12.8 | 1.802 | 6.582 |
| 29 | 05:54:12.8 | 3.949 | -0.957 |
| 30 | 05:54:12.8 | -3.572 | 5.797 |
| 31 | 05:54:12.8 | -4.448 | -6.956 |
| 32 | 05:54:12.8 | 4.078 | 3.799 |
| 33 | 05:54:12.8 | 4.428 | -0.400 |
| 34 | 05:54:12.8 | -4.050 | 5.370 |
| 35 | 05:54:12.8 | -3.923 | -6.399 |
| 36 | 05:54:12.8 | 3.552 | 3.371 |
| 37 | 05:54:12.8 | 1.700 | -5.246 |
| 38 | 05:54:12.8 | -1.822 | 0.031 |
| 39 | 05:54:12.9 | -6.197 | -3.248 |
| 40 | 05:54:12.9 | 6.328 | 6.030 |
| 41 | 05:54:12.9 | 7.295 | -7.666 |
| 42 | 05:54:12.9 | -7.168 | 2.573 |
| 43 | 05:54:12.9 | -0.789 | -1.665 |
| 44 | 05:54:12.9 | 0.670 | 4.573 |
| 45 | 05:54:12.9 | 2.583 | -2.949 |
| 46 | 05:54:12.9 | -2.954 | 7.796 |
| 47 | 05:54:12.9 | -5.081 | -4.951 |
| 48 | 05:54:12.9 | 5.460 | 1.796 |
| 49 | 05:54:12.9 | 5.983 | -4.175 |
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 50 | 05:54:12.9 | -5.605 | 1.079 |
| 51 | 05:54:12.9 | -2.477 | -2.175 |
| 52 | 05:54:12.9 | 2.107 | 7.080 |
| 53 | 05:54:12.9 | 0.145 | -1.460 |
| 54 | 05:54:12.9 | -0.267 | 4.302 |
| 55 | 05:54:12.9 | -7.643 | -7.460 |
| 56 | 05:54:12.9 | 7.773 | 2.301 |
| 57 | 05:54:12.9 | 6.865 | -3.878 |
| 58 | 05:54:12.9 | -6.738 | 6.844 |
| 59 | 05:54:12.9 | -1.360 | -5.878 |
| 60 | 05:54:12.9 | 1.240 | 0.846 |
| 61 | 05:54:12.9 | 3.013 | -6.725 |
| 62 | 05:54:12.9 | -3.384 | 3.506 |
| 63 | 05:54:12.9 | -4.510 | -0.726 |
| 64 | 05:54:12.9 | 4.890 | 5.504 |
+-----------+------------+------------+------------+
generator list_scan ['28a13d88'] (scan num: 1)
In addition to modeling the fitness of the task, the agent models the probability that an input will be feasible:
[4]:
agent.plot_feasibility()
It combines the estimate of the objective and the estimate of the feasibility in deciding where to go:
[5]:
agent.plot_acquisition(acq_func=["ei", "pi", "ucb"])
[6]:
RE(agent.learn("ei", n_per_iter=4))
Transient Scan ID: 2 Time: 2023-08-11 05:54:18
Persistent Unique Scan ID: '690bbbf0-5ece-4e44-879d-8876903d023c'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:18.3 | 2.393 | 2.587 |
| 2 | 05:54:18.3 | -2.336 | 3.083 |
| 3 | 05:54:18.3 | -2.886 | 2.681 |
| 4 | 05:54:18.3 | -3.845 | -2.566 |
+-----------+------------+------------+------------+
generator list_scan ['690bbbf0'] (scan num: 2)
[6]:
('690bbbf0-5ece-4e44-879d-8876903d023c',)
The agent automatically tries to avoid infeasible points, but will end up naturally exploring the boundary of the constraint. Let’s see where the agent is thinking of going:
[7]:
agent.plot_tasks()
agent.plot_acquisition(strategy=["ei", "pi", "ucb"])
The agent will naturally explore the whole parameter space
[8]:
RE(agent.learn("ei", n_iter=16))
agent.plot_tasks()
Transient Scan ID: 3 Time: 2023-08-11 05:54:21
Persistent Unique Scan ID: '47d8f47f-1b07-4371-8868-806377508218'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:21.5 | 3.376 | 0.150 |
+-----------+------------+------------+------------+
generator list_scan ['47d8f47f'] (scan num: 3)
Transient Scan ID: 4 Time: 2023-08-11 05:54:22
Persistent Unique Scan ID: '61f3e362-c16e-45d9-9460-93ca633ce219'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:22.4 | -3.170 | -3.457 |
+-----------+------------+------------+------------+
generator list_scan ['61f3e362'] (scan num: 4)
Transient Scan ID: 5 Time: 2023-08-11 05:54:23
Persistent Unique Scan ID: 'be2de37f-59a7-49fe-a6df-b46219252303'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:23.2 | 3.857 | -1.710 |
+-----------+------------+------------+------------+
generator list_scan ['be2de37f'] (scan num: 5)
Transient Scan ID: 6 Time: 2023-08-11 05:54:24
Persistent Unique Scan ID: '388de2b1-e20c-42ac-a670-53f65fabf3b8'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:24.1 | 3.280 | 2.016 |
+-----------+------------+------------+------------+
generator list_scan ['388de2b1'] (scan num: 6)
Transient Scan ID: 7 Time: 2023-08-11 05:54:25
Persistent Unique Scan ID: 'ff51fbec-0cca-4caa-bc9f-4b9ad890079d'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:25.1 | 3.125 | -2.246 |
+-----------+------------+------------+------------+
generator list_scan ['ff51fbec'] (scan num: 7)
Transient Scan ID: 8 Time: 2023-08-11 05:54:26
Persistent Unique Scan ID: '824ffca6-aced-49ee-b8eb-0442806e8bd8'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:26.0 | 3.899 | -2.696 |
+-----------+------------+------------+------------+
generator list_scan ['824ffca6'] (scan num: 8)
Transient Scan ID: 9 Time: 2023-08-11 05:54:26
Persistent Unique Scan ID: '2c63f650-8368-4cc0-80c7-d79fe79f4e46'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:26.8 | -2.581 | 3.735 |
+-----------+------------+------------+------------+
generator list_scan ['2c63f650'] (scan num: 9)
Transient Scan ID: 10 Time: 2023-08-11 05:54:27
Persistent Unique Scan ID: 'c44c6c1b-07d4-42b2-8e0c-fce59116c5de'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:27.8 | -4.231 | -3.395 |
+-----------+------------+------------+------------+
generator list_scan ['c44c6c1b'] (scan num: 10)
Transient Scan ID: 11 Time: 2023-08-11 05:54:28
Persistent Unique Scan ID: '8e64a5da-4462-4c8b-a2c3-7109081b394a'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:28.6 | 3.464 | 1.315 |
+-----------+------------+------------+------------+
generator list_scan ['8e64a5da'] (scan num: 11)
Transient Scan ID: 12 Time: 2023-08-11 05:54:29
Persistent Unique Scan ID: 'ad20ba6f-ba4e-4711-aae5-7ae9af21938c'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:29.7 | -2.969 | 3.077 |
+-----------+------------+------------+------------+
generator list_scan ['ad20ba6f'] (scan num: 12)
Transient Scan ID: 13 Time: 2023-08-11 05:54:30
Persistent Unique Scan ID: '9d30d1cb-2573-43b6-ba79-0647d2f78ce4'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:30.5 | 3.650 | -2.133 |
+-----------+------------+------------+------------+
generator list_scan ['9d30d1cb'] (scan num: 13)
Transient Scan ID: 14 Time: 2023-08-11 05:54:31
Persistent Unique Scan ID: '42e27d0d-2f52-4316-8064-17937a52b9a5'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:31.5 | 3.564 | -2.076 |
+-----------+------------+------------+------------+
generator list_scan ['42e27d0d'] (scan num: 14)
Transient Scan ID: 15 Time: 2023-08-11 05:54:32
Persistent Unique Scan ID: '63764d21-6b9b-401a-b303-d57e0bb3425c'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:32.2 | 3.418 | -1.146 |
+-----------+------------+------------+------------+
generator list_scan ['63764d21'] (scan num: 15)
Transient Scan ID: 16 Time: 2023-08-11 05:54:33
Persistent Unique Scan ID: '21eaa49a-7826-4cd0-b5aa-e2433381eddc'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:33.3 | -2.979 | 2.947 |
+-----------+------------+------------+------------+
generator list_scan ['21eaa49a'] (scan num: 16)
Transient Scan ID: 17 Time: 2023-08-11 05:54:34
Persistent Unique Scan ID: '8c16ab5c-3b87-4afb-b0c3-c5a3068e45ca'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:34.2 | 2.809 | 2.189 |
+-----------+------------+------------+------------+
generator list_scan ['8c16ab5c'] (scan num: 17)
Transient Scan ID: 18 Time: 2023-08-11 05:54:35
Persistent Unique Scan ID: '7f23be5a-82d5-4ae4-9bfa-d408b556f211'
New stream: 'primary'
+-----------+------------+------------+------------+
| seq_num | time | x1 | x2 |
+-----------+------------+------------+------------+
| 1 | 05:54:35.4 | 3.592 | -1.757 |
+-----------+------------+------------+------------+
generator list_scan ['7f23be5a'] (scan num: 18)
