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 06-08 19:44:53] ax.storage.sqa_store.with_db_settings_base: Ax SQL storage initialized with SQLAlchemy 2.0.50

# 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 0.2.11

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    8862e87e-8082-4ba0-971f-94c308ba9061                                                                 │
╰─────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯



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





[INFO 06-08 19:44:58] 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 06-08 19:44:58] ax.api.client: Generated new trial 0 with parameters {'x1': 0.0, 'x2': 0.0} using GenerationNode CenterOfSearchSpace.
[INFO 06-08 19:44:58] ax.api.client: Generated new trial 1 with parameters {'x1': -2.59155, 'x2': 0.987569} using GenerationNode Sobol.
[INFO 06-08 19:44:58] ax.api.client: Generated new trial 2 with parameters {'x1': 4.066084, 'x2': -4.750652} using GenerationNode Sobol.
[INFO 06-08 19:44:58] ax.api.client: Generated new trial 3 with parameters {'x1': 0.662847, 'x2': 4.515526} using GenerationNode Sobol.
[INFO 06-08 19:44:58] ax.api.client: Generated new trial 4 with parameters {'x1': -2.293787, 'x2': -0.753966} using GenerationNode Sobol.
[INFO 06-08 19:44:58] ax.api.client: Generated new trial 5 with parameters {'x1': -0.513648, 'x2': 3.665396} using GenerationNode Sobol.
[INFO 06-08 19:44:58] ax.api.client: Generated new trial 6 with parameters {'x1': 1.539112, 'x2': -2.382856} using GenerationNode Sobol.
[INFO 06-08 19:44:58] ax.api.client: Generated new trial 7 with parameters {'x1': 3.731964, 'x2': 2.149255} using GenerationNode Sobol.
[INFO 06-08 19:44:58] ax.api.client: Trial 0 marked COMPLETED.
[INFO 06-08 19:44:58] ax.api.client: Trial 4 marked COMPLETED.
[INFO 06-08 19:44:58] ax.api.client: Trial 1 marked COMPLETED.
[INFO 06-08 19:44:58] ax.api.client: Trial 5 marked COMPLETED.
[INFO 06-08 19:44:58] ax.api.client: Trial 3 marked COMPLETED.
[INFO 06-08 19:44:58] ax.api.client: Trial 7 marked COMPLETED.
[INFO 06-08 19:44:58] ax.api.client: Trial 6 marked COMPLETED.
[INFO 06-08 19:44:58] ax.api.client: Trial 2 marked COMPLETED.
[INFO 06-08 19:45:00] ax.api.client: Generated new trial 8 with parameters {'x1': 3.909665, 'x2': 4.152038} using GenerationNode MBM.
[INFO 06-08 19:45:00] ax.api.client: Generated new trial 9 with parameters {'x1': 2.983638, 'x2': 1.693101} using GenerationNode MBM.
[INFO 06-08 19:45:00] ax.api.client: Generated new trial 10 with parameters {'x1': -1.631729, 'x2': 3.696828} using GenerationNode MBM.
[INFO 06-08 19:45:00] ax.api.client: Generated new trial 11 with parameters {'x1': 4.570645, 'x2': 2.037308} using GenerationNode MBM.
[INFO 06-08 19:45:00] ax.api.client: Generated new trial 12 with parameters {'x1': 3.159051, 'x2': 4.14502} using GenerationNode MBM.
[INFO 06-08 19:45:00] ax.api.client: Generated new trial 13 with parameters {'x1': -3.938192, 'x2': 0.434307} using GenerationNode MBM.
[INFO 06-08 19:45:00] ax.api.client: Generated new trial 14 with parameters {'x1': -3.280883, 'x2': 5.0} using GenerationNode MBM.
[INFO 06-08 19:45:00] ax.api.client: Generated new trial 15 with parameters {'x1': -1.401927, 'x2': 1.78598} using GenerationNode MBM.
[INFO 06-08 19:45:01] ax.api.client: Trial 13 marked COMPLETED.
[INFO 06-08 19:45:01] ax.api.client: Trial 14 marked COMPLETED.
[INFO 06-08 19:45:01] ax.api.client: Trial 10 marked COMPLETED.
[INFO 06-08 19:45:01] ax.api.client: Trial 15 marked COMPLETED.
[INFO 06-08 19:45:01] ax.api.client: Trial 9 marked COMPLETED.
[INFO 06-08 19:45:01] ax.api.client: Trial 12 marked COMPLETED.
[INFO 06-08 19:45:01] ax.api.client: Trial 8 marked COMPLETED.
[INFO 06-08 19:45:01] ax.api.client: Trial 11 marked COMPLETED.
[INFO 06-08 19:45:03] ax.api.client: Generated new trial 16 with parameters {'x1': 3.428182, 'x2': 1.303535} using GenerationNode MBM.
[INFO 06-08 19:45:03] ax.api.client: Generated new trial 17 with parameters {'x1': 3.051406, 'x2': 2.171616} using GenerationNode MBM.
[INFO 06-08 19:45:03] ax.api.client: Generated new trial 18 with parameters {'x1': 3.497245, 'x2': 0.413395} using GenerationNode MBM.
[INFO 06-08 19:45:03] ax.api.client: Generated new trial 19 with parameters {'x1': 3.270899, 'x2': 1.779894} using GenerationNode MBM.
[INFO 06-08 19:45:03] ax.api.client: Generated new trial 20 with parameters {'x1': -0.133528, 'x2': -3.491789} using GenerationNode MBM.
[INFO 06-08 19:45:03] ax.api.client: Generated new trial 21 with parameters {'x1': 2.659967, 'x2': -0.382577} using GenerationNode MBM.
[INFO 06-08 19:45:03] ax.api.client: Generated new trial 22 with parameters {'x1': 2.422914, 'x2': 2.447399} using GenerationNode MBM.
[INFO 06-08 19:45:03] ax.api.client: Generated new trial 23 with parameters {'x1': 3.843924, 'x2': -0.732444} using GenerationNode MBM.
[INFO 06-08 19:45:03] ax.api.client: Trial 16 marked COMPLETED.
[INFO 06-08 19:45:03] ax.api.client: Trial 18 marked COMPLETED.
[INFO 06-08 19:45:03] ax.api.client: Trial 23 marked COMPLETED.
[INFO 06-08 19:45:03] ax.api.client: Trial 20 marked COMPLETED.
[INFO 06-08 19:45:03] ax.api.client: Trial 21 marked COMPLETED.
[INFO 06-08 19:45:03] ax.api.client: Trial 19 marked COMPLETED.
[INFO 06-08 19:45:03] ax.api.client: Trial 22 marked COMPLETED.
[INFO 06-08 19:45:03] ax.api.client: Trial 17 marked COMPLETED.
[INFO 06-08 19:45:05] ax.api.client: Generated new trial 24 with parameters {'x1': 3.188673, 'x2': -1.312887} using GenerationNode MBM.
[INFO 06-08 19:45:05] ax.api.client: Generated new trial 25 with parameters {'x1': -4.465638, 'x2': -3.559069} using GenerationNode MBM.
[INFO 06-08 19:45:05] ax.api.client: Generated new trial 26 with parameters {'x1': -5.0, 'x2': -5.0} using GenerationNode MBM.
[INFO 06-08 19:45:05] ax.api.client: Generated new trial 27 with parameters {'x1': -2.882559, 'x2': -5.0} using GenerationNode MBM.
[INFO 06-08 19:45:05] ax.api.client: Generated new trial 28 with parameters {'x1': 5.0, 'x2': -0.884748} using GenerationNode MBM.
[INFO 06-08 19:45:05] ax.api.client: Generated new trial 29 with parameters {'x1': -2.796722, 'x2': 2.648105} using GenerationNode MBM.
[INFO 06-08 19:45:05] ax.api.client: Generated new trial 30 with parameters {'x1': -5.0, 'x2': -2.195891} using GenerationNode MBM.
[INFO 06-08 19:45:05] ax.api.client: Generated new trial 31 with parameters {'x1': -3.596676, 'x2': -3.040158} using GenerationNode MBM.
[INFO 06-08 19:45:06] ax.api.client: Trial 29 marked COMPLETED.
[INFO 06-08 19:45:06] ax.api.client: Trial 30 marked COMPLETED.
[INFO 06-08 19:45:06] ax.api.client: Trial 25 marked COMPLETED.
[INFO 06-08 19:45:06] ax.api.client: Trial 27 marked COMPLETED.
[INFO 06-08 19:45:06] ax.api.client: Trial 26 marked COMPLETED.
[INFO 06-08 19:45:06] ax.api.client: Trial 31 marked COMPLETED.
[INFO 06-08 19:45:06] ax.api.client: Trial 24 marked COMPLETED.
[INFO 06-08 19:45:06] ax.api.client: Trial 28 marked COMPLETED.
[INFO 06-08 19:45:08] ax.api.client: Generated new trial 32 with parameters {'x1': -2.017624, 'x2': 2.787529} using GenerationNode MBM.
[INFO 06-08 19:45:08] ax.api.client: Generated new trial 33 with parameters {'x1': -4.135185, 'x2': 2.361989} using GenerationNode MBM.
[INFO 06-08 19:45:08] ax.api.client: Generated new trial 34 with parameters {'x1': -3.762604, 'x2': -3.346858} using GenerationNode MBM.
[INFO 06-08 19:45:08] ax.api.client: Generated new trial 35 with parameters {'x1': 3.327393, 'x2': -0.698863} using GenerationNode MBM.
[INFO 06-08 19:45:08] ax.api.client: Generated new trial 36 with parameters {'x1': -5.0, 'x2': 3.099192} using GenerationNode MBM.
[INFO 06-08 19:45:08] ax.api.client: Generated new trial 37 with parameters {'x1': -2.594224, 'x2': -2.652783} using GenerationNode MBM.
[INFO 06-08 19:45:08] ax.api.client: Generated new trial 38 with parameters {'x1': -3.588127, 'x2': 2.101332} using GenerationNode MBM.
[INFO 06-08 19:45:08] ax.api.client: Generated new trial 39 with parameters {'x1': 0.606864, 'x2': 2.221976} using GenerationNode MBM.
[INFO 06-08 19:45:08] ax.api.client: Trial 34 marked COMPLETED.
[INFO 06-08 19:45:08] ax.api.client: Trial 37 marked COMPLETED.
[INFO 06-08 19:45:08] ax.api.client: Trial 38 marked COMPLETED.
[INFO 06-08 19:45:08] ax.api.client: Trial 33 marked COMPLETED.
[INFO 06-08 19:45:08] ax.api.client: Trial 36 marked COMPLETED.
[INFO 06-08 19:45:08] ax.api.client: Trial 32 marked COMPLETED.
[INFO 06-08 19:45:08] ax.api.client: Trial 39 marked COMPLETED.
[INFO 06-08 19:45:08] ax.api.client: Trial 35 marked COMPLETED.





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



  Acquire UID  152281ac-0f7b-49f5-9668-2b22541eb584



┏━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
┃ Event ┃ Suggestion ID ┃        x1 ┃        x2 ┃ himmelblau_2d ┃
┡━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
│     0 │             0 │         0 │         0 │           170 │
│     1 │             1 │  -2.59155 │  0.987569 │       85.1055 │
│     2 │             2 │   4.06608 │  -4.75065 │       386.137 │
│     3 │             3 │  0.662847 │   4.51553 │       234.025 │
│     4 │             4 │  -2.29379 │ -0.753966 │       118.284 │
│     5 │             5 │ -0.513648 │    3.6654 │       85.0597 │
│     6 │             6 │   1.53911 │  -2.38286 │       121.355 │
│     7 │             7 │   3.73196 │   2.14925 │       27.5999 │
└───────┴───────────────┴───────────┴───────────┴───────────────┘



  himmelblau_2d  min: 27.5999  max: 386.137  mean: 153.446
  (8 pts sampled)



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



  Acquire UID  0b696f7f-86ef-40bb-b757-05d924354768



┏━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
┃ Event ┃ Suggestion ID ┃       x1 ┃       x2 ┃ himmelblau_2d ┃
┡━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
│     0 │            10 │ -1.63173 │  3.69683 │       46.8848 │
│     1 │            11 │  4.57064 │  2.03731 │       145.242 │
│     2 │            12 │  3.15905 │  4.14502 │       187.725 │
│     3 │            13 │ -3.93819 │ 0.434307 │       139.993 │
│     4 │            14 │ -3.28088 │        5 │        239.35 │
│     5 │            15 │ -1.40193 │  1.78598 │       79.7095 │
│     6 │             8 │  3.90967 │  4.15204 │       271.388 │
│     7 │             9 │  2.98364 │   1.6931 │       1.48584 │
└───────┴───────────────┴──────────┴──────────┴───────────────┘



  himmelblau_2d  min: 1.48584  max: 386.137  mean: 146.209
  (16 pts sampled)



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



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┏━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
┃ Event ┃ Suggestion ID ┃        x1 ┃        x2 ┃ himmelblau_2d ┃
┡━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
│     0 │            16 │   3.42818 │   1.30354 │       7.73367 │
│     1 │            17 │   3.05141 │   2.17162 │      0.821782 │
│     2 │            18 │   3.49725 │  0.413395 │       13.8044 │
│     3 │            19 │    3.2709 │   1.77989 │       2.50128 │
│     4 │            20 │ -0.133528 │  -3.49179 │        235.09 │
│     5 │            21 │   2.65997 │ -0.382577 │       36.1384 │
│     6 │            22 │   2.42291 │    2.4474 │       9.18924 │
│     7 │            23 │   3.84392 │ -0.732444 │        16.124 │
└───────┴───────────────┴───────────┴───────────┴───────────────┘



  himmelblau_2d  min: 0.821782  max: 386.137  mean: 110.864
  (24 pts sampled)



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



  Acquire UID  78184f36-1be3-4a4a-a90b-6c98ffdec0f2



┏━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
┃ Event ┃ Suggestion ID ┃       x1 ┃        x2 ┃ himmelblau_2d ┃
┡━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
│     0 │            24 │  3.18867 │  -1.31289 │       8.96041 │
│     1 │            25 │ -4.46564 │  -3.55907 │       30.4184 │
│     2 │            26 │       -5 │        -5 │           250 │
│     3 │            27 │ -2.88256 │        -5 │       287.686 │
│     4 │            28 │        5 │ -0.884748 │       173.491 │
│     5 │            29 │ -2.79672 │    2.6481 │       8.03328 │
│     6 │            30 │       -5 │  -2.19589 │       190.862 │
│     7 │            31 │ -3.59668 │  -3.04016 │       3.05263 │
└───────┴───────────────┴──────────┴───────────┴───────────────┘



  himmelblau_2d  min: 0.821782  max: 386.137  mean: 112.914
  (32 pts sampled)



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



  Acquire UID  567f3ca7-5976-4b30-8481-27de0b9a9083



┏━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
┃ Event ┃ Suggestion ID ┃       x1 ┃        x2 ┃ himmelblau_2d ┃
┡━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
│     0 │            32 │ -2.01762 │   2.78753 │       18.7091 │
│     1 │            33 │ -4.13519 │   2.36199 │       102.472 │
│     2 │            34 │  -3.7626 │  -3.34686 │      0.228565 │
│     3 │            35 │  3.32739 │ -0.698863 │       10.5326 │
│     4 │            36 │       -5 │   3.09919 │       298.118 │
│     5 │            37 │ -2.59422 │  -2.65278 │       54.4631 │
│     6 │            38 │ -3.58813 │   2.10133 │       53.9086 │
│     7 │            39 │ 0.606864 │   2.22198 │       72.8436 │
└───────┴───────────────┴──────────┴───────────┴───────────────┘



  himmelblau_2d  min: 0.228565  max: 386.137  mean: 105.613
  (40 pts sampled)





                              Summary Statistics                               
┏━━━━━━━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━━┳━━━━━━━┓
┃ Name          ┃ Type    ┃      Min ┃     Max ┃       Mean ┃     Std ┃ Count ┃
┡━━━━━━━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━━╇━━━━━━━┩
│ x1            │ param   │       -5 │       5 │ -0.0426033 │ 3.31538 │    40 │
│ x2            │ param   │       -5 │       5 │   0.435319 │ 2.81953 │    40 │
│ himmelblau_2d │ outcome │ 0.228565 │ 386.137 │    105.613 │ 104.642 │    40 │
└───────────────┴─────────┴──────────┴─────────┴────────────┴─────────┴───────┘



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





('8862e87e-8082-4ba0-971f-94c308ba9061',
 '152281ac-0f7b-49f5-9668-2b22541eb584',
 '0b696f7f-86ef-40bb-b757-05d924354768',
 '87ef7af4-f2ef-4d55-90b2-3bac0b1fb9ae',
 '78184f36-1be3-4a4a-a90b-6c98ffdec0f2',
 '567f3ca7-5976-4b30-8481-27de0b9a9083')













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 17_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
      85.105479
      -2.591550
      0.987569
    

    

      2
      2
      2_0
      COMPLETED
      Sobol
      386.136790
      4.066084
      -4.750652
    

    

      3
      3
      3_0
      COMPLETED
      Sobol
      234.025144
      0.662847
      4.515526
    

    

      4
      4
      4_0
      COMPLETED
      Sobol
      118.283910
      -2.293787
      -0.753966
    

    

      5
      5
      5_0
      COMPLETED
      Sobol
      85.059719
      -0.513648
      3.665396
    

    

      6
      6
      6_0
      COMPLETED
      Sobol
      121.355125
      1.539112
      -2.382856
    

    

      7
      7
      7_0
      COMPLETED
      Sobol
      27.599923
      3.731964
      2.149255
    

    

      8
      8
      8_0
      COMPLETED
      MBM
      271.388424
      3.909665
      4.152038
    

    

      9
      9
      9_0
      COMPLETED
      MBM
      1.485841
      2.983638
      1.693101
    

    

      10
      10
      10_0
      COMPLETED
      MBM
      46.884780
      -1.631729
      3.696828
    

    

      11
      11
      11_0
      COMPLETED
      MBM
      145.242348
      4.570645
      2.037308
    

    

      12
      12
      12_0
      COMPLETED
      MBM
      187.725337
      3.159051
      4.145020
    

    

      13
      13
      13_0
      COMPLETED
      MBM
      139.993077
      -3.938192
      0.434307
    

    

      14
      14
      14_0
      COMPLETED
      MBM
      239.349956
      -3.280883
      5.000000
    

    

      15
      15
      15_0
      COMPLETED
      MBM
      79.709549
      -1.401927
      1.785980
    

    

      16
      16
      16_0
      COMPLETED
      MBM
      7.733674
      3.428182
      1.303535
    

    

      17
      17
      17_0
      COMPLETED
      MBM
      0.821782
      3.051406
      2.171616
    

    

      18
      18
      18_0
      COMPLETED
      MBM
      13.804417
      3.497245
      0.413395
    

    

      19
      19
      19_0
      COMPLETED
      MBM
      2.501280
      3.270899
      1.779894
    

    

      20
      20
      20_0
      COMPLETED
      MBM
      235.089599
      -0.133528
      -3.491789
    

    

      21
      21
      21_0
      COMPLETED
      MBM
      36.138426
      2.659967
      -0.382577
    

    

      22
      22
      22_0
      COMPLETED
      MBM
      9.189243
      2.422914
      2.447399
    

    

      23
      23
      23_0
      COMPLETED
      MBM
      16.124045
      3.843924
      -0.732444
    

    

      24
      24
      24_0
      COMPLETED
      MBM
      8.960413
      3.188673
      -1.312887
    

    

      25
      25
      25_0
      COMPLETED
      MBM
      30.418356
      -4.465638
      -3.559069
    

    

      26
      26
      26_0
      COMPLETED
      MBM
      250.000000
      -5.000000
      -5.000000
    

    

      27
      27
      27_0
      COMPLETED
      MBM
      287.686306
      -2.882559
      -5.000000
    

    

      28
      28
      28_0
      COMPLETED
      MBM
      173.491474
      5.000000
      -0.884748
    

    

      29
      29
      29_0
      COMPLETED
      MBM
      8.033280
      -2.796722
      2.648105
    

    

      30
      30
      30_0
      COMPLETED
      MBM
      190.861566
      -5.000000
      -2.195891
    

    

      31
      31
      31_0
      COMPLETED
      MBM
      3.052627
      -3.596676
      -3.040158
    

    

      32
      32
      32_0
      COMPLETED
      MBM
      18.709142
      -2.017624
      2.787529
    

    

      33
      33
      33_0
      COMPLETED
      MBM
      102.472411
      -4.135185
      2.361989
    

    

      34
      34
      34_0
      COMPLETED
      MBM
      0.228565
      -3.762604
      -3.346858
    

    

      35
      35
      35_0
      COMPLETED
      MBM
      10.532638
      3.327393
      -0.698863
    

    

      36
      36
      36_0
      COMPLETED
      MBM
      298.118435
      -5.000000
      3.099192
    

    

      37
      37
      37_0
      COMPLETED
      MBM
      54.463053
      -2.594224
      -2.652783
    

    

      38
      38
      38_0
      COMPLETED
      MBM
      53.908603
      -3.588127
      2.101332
    

    

      39
      39
      39_0
      COMPLETED
      MBM
      72.843563
      0.606864
      2.221976
    

  







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.