Your first Bayesian optimization with Blop#

In this tutorial, you will learn the three core concepts of Blop: DOFs (the parameters you can adjust), objectives (what you want to optimize), and the Agent (which coordinates the optimization). We’ll optimize a simple mathematical function using simulated devices—the same patterns apply to real hardware.

Setup#

First, let’s import what we need and start the data infrastructure:

import logging
import time
from typing import Any
import warnings

from blop.ax import Agent, RangeDOF, Objective

from bluesky.protocols import NamedMovable, Readable, Status, Hints, HasHints, HasParent
from bluesky.run_engine import RunEngine
from bluesky_tiled_plugins import TiledWriter
from tiled.client import from_uri
from tiled.client.container import Container
from tiled.server import SimpleTiledServer

# Suppress noisy logs from httpx 
logging.getLogger("httpx").setLevel(logging.WARNING)
# Suppress noisy dependency deprecations from within Ax
warnings.filterwarnings('ignore',category=FutureWarning)

[INFO 07-28 17:28:09] ax.storage.sqa_store.with_db_settings_base: Ax SQL storage initialized with SQLAlchemy 2.0.51

# Start a local Tiled server for data storage
tiled_server = SimpleTiledServer()

# Set up the Bluesky RunEngine and connect it to Tiled
RE = RunEngine({})
tiled_client = from_uri(tiled_server.uri)
tiled_writer = TiledWriter(tiled_client)
RE.subscribe(tiled_writer)

Tiled version 0.2.14

0

Creating simulated devices#

Bluesky controls devices through protocols. For this tutorial, we create simple simulated “movable” devices. In real experiments, you would use Ophyd devices or similar—the code below is just boilerplate to simulate hardware:

class AlwaysSuccessfulStatus(Status):
    def add_callback(self, callback) -> None:
        callback(self)
    def exception(self, timeout = 0.0):
        return None
    @property
    def done(self) -> bool:
        return True
    @property
    def success(self) -> bool:
        return True

class ReadableSignal(Readable, HasHints, HasParent):
    def __init__(self, name: str) -> None:
        self._name = name
        self._value = 0.0
    @property
    def name(self) -> str:
        return self._name
    @property
    def hints(self) -> Hints:
        return {"fields": [self._name], "dimensions": [], "gridding": "rectilinear"}
    @property
    def parent(self) -> Any | None:
        return None
    def read(self):
        return {self._name: {"value": self._value, "timestamp": time.time()}}
    def describe(self):
        return {self._name: {"source": self._name, "dtype": "number", "shape": []}}

class MovableSignal(ReadableSignal, NamedMovable):
    def __init__(self, name: str, initial_value: float = 0.0) -> None:
        super().__init__(name)
        self._value: float = initial_value
    def set(self, value: float) -> Status:
        self._value = value
        return AlwaysSuccessfulStatus()

Defining DOFs and objectives#

DOFs (degrees of freedom) are the parameters the optimizer can adjust. Objectives are what you want to optimize. Here we define two DOFs (x1 and x2) that can range from -5 to 5, and one objective (the Himmelblau function) that we want to minimize:

x1 = MovableSignal("x1", initial_value=0.1)
x2 = MovableSignal("x2", initial_value=0.23)

dofs = [
    RangeDOF(actuator=x1, bounds=(-5, 5), parameter_type="float"),
    RangeDOF(actuator=x2, bounds=(-5, 5), parameter_type="float"),
]
objectives = [
    Objective(name="himmelblau_2d", minimize=True),
]
sensors = []

Writing the evaluation function#

The evaluation function computes objective values from experimental data. After each run, Blop calls this function with the run’s unique ID and the suggestions that were tried. It returns the computed objective values:

class Himmelblau2DEvaluation():
    def __init__(self, tiled_client: Container):
        self.tiled_client = tiled_client

    def __call__(self, uid: str, suggestions: list[dict]) -> list[dict]:
        run = self.tiled_client[uid]
        outcomes = []
        reordered_suggestions = run.start["blop_suggestions"]
        x1_data = run["primary/x1"].read()
        x2_data = run["primary/x2"].read()

        print("[Himmelblau] evaluating suggestions: ", [s["_id"] for s in suggestions], " reordered to: ", [s["_id"] for s in reordered_suggestions])
        for index, suggestion in enumerate(reordered_suggestions):
            # Special key to identify a suggestion
            suggestion_id = suggestion["_id"]
            x1 = x1_data[index]
            x2 = x2_data[index]
            # Himmelblau function: has four global minima where value = 0
            outcomes.append({
                "himmelblau_2d": (x1 ** 2 + x2 - 11) ** 2 + (x1 + x2 ** 2 - 7) ** 2,
                "_id": suggestion_id
            })
        
        return outcomes

Running the optimization#

The Agent brings everything together. Create one with your DOFs, objectives, and evaluation function, then run the optimization:

agent = Agent(
    sensors=sensors,
    dofs=dofs,
    objectives=objectives,
    evaluation_function=Himmelblau2DEvaluation(tiled_client=tiled_client),
    name="simple-experiment",
    description="A simple experiment optimizing the Himmelblau function",
)

RE(agent.optimize(5,n_points=8))



╭───────────────────────────────────────────────── Optimization ──────────────────────────────────────────────────╮
│ Optimizer  AxOptimizer                                                                                          │
│ Actuators  x1, x2                                                                                               │
│ Sensors    N/A                                                                                                  │
│ Iterations 5  Points/iter 8                                                                                     │
│ Run UID    6f7f133f-f65e-4804-89ef-ae3b09d2124d                                                                 │
╰─────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯



[Himmelblau] evaluating suggestions:
[0, 1, 2, 3, 4, 5, 6, 7]
 reordered to:
[0, 5, 3, 7, 2, 6, 4, 1]
[Himmelblau] evaluating suggestions:
[8, 9, 10, 11, 12, 13, 14, 15]
 reordered to:
[12, 9, 8, 11, 13, 10, 15, 14]
[Himmelblau] evaluating suggestions:
[16, 17, 18, 19, 20, 21, 22, 23]
 reordered to:
[23, 18, 16, 19, 22, 20, 21, 17]
[Himmelblau] evaluating suggestions:
[24, 25, 26, 27, 28, 29, 30, 31]
 reordered to:
[30, 31, 29, 28, 24, 27, 25, 26]
[Himmelblau] evaluating suggestions:
[32, 33, 34, 35, 36, 37, 38, 39]
 reordered to:
[34, 32, 36, 38, 39, 37, 35, 33]





[INFO 07-28 17:28:14] ax.api.client: GenerationStrategy(name='Center+Sobol+MBM:fast', nodes=[CenterGenerationNode(next_node_name='Sobol', use_existing_trials_for_initialization=True), GenerationNode(name='Sobol', generator_specs=[GeneratorSpec(generator_enum=Sobol, generator_key_override=None)], transition_criteria=[MinTrials(transition_to='MBM'), MinTrials(transition_to='MBM')], suggested_experiment_status=ExperimentStatus.INITIALIZATION, pausing_criteria=[MaxTrialsAwaitingData(threshold=5)]), GenerationNode(name='MBM', generator_specs=[GeneratorSpec(generator_enum=BoTorch, generator_key_override=None)], transition_criteria=None, suggested_experiment_status=ExperimentStatus.OPTIMIZATION, pausing_criteria=None)]) chosen based on user input and problem structure.
[INFO 07-28 17:28:14] ax.api.client: Generated new trial 0 with parameters {'x1': 0.0, 'x2': 0.0} using GenerationNode CenterOfSearchSpace.
[INFO 07-28 17:28:14] ax.api.client: Generated new trial 1 with parameters {'x1': -3.489242, 'x2': 0.309227} using GenerationNode Sobol.
[INFO 07-28 17:28:14] ax.api.client: Generated new trial 2 with parameters {'x1': 3.669652, 'x2': -0.584508} using GenerationNode Sobol.
[INFO 07-28 17:28:14] ax.api.client: Generated new trial 3 with parameters {'x1': 1.293341, 'x2': 4.18891} using GenerationNode Sobol.
[INFO 07-28 17:28:14] ax.api.client: Generated new trial 4 with parameters {'x1': -1.47438, 'x2': -3.833065} using GenerationNode Sobol.
[INFO 07-28 17:28:14] ax.api.client: Generated new trial 5 with parameters {'x1': -0.044495, 'x2': 3.274535} using GenerationNode Sobol.
[INFO 07-28 17:28:14] ax.api.client: Generated new trial 6 with parameters {'x1': 0.215139, 'x2': -3.547335} using GenerationNode Sobol.
[INFO 07-28 17:28:14] ax.api.client: Generated new trial 7 with parameters {'x1': 4.743123, 'x2': 2.461702} using GenerationNode Sobol.
[INFO 07-28 17:28:15] ax.api.client: Trial 0 marked COMPLETED.
[INFO 07-28 17:28:15] ax.api.client: Trial 5 marked COMPLETED.
[INFO 07-28 17:28:15] ax.api.client: Trial 3 marked COMPLETED.
[INFO 07-28 17:28:15] ax.api.client: Trial 7 marked COMPLETED.
[INFO 07-28 17:28:15] ax.api.client: Trial 2 marked COMPLETED.
[INFO 07-28 17:28:15] ax.api.client: Trial 6 marked COMPLETED.
[INFO 07-28 17:28:15] ax.api.client: Trial 4 marked COMPLETED.
[INFO 07-28 17:28:15] ax.api.client: Trial 1 marked COMPLETED.
[INFO 07-28 17:28:20] ax.api.client: Generated new trial 8 with parameters {'x1': 4.566686, 'x2': -0.892104} using GenerationNode MBM.
[INFO 07-28 17:28:20] ax.api.client: Generated new trial 9 with parameters {'x1': 3.708838, 'x2': -0.007655} using GenerationNode MBM.
[INFO 07-28 17:28:20] ax.api.client: Generated new trial 10 with parameters {'x1': 3.041952, 'x2': -1.050081} using GenerationNode MBM.
[INFO 07-28 17:28:20] ax.api.client: Generated new trial 11 with parameters {'x1': 4.916381, 'x2': -0.243857} using GenerationNode MBM.
[INFO 07-28 17:28:20] ax.api.client: Generated new trial 12 with parameters {'x1': 2.852204, 'x2': -0.368686} using GenerationNode MBM.
[INFO 07-28 17:28:20] ax.api.client: Generated new trial 13 with parameters {'x1': 3.98451, 'x2': -1.397775} using GenerationNode MBM.
[INFO 07-28 17:28:20] ax.api.client: Generated new trial 14 with parameters {'x1': -1.826909, 'x2': 2.576162} using GenerationNode MBM.
[INFO 07-28 17:28:20] ax.api.client: Generated new trial 15 with parameters {'x1': -2.003859, 'x2': 3.890549} using GenerationNode MBM.
[INFO 07-28 17:28:20] ax.api.client: Trial 12 marked COMPLETED.
[INFO 07-28 17:28:20] ax.api.client: Trial 9 marked COMPLETED.
[INFO 07-28 17:28:20] ax.api.client: Trial 8 marked COMPLETED.
[INFO 07-28 17:28:20] ax.api.client: Trial 11 marked COMPLETED.
[INFO 07-28 17:28:20] ax.api.client: Trial 13 marked COMPLETED.
[INFO 07-28 17:28:20] ax.api.client: Trial 10 marked COMPLETED.
[INFO 07-28 17:28:20] ax.api.client: Trial 15 marked COMPLETED.
[INFO 07-28 17:28:20] ax.api.client: Trial 14 marked COMPLETED.
[INFO 07-28 17:28:25] ax.api.client: Generated new trial 16 with parameters {'x1': 4.055819, 'x2': -4.109752} using GenerationNode MBM.
[INFO 07-28 17:28:25] ax.api.client: Generated new trial 17 with parameters {'x1': -1.042798, 'x2': 4.220131} using GenerationNode MBM.
[INFO 07-28 17:28:25] ax.api.client: Generated new trial 18 with parameters {'x1': 3.618731, 'x2': -1.755162} using GenerationNode MBM.
[INFO 07-28 17:28:25] ax.api.client: Generated new trial 19 with parameters {'x1': 4.490632, 'x2': -5.0} using GenerationNode MBM.
[INFO 07-28 17:28:25] ax.api.client: Generated new trial 20 with parameters {'x1': -5.0, 'x2': -5.0} using GenerationNode MBM.
[INFO 07-28 17:28:25] ax.api.client: Generated new trial 21 with parameters {'x1': -5.0, 'x2': 5.0} using GenerationNode MBM.
[INFO 07-28 17:28:25] ax.api.client: Generated new trial 22 with parameters {'x1': 3.504528, 'x2': -5.0} using GenerationNode MBM.
[INFO 07-28 17:28:25] ax.api.client: Generated new trial 23 with parameters {'x1': 3.162337, 'x2': 5.0} using GenerationNode MBM.
[INFO 07-28 17:28:25] ax.api.client: Trial 23 marked COMPLETED.
[INFO 07-28 17:28:25] ax.api.client: Trial 18 marked COMPLETED.
[INFO 07-28 17:28:25] ax.api.client: Trial 16 marked COMPLETED.
[INFO 07-28 17:28:25] ax.api.client: Trial 19 marked COMPLETED.
[INFO 07-28 17:28:25] ax.api.client: Trial 22 marked COMPLETED.
[INFO 07-28 17:28:25] ax.api.client: Trial 20 marked COMPLETED.
[INFO 07-28 17:28:25] ax.api.client: Trial 21 marked COMPLETED.
[INFO 07-28 17:28:25] ax.api.client: Trial 17 marked COMPLETED.
[INFO 07-28 17:28:29] ax.api.client: Generated new trial 24 with parameters {'x1': 4.126131, 'x2': -2.757846} using GenerationNode MBM.
[INFO 07-28 17:28:29] ax.api.client: Generated new trial 25 with parameters {'x1': 2.233637, 'x2': 1.8384} using GenerationNode MBM.
[INFO 07-28 17:28:29] ax.api.client: Generated new trial 26 with parameters {'x1': -3.225121, 'x2': 2.752523} using GenerationNode MBM.
[INFO 07-28 17:28:29] ax.api.client: Generated new trial 27 with parameters {'x1': 3.219664, 'x2': -2.91254} using GenerationNode MBM.
[INFO 07-28 17:28:29] ax.api.client: Generated new trial 28 with parameters {'x1': 5.0, 'x2': -2.828056} using GenerationNode MBM.
[INFO 07-28 17:28:29] ax.api.client: Generated new trial 29 with parameters {'x1': -2.613063, 'x2': -1.452091} using GenerationNode MBM.
[INFO 07-28 17:28:29] ax.api.client: Generated new trial 30 with parameters {'x1': -5.0, 'x2': -1.218155} using GenerationNode MBM.
[INFO 07-28 17:28:29] ax.api.client: Generated new trial 31 with parameters {'x1': -3.721742, 'x2': -2.691551} using GenerationNode MBM.
[INFO 07-28 17:28:30] ax.api.client: Trial 30 marked COMPLETED.
[INFO 07-28 17:28:30] ax.api.client: Trial 31 marked COMPLETED.
[INFO 07-28 17:28:30] ax.api.client: Trial 29 marked COMPLETED.
[INFO 07-28 17:28:30] ax.api.client: Trial 28 marked COMPLETED.
[INFO 07-28 17:28:30] ax.api.client: Trial 24 marked COMPLETED.
[INFO 07-28 17:28:30] ax.api.client: Trial 27 marked COMPLETED.
[INFO 07-28 17:28:30] ax.api.client: Trial 25 marked COMPLETED.
[INFO 07-28 17:28:30] ax.api.client: Trial 26 marked COMPLETED.
[INFO 07-28 17:28:35] ax.api.client: Generated new trial 32 with parameters {'x1': 3.01036, 'x2': 1.104547} using GenerationNode MBM.
[INFO 07-28 17:28:35] ax.api.client: Generated new trial 33 with parameters {'x1': -2.535544, 'x2': 3.042677} using GenerationNode MBM.
[INFO 07-28 17:28:35] ax.api.client: Generated new trial 34 with parameters {'x1': 0.961734, 'x2': 1.984885} using GenerationNode MBM.
[INFO 07-28 17:28:35] ax.api.client: Generated new trial 35 with parameters {'x1': -3.073538, 'x2': 1.824058} using GenerationNode MBM.
[INFO 07-28 17:28:35] ax.api.client: Generated new trial 36 with parameters {'x1': -2.981361, 'x2': -2.82705} using GenerationNode MBM.
[INFO 07-28 17:28:35] ax.api.client: Generated new trial 37 with parameters {'x1': -4.973582, 'x2': 1.672803} using GenerationNode MBM.
[INFO 07-28 17:28:35] ax.api.client: Generated new trial 38 with parameters {'x1': -3.720657, 'x2': -3.476443} using GenerationNode MBM.
[INFO 07-28 17:28:35] ax.api.client: Generated new trial 39 with parameters {'x1': -5.0, 'x2': -3.194673} using GenerationNode MBM.
[INFO 07-28 17:28:36] ax.api.client: Trial 34 marked COMPLETED.
[INFO 07-28 17:28:36] ax.api.client: Trial 32 marked COMPLETED.
[INFO 07-28 17:28:36] ax.api.client: Trial 36 marked COMPLETED.
[INFO 07-28 17:28:36] ax.api.client: Trial 38 marked COMPLETED.
[INFO 07-28 17:28:36] ax.api.client: Trial 39 marked COMPLETED.
[INFO 07-28 17:28:36] ax.api.client: Trial 37 marked COMPLETED.
[INFO 07-28 17:28:36] ax.api.client: Trial 35 marked COMPLETED.
[INFO 07-28 17:28:36] ax.api.client: Trial 33 marked COMPLETED.





─────────────────────────────────────────── Iteration 1 / 5  (8 points) ───────────────────────────────────────────



  Acquire UID  65ea1e50-9e3a-4ef4-a7e7-563273dcaab1



┏━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
┃ Event ┃ Suggestion ID ┃         x1 ┃        x2 ┃ himmelblau_2d ┃
┡━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
│     0 │             0 │          0 │         0 │           170 │
│     1 │             1 │   -3.48924 │  0.309227 │        110.23 │
│     2 │             2 │    3.66965 │ -0.584508 │       12.4736 │
│     3 │             3 │    1.29334 │   4.18891 │       166.596 │
│     4 │             4 │   -1.47438 │  -3.83306 │       198.921 │
│     5 │             5 │ -0.0444949 │   3.27453 │       73.1805 │
│     6 │             6 │   0.215139 │  -3.54734 │       243.906 │
│     7 │             7 │    4.74312 │    2.4617 │       209.315 │
└───────┴───────────────┴────────────┴───────────┴───────────────┘



  himmelblau_2d  min: 12.4736  max: 243.906  mean: 148.078
  (8 pts sampled)



─────────────────────────────────────────── Iteration 2 / 5  (8 points) ───────────────────────────────────────────



  Acquire UID  22bbbcf6-fb2e-4919-9e19-13545089ec48



┏━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
┃ Event ┃ Suggestion ID ┃       x1 ┃          x2 ┃ himmelblau_2d ┃
┡━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
│     0 │            10 │  3.04195 │    -1.05008 │       15.9742 │
│     1 │            11 │  4.91638 │   -0.243857 │       171.203 │
│     2 │            12 │   2.8522 │   -0.368686 │       26.5514 │
│     3 │            13 │  3.98451 │    -1.39778 │       13.2275 │
│     4 │            14 │ -1.82691 │     2.57616 │       30.6672 │
│     5 │            15 │ -2.00386 │     3.89055 │       47.1805 │
│     6 │             8 │  4.56669 │   -0.892104 │        83.008 │
│     7 │             9 │  3.70884 │ -0.00765519 │       18.3819 │
└───────┴───────────────┴──────────┴─────────────┴───────────────┘



  himmelblau_2d  min: 12.4736  max: 243.906  mean: 99.4259
  (16 pts sampled)



─────────────────────────────────────────── Iteration 3 / 5  (8 points) ───────────────────────────────────────────



  Acquire UID  7f71fdcc-7cb3-4e39-8897-c038978dc620



┏━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
┃ Event ┃ Suggestion ID ┃      x1 ┃       x2 ┃ himmelblau_2d ┃
┡━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
│     0 │            16 │ 4.05582 │ -4.10975 │       196.283 │
│     1 │            17 │ -1.0428 │  4.22013 │       127.793 │
│     2 │            18 │ 3.61873 │ -1.75516 │      0.206041 │
│     3 │            19 │ 4.49063 │       -5 │       523.182 │
│     4 │            20 │      -5 │       -5 │           250 │
│     5 │            21 │      -5 │        5 │           530 │
│     6 │            22 │ 3.50453 │       -5 │        476.27 │
│     7 │            23 │ 3.16234 │        5 │       463.847 │
└───────┴───────────────┴─────────┴──────────┴───────────────┘



  himmelblau_2d  min: 0.206041  max: 530  mean: 173.267
  (24 pts sampled)



─────────────────────────────────────────── Iteration 4 / 5  (8 points) ───────────────────────────────────────────



  Acquire UID  81088b98-cce6-471c-8c56-22893e1af9a4



┏━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
┃ Event ┃ Suggestion ID ┃       x1 ┃       x2 ┃ himmelblau_2d ┃
┡━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
│     0 │            24 │  4.12613 │ -2.75785 │       33.0643 │
│     1 │            25 │  2.23364 │   1.8384 │       19.3323 │
│     2 │            26 │ -3.22512 │  2.75252 │       11.6552 │
│     3 │            27 │  3.21966 │ -2.91254 │       34.6903 │
│     4 │            28 │        5 │ -2.82806 │       160.787 │
│     5 │            29 │ -2.61306 │ -1.45209 │       87.9467 │
│     6 │            30 │       -5 │ -1.21815 │       273.964 │
│     7 │            31 │ -3.72174 │ -2.69155 │       12.1171 │
└───────┴───────────────┴──────────┴──────────┴───────────────┘



  himmelblau_2d  min: 0.206041  max: 530  mean: 149.749
  (32 pts sampled)



─────────────────────────────────────────── Iteration 5 / 5  (8 points) ───────────────────────────────────────────



  Acquire UID  db5e3fb3-1e19-414a-bb57-e13490b2c4fb



┏━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
┃ Event ┃ Suggestion ID ┃       x1 ┃       x2 ┃ himmelblau_2d ┃
┡━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
│     0 │            32 │  3.01036 │  1.10455 │       8.36497 │
│     1 │            33 │ -2.53554 │  3.04268 │       2.41291 │
│     2 │            34 │ 0.961734 │  1.98488 │       69.8547 │
│     3 │            35 │ -3.07354 │  1.82406 │       45.5865 │
│     4 │            36 │ -2.98136 │ -2.82705 │       28.3459 │
│     5 │            37 │ -4.97358 │   1.6728 │       321.634 │
│     6 │            38 │ -3.72066 │ -3.47644 │       2.26412 │
│     7 │            39 │       -5 │ -3.19467 │       119.974 │
└───────┴───────────────┴──────────┴──────────┴───────────────┘



  himmelblau_2d  min: 0.206041  max: 530  mean: 134.76
  (40 pts sampled)





                            Summary Statistics                            
┏━━━━━━━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━━┳━━━━━┳━━━━━━━━━━━┳━━━━━━━━━┳━━━━━━━┓
┃ Name          ┃ Type    ┃      Min ┃ Max ┃      Mean ┃     Std ┃ Count ┃
┡━━━━━━━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━━╇━━━━━╇━━━━━━━━━━━╇━━━━━━━━━╇━━━━━━━┩
│ x1            │ param   │       -5 │   5 │  0.341228 │ 3.51425 │    40 │
│ x2            │ param   │       -5 │   5 │ -0.275182 │ 2.97132 │    40 │
│ himmelblau_2d │ outcome │ 0.206041 │ 530 │    134.76 │ 150.458 │    40 │
└───────────────┴─────────┴──────────┴─────┴───────────┴─────────┴───────┘



────────────────────────────────────────────── Optimization Complete ──────────────────────────────────────────────





('6f7f133f-f65e-4804-89ef-ae3b09d2124d',
 '65ea1e50-9e3a-4ef4-a7e7-563273dcaab1',
 '22bbbcf6-fb2e-4919-9e19-13545089ec48',
 '7f71fdcc-7cb3-4e39-8897-c038978dc620',
 '81088b98-cce6-471c-8c56-22893e1af9a4',
 'db5e3fb3-1e19-414a-bb57-e13490b2c4fb')













Viewing the results#


After optimization, visualize what the Agent learned and see the best parameters found:






agent.plot_objective("x1", "x2", "himmelblau_2d")
agent.ax_client.summarize()













    

        himmelblau_2d (Mean) vs. x1, x2
        
The contour plot visualizes the predicted outcomes for himmelblau_2d across a two-dimensional parameter space, with other parameters held fixed at their best trial value (Arm 18_0). This plot helps in identifying regions of optimal performance and understanding how changes in the selected parameters influence the predicted outcomes. Contour lines represent levels of constant predicted values, providing insights into the gradient and potential optima within the parameter space.

        
    

    

        




    
                            
                    




    









  
    

      
      trial_index
      arm_name
      trial_status
      generation_node
      himmelblau_2d
      x1
      x2
    

  
  
    

      0
      0
      0_0
      COMPLETED
      CenterOfSearchSpace
      170.000000
      0.000000
      0.000000
    

    

      1
      1
      1_0
      COMPLETED
      Sobol
      110.229710
      -3.489242
      0.309227
    

    

      2
      2
      2_0
      COMPLETED
      Sobol
      12.473618
      3.669652
      -0.584508
    

    

      3
      3
      3_0
      COMPLETED
      Sobol
      166.595583
      1.293341
      4.188910
    

    

      4
      4
      4_0
      COMPLETED
      Sobol
      198.920619
      -1.474380
      -3.833065
    

    

      5
      5
      5_0
      COMPLETED
      Sobol
      73.180529
      -0.044495
      3.274535
    

    

      6
      6
      6_0
      COMPLETED
      Sobol
      243.905708
      0.215139
      -3.547335
    

    

      7
      7
      7_0
      COMPLETED
      Sobol
      209.315068
      4.743123
      2.461702
    

    

      8
      8
      8_0
      COMPLETED
      MBM
      83.008012
      4.566686
      -0.892104
    

    

      9
      9
      9_0
      COMPLETED
      MBM
      18.381911
      3.708838
      -0.007655
    

    

      10
      10
      10_0
      COMPLETED
      MBM
      15.974199
      3.041952
      -1.050081
    

    

      11
      11
      11_0
      COMPLETED
      MBM
      171.203073
      4.916381
      -0.243857
    

    

      12
      12
      12_0
      COMPLETED
      MBM
      26.551372
      2.852204
      -0.368686
    

    

      13
      13
      13_0
      COMPLETED
      MBM
      13.227494
      3.984510
      -1.397775
    

    

      14
      14
      14_0
      COMPLETED
      MBM
      30.667243
      -1.826909
      2.576162
    

    

      15
      15
      15_0
      COMPLETED
      MBM
      47.180506
      -2.003859
      3.890549
    

    

      16
      16
      16_0
      COMPLETED
      MBM
      196.283012
      4.055819
      -4.109752
    

    

      17
      17
      17_0
      COMPLETED
      MBM
      127.792519
      -1.042798
      4.220131
    

    

      18
      18
      18_0
      COMPLETED
      MBM
      0.206041
      3.618731
      -1.755162
    

    

      19
      19
      19_0
      COMPLETED
      MBM
      523.182209
      4.490632
      -5.000000
    

    

      20
      20
      20_0
      COMPLETED
      MBM
      250.000000
      -5.000000
      -5.000000
    

    

      21
      21
      21_0
      COMPLETED
      MBM
      530.000000
      -5.000000
      5.000000
    

    

      22
      22
      22_0
      COMPLETED
      MBM
      476.270357
      3.504528
      -5.000000
    

    

      23
      23
      23_0
      COMPLETED
      MBM
      463.847493
      3.162337
      5.000000
    

    

      24
      24
      24_0
      COMPLETED
      MBM
      33.064328
      4.126131
      -2.757846
    

    

      25
      25
      25_0
      COMPLETED
      MBM
      19.332266
      2.233637
      1.838400
    

    

      26
      26
      26_0
      COMPLETED
      MBM
      11.655233
      -3.225121
      2.752523
    

    

      27
      27
      27_0
      COMPLETED
      MBM
      34.690300
      3.219664
      -2.912540
    

    

      28
      28
      28_0
      COMPLETED
      MBM
      160.787143
      5.000000
      -2.828056
    

    

      29
      29
      29_0
      COMPLETED
      MBM
      87.946730
      -2.613063
      -1.452091
    

    

      30
      30
      30_0
      COMPLETED
      MBM
      273.963916
      -5.000000
      -1.218155
    

    

      31
      31
      31_0
      COMPLETED
      MBM
      12.117114
      -3.721742
      -2.691551
    

    

      32
      32
      32_0
      COMPLETED
      MBM
      8.364971
      3.010360
      1.104547
    

    

      33
      33
      33_0
      COMPLETED
      MBM
      2.412913
      -2.535544
      3.042677
    

    

      34
      34
      34_0
      COMPLETED
      MBM
      69.854746
      0.961734
      1.984885
    

    

      35
      35
      35_0
      COMPLETED
      MBM
      45.586512
      -3.073538
      1.824058
    

    

      36
      36
      36_0
      COMPLETED
      MBM
      28.345886
      -2.981361
      -2.827050
    

    

      37
      37
      37_0
      COMPLETED
      MBM
      321.633514
      -4.973582
      1.672803
    

    

      38
      38
      38_0
      COMPLETED
      MBM
      2.264117
      -3.720657
      -3.476443
    

    

      39
      39
      39_0
      COMPLETED
      MBM
      119.973746
      -5.000000
      -3.194673
    

  







The Himmelblau function has four global minima (all with value 0). The summarize output shows which one(s) the optimizer found.






What you learned#


You now understand the three core concepts of Blop:


    

  • DOFs: The parameters the optimizer adjusts (here, x1 and x2 with bounds)
    • 

  • Objectives: What you’re optimizing (here, minimizing the Himmelblau function)
    • 

  • Agent: Coordinates the optimization loop between Bluesky and the evaluation function
    • 







Next steps#


For a more comprehensive tutorial with multiple objectives and diagnostic tools, see Optimizing KB Mirrors.