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)

/home/runner/work/blop/blop/.pixi/envs/docs/lib/python3.13/site-packages/torch/jit/_script.py:1491: FutureWarning: `torch.jit.script` is deprecated. Please switch to `torch.compile` or `torch.export`.
  warnings.warn(
[INFO 09-03 14:30:35] ax.storage.sqa_store.with_db_settings_base: Ax SQL storage initialized with SQLAlchemy 2.0.52

# 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)

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. Blop passes it the hashable identifier returned by the acquisition plan and the suggestions that were tried. This tutorial uses the default acquisition plan, so the identifier is a Bluesky run UID and blop_acquisition_order associates measurements with outcomes.

from collections.abc import Hashable, Mapping, Sequence

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

    def __call__(self, uid: Hashable, suggestions: Sequence[Mapping]) -> Sequence[Mapping]:
        if not isinstance(uid, str):
            raise TypeError(f"Himmelblau2DEvaluation requires a Bluesky run UID string, got {uid!r}")
        run = self.tiled_client[uid]
        outcomes = []
        acquisition_order = run.start["blop_acquisition_order"]
        x1_data = run["primary/x1"].read()
        x2_data = run["primary/x2"].read()

        print("[Himmelblau] evaluating acquired order: ", acquisition_order)
        for index, suggestion_id in enumerate(acquisition_order):
            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    695220f3-f87b-4b9b-915c-562c26dacf84                                                                 │
╰─────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯



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





[INFO 09-03 14:30:40] 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 09-03 14:30:40] ax.api.client: Generated new trial 0 with parameters {'x1': 0.0, 'x2': 0.0} using GenerationNode CenterOfSearchSpace.
[INFO 09-03 14:30:40] ax.api.client: Generated new trial 1 with parameters {'x1': 4.19982, 'x2': 3.038247} using GenerationNode Sobol.
[INFO 09-03 14:30:40] ax.api.client: Generated new trial 2 with parameters {'x1': -0.062134, 'x2': -0.574649} using GenerationNode Sobol.
[INFO 09-03 14:30:40] ax.api.client: Generated new trial 3 with parameters {'x1': -3.187397, 'x2': 1.819061} using GenerationNode Sobol.
[INFO 09-03 14:30:40] ax.api.client: Generated new trial 4 with parameters {'x1': 2.326078, 'x2': -4.292002} using GenerationNode Sobol.
[INFO 09-03 14:30:40] ax.api.client: Generated new trial 5 with parameters {'x1': 1.110098, 'x2': 0.602459} using GenerationNode Sobol.
[INFO 09-03 14:30:40] ax.api.client: Generated new trial 6 with parameters {'x1': -4.628888, 'x2': -2.973204} using GenerationNode Sobol.
[INFO 09-03 14:30:40] ax.api.client: Generated new trial 7 with parameters {'x1': -1.501503, 'x2': 4.22765} using GenerationNode Sobol.
[INFO 09-03 14:30:41] ax.api.client: Trial 0 marked COMPLETED.
[INFO 09-03 14:30:41] ax.api.client: Trial 2 marked COMPLETED.
[INFO 09-03 14:30:41] ax.api.client: Trial 5 marked COMPLETED.
[INFO 09-03 14:30:41] ax.api.client: Trial 1 marked COMPLETED.
[INFO 09-03 14:30:41] ax.api.client: Trial 7 marked COMPLETED.
[INFO 09-03 14:30:41] ax.api.client: Trial 3 marked COMPLETED.
[INFO 09-03 14:30:41] ax.api.client: Trial 6 marked COMPLETED.
[INFO 09-03 14:30:41] ax.api.client: Trial 4 marked COMPLETED.
[INFO 09-03 14:30:45] ax.api.client: Generated new trial 8 with parameters {'x1': -4.181839, 'x2': 0.174944} using GenerationNode MBM.
[INFO 09-03 14:30:45] ax.api.client: Generated new trial 9 with parameters {'x1': -3.618073, 'x2': 4.283337} using GenerationNode MBM.
[INFO 09-03 14:30:45] ax.api.client: Generated new trial 10 with parameters {'x1': -3.238268, 'x2': -1.347188} using GenerationNode MBM.
[INFO 09-03 14:30:45] ax.api.client: Generated new trial 11 with parameters {'x1': 1.727107, 'x2': 4.397523} using GenerationNode MBM.
[INFO 09-03 14:30:45] ax.api.client: Generated new trial 12 with parameters {'x1': -3.630069, 'x2': -5.0} using GenerationNode MBM.
[INFO 09-03 14:30:45] ax.api.client: Generated new trial 13 with parameters {'x1': -5.0, 'x2': 1.484998} using GenerationNode MBM.
[INFO 09-03 14:30:45] ax.api.client: Generated new trial 14 with parameters {'x1': -5.0, 'x2': -5.0} using GenerationNode MBM.
[INFO 09-03 14:30:45] ax.api.client: Generated new trial 15 with parameters {'x1': -5.0, 'x2': 5.0} using GenerationNode MBM.
[INFO 09-03 14:30:45] ax.api.client: Trial 12 marked COMPLETED.
[INFO 09-03 14:30:45] ax.api.client: Trial 14 marked COMPLETED.
[INFO 09-03 14:30:45] ax.api.client: Trial 10 marked COMPLETED.
[INFO 09-03 14:30:45] ax.api.client: Trial 8 marked COMPLETED.
[INFO 09-03 14:30:45] ax.api.client: Trial 13 marked COMPLETED.
[INFO 09-03 14:30:45] ax.api.client: Trial 9 marked COMPLETED.
[INFO 09-03 14:30:45] ax.api.client: Trial 15 marked COMPLETED.
[INFO 09-03 14:30:45] ax.api.client: Trial 11 marked COMPLETED.
[INFO 09-03 14:30:56] ax.api.client: Generated new trial 16 with parameters {'x1': -4.425598, 'x2': -4.970557} using GenerationNode MBM.
[INFO 09-03 14:30:56] ax.api.client: Generated new trial 17 with parameters {'x1': -2.89662, 'x2': -0.074709} using GenerationNode MBM.
[INFO 09-03 14:30:56] ax.api.client: Generated new trial 18 with parameters {'x1': -3.380211, 'x2': 1.453249} using GenerationNode MBM.
[INFO 09-03 14:30:56] ax.api.client: Generated new trial 19 with parameters {'x1': 0.677539, 'x2': 3.576455} using GenerationNode MBM.
[INFO 09-03 14:30:56] ax.api.client: Generated new trial 20 with parameters {'x1': -3.253807, 'x2': 5.0} using GenerationNode MBM.
[INFO 09-03 14:30:56] ax.api.client: Generated new trial 21 with parameters {'x1': 0.717192, 'x2': -3.390997} using GenerationNode MBM.
[INFO 09-03 14:30:56] ax.api.client: Generated new trial 22 with parameters {'x1': -1.497899, 'x2': -1.676488} using GenerationNode MBM.
[INFO 09-03 14:30:56] ax.api.client: Generated new trial 23 with parameters {'x1': -1.989265, 'x2': 5.0} using GenerationNode MBM.
[INFO 09-03 14:30:56] ax.api.client: Trial 19 marked COMPLETED.
[INFO 09-03 14:30:56] ax.api.client: Trial 23 marked COMPLETED.
[INFO 09-03 14:30:56] ax.api.client: Trial 20 marked COMPLETED.
[INFO 09-03 14:30:56] ax.api.client: Trial 18 marked COMPLETED.
[INFO 09-03 14:30:56] ax.api.client: Trial 17 marked COMPLETED.
[INFO 09-03 14:30:56] ax.api.client: Trial 22 marked COMPLETED.
[INFO 09-03 14:30:56] ax.api.client: Trial 21 marked COMPLETED.
[INFO 09-03 14:30:56] ax.api.client: Trial 16 marked COMPLETED.
[INFO 09-03 14:31:06] ax.api.client: Generated new trial 24 with parameters {'x1': -3.165345, 'x2': 0.562693} using GenerationNode MBM.
[INFO 09-03 14:31:06] ax.api.client: Generated new trial 25 with parameters {'x1': -4.562655, 'x2': -1.069194} using GenerationNode MBM.
[INFO 09-03 14:31:06] ax.api.client: Generated new trial 26 with parameters {'x1': 0.973625, 'x2': 4.130264} using GenerationNode MBM.
[INFO 09-03 14:31:06] ax.api.client: Generated new trial 27 with parameters {'x1': -3.910927, 'x2': 4.597795} using GenerationNode MBM.
[INFO 09-03 14:31:06] ax.api.client: Generated new trial 28 with parameters {'x1': -3.767511, 'x2': 1.8659} using GenerationNode MBM.
[INFO 09-03 14:31:06] ax.api.client: Generated new trial 29 with parameters {'x1': -1.238337, 'x2': 2.087124} using GenerationNode MBM.
[INFO 09-03 14:31:06] ax.api.client: Generated new trial 30 with parameters {'x1': 0.370831, 'x2': 4.566838} using GenerationNode MBM.
[INFO 09-03 14:31:06] ax.api.client: Generated new trial 31 with parameters {'x1': 0.515086, 'x2': 1.136697} using GenerationNode MBM.
[INFO 09-03 14:31:06] ax.api.client: Trial 25 marked COMPLETED.
[INFO 09-03 14:31:06] ax.api.client: Trial 24 marked COMPLETED.
[INFO 09-03 14:31:06] ax.api.client: Trial 28 marked COMPLETED.
[INFO 09-03 14:31:06] ax.api.client: Trial 29 marked COMPLETED.
[INFO 09-03 14:31:06] ax.api.client: Trial 31 marked COMPLETED.
[INFO 09-03 14:31:06] ax.api.client: Trial 26 marked COMPLETED.
[INFO 09-03 14:31:06] ax.api.client: Trial 30 marked COMPLETED.
[INFO 09-03 14:31:06] ax.api.client: Trial 27 marked COMPLETED.
[INFO 09-03 14:31:15] ax.api.client: Generated new trial 32 with parameters {'x1': -3.40132, 'x2': 3.045053} using GenerationNode MBM.
[INFO 09-03 14:31:15] ax.api.client: Generated new trial 33 with parameters {'x1': -2.007575, 'x2': 2.754078} using GenerationNode MBM.
[INFO 09-03 14:31:15] ax.api.client: Generated new trial 34 with parameters {'x1': 1.182725, 'x2': 2.484993} using GenerationNode MBM.
[INFO 09-03 14:31:15] ax.api.client: Generated new trial 35 with parameters {'x1': -0.859376, 'x2': 3.095207} using GenerationNode MBM.
[INFO 09-03 14:31:15] ax.api.client: Generated new trial 36 with parameters {'x1': -3.882716, 'x2': -2.829839} using GenerationNode MBM.
[INFO 09-03 14:31:15] ax.api.client: Generated new trial 37 with parameters {'x1': -3.130026, 'x2': 3.075887} using GenerationNode MBM.
[INFO 09-03 14:31:15] ax.api.client: Generated new trial 38 with parameters {'x1': -3.572554, 'x2': 3.079422} using GenerationNode MBM.
[INFO 09-03 14:31:15] ax.api.client: Generated new trial 39 with parameters {'x1': -0.37066, 'x2': 2.617325} using GenerationNode MBM.
[INFO 09-03 14:31:15] ax.api.client: Trial 38 marked COMPLETED.
[INFO 09-03 14:31:15] ax.api.client: Trial 32 marked COMPLETED.
[INFO 09-03 14:31:15] ax.api.client: Trial 37 marked COMPLETED.
[INFO 09-03 14:31:15] ax.api.client: Trial 33 marked COMPLETED.
[INFO 09-03 14:31:15] ax.api.client: Trial 35 marked COMPLETED.
[INFO 09-03 14:31:15] ax.api.client: Trial 39 marked COMPLETED.
[INFO 09-03 14:31:15] ax.api.client: Trial 34 marked COMPLETED.
[INFO 09-03 14:31:15] ax.api.client: Trial 36 marked COMPLETED.





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



  Acquire UID  29eec052-04c1-4520-882a-5f9d79ca62aa



┏━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
┃ Event ┃ Suggestion ID ┃        x1 ┃        x2 ┃ himmelblau_2d ┃
┡━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
│     0 │             0 │         0 │         0 │           170 │
│     1 │             1 │   4.19982 │   3.03825 │       134.994 │
│     2 │             2 │ -0.062134 │ -0.574649 │       179.202 │
│     3 │             3 │   -3.1874 │   1.81906 │       48.2702 │
│     4 │             4 │   2.32608 │    -4.292 │       286.631 │
│     5 │             5 │    1.1101 │  0.602459 │       114.548 │
│     6 │             6 │  -4.62889 │   -2.9732 │       63.3314 │
│     7 │             7 │   -1.5015 │   4.22765 │       108.236 │
└───────┴───────────────┴───────────┴───────────┴───────────────┘



  himmelblau_2d  min: 48.2702  max: 286.631  mean: 138.152
  (8 pts sampled)



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



  Acquire UID  3c2874a5-ec45-4f83-b09f-bab20fd3cb3b



┏━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
┃ Event ┃ Suggestion ID ┃       x1 ┃       x2 ┃ himmelblau_2d ┃
┡━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
│     0 │            10 │ -3.23827 │ -1.34719 │       74.4155 │
│     1 │            11 │  1.72711 │  4.39752 │       210.934 │
│     2 │            12 │ -3.63007 │       -5 │       214.462 │
│     3 │            13 │       -5 │    1.485 │       335.723 │
│     4 │            14 │       -5 │       -5 │           250 │
│     5 │            15 │       -5 │        5 │           530 │
│     6 │             8 │ -4.18184 │ 0.174944 │       168.742 │
│     7 │             9 │ -3.61807 │  4.28334 │       100.361 │
└───────┴───────────────┴──────────┴──────────┴───────────────┘



  himmelblau_2d  min: 48.2702  max: 530  mean: 186.866
  (16 pts sampled)



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



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┏━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
┃ Event ┃ Suggestion ID ┃       x1 ┃         x2 ┃ himmelblau_2d ┃
┡━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
│     0 │            16 │  -4.4256 │   -4.97056 │       189.451 │
│     1 │            17 │ -2.89662 │ -0.0747093 │       105.038 │
│     2 │            18 │ -3.38021 │    1.45325 │       71.8954 │
│     3 │            19 │ 0.677539 │    3.57646 │       90.3465 │
│     4 │            20 │ -3.25381 │          5 │       238.493 │
│     5 │            21 │ 0.717192 │     -3.391 │       219.768 │
│     6 │            22 │  -1.4979 │   -1.67649 │       141.188 │
│     7 │            23 │ -1.98926 │          5 │       260.517 │
└───────┴───────────────┴──────────┴────────────┴───────────────┘



  himmelblau_2d  min: 48.2702  max: 530  mean: 179.44
  (24 pts sampled)



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



  Acquire UID  1dcd32e3-bb60-42d3-81a2-ed69fff085d1



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┃ Event ┃ Suggestion ID ┃       x1 ┃       x2 ┃ himmelblau_2d ┃
┡━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
│     0 │            24 │ -3.16535 │ 0.562693 │        97.172 │
│     1 │            25 │ -4.56265 │ -1.06919 │       185.104 │
│     2 │            26 │ 0.973625 │  4.13026 │       156.788 │
│     3 │            27 │ -3.91093 │  4.59779 │       183.716 │
│     4 │            28 │ -3.76751 │   1.8659 │       78.6887 │
│     5 │            29 │ -1.23834 │  2.08712 │       69.5274 │
│     6 │            30 │ 0.370831 │  4.56684 │       242.038 │
│     7 │            31 │ 0.515086 │   1.1367 │       119.087 │
└───────┴───────────────┴──────────┴──────────┴───────────────┘



  himmelblau_2d  min: 48.2702  max: 530  mean: 169.958
  (32 pts sampled)



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



  Acquire UID  6193bf48-f2ce-4a84-ad15-880d0e90c190



┏━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
┃ Event ┃ Suggestion ID ┃        x1 ┃       x2 ┃ himmelblau_2d ┃
┡━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
│     0 │            32 │  -3.40132 │  3.04505 │       14.3358 │
│     1 │            33 │  -2.00757 │  2.75408 │       19.7949 │
│     2 │            34 │   1.18272 │  2.48499 │        50.768 │
│     3 │            35 │ -0.859376 │  3.09521 │        54.317 │
│     4 │            36 │  -3.88272 │ -2.82984 │       9.81571 │
│     5 │            37 │  -3.13003 │  3.07589 │       3.95542 │
│     6 │            38 │  -3.57255 │  3.07942 │       24.6379 │
│     7 │            39 │  -0.37066 │  2.61733 │       68.2554 │
└───────┴───────────────┴───────────┴──────────┴───────────────┘



  himmelblau_2d  min: 3.95542  max: 530  mean: 142.114
  (40 pts sampled)





                             Summary Statistics                             
┏━━━━━━━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━┳━━━━━━━┓
┃ Name          ┃ Type    ┃     Min ┃     Max ┃     Mean ┃     Std ┃ Count ┃
┡━━━━━━━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━╇━━━━━━━┩
│ x1            │ param   │      -5 │ 4.19982 │ -1.91401 │ 2.37345 │    40 │
│ x2            │ param   │      -5 │       5 │  1.14896 │ 3.04784 │    40 │
│ himmelblau_2d │ outcome │ 3.95542 │     530 │  142.114 │  104.51 │    40 │
└───────────────┴─────────┴─────────┴─────────┴──────────┴─────────┴───────┘



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





('695220f3-f87b-4b9b-915c-562c26dacf84',
 '29eec052-04c1-4520-882a-5f9d79ca62aa',
 '3c2874a5-ec45-4f83-b09f-bab20fd3cb3b',
 '15f3af1f-6a6e-454c-83cc-6721f773f11e',
 '1dcd32e3-bb60-42d3-81a2-ed69fff085d1',
 '6193bf48-f2ce-4a84-ad15-880d0e90c190')













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 3_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
      134.993930
      4.199820
      3.038247
    

    

      2
      2
      2_0
      COMPLETED
      Sobol
      179.201791
      -0.062134
      -0.574649
    

    

      3
      3
      3_0
      COMPLETED
      Sobol
      48.270153
      -3.187397
      1.819061
    

    

      4
      4
      4_0
      COMPLETED
      Sobol
      286.631191
      2.326078
      -4.292002
    

    

      5
      5
      5_0
      COMPLETED
      Sobol
      114.548428
      1.110098
      0.602459
    

    

      6
      6
      6_0
      COMPLETED
      Sobol
      63.331395
      -4.628888
      -2.973204
    

    

      7
      7
      7_0
      COMPLETED
      Sobol
      108.236283
      -1.501503
      4.227650
    

    

      8
      8
      8_0
      COMPLETED
      MBM
      168.741935
      -4.181839
      0.174944
    

    

      9
      9
      9_0
      COMPLETED
      MBM
      100.361186
      -3.618073
      4.283337
    

    

      10
      10
      10_0
      COMPLETED
      MBM
      74.415458
      -3.238268
      -1.347188
    

    

      11
      11
      11_0
      COMPLETED
      MBM
      210.934457
      1.727107
      4.397523
    

    

      12
      12
      12_0
      COMPLETED
      MBM
      214.461996
      -3.630069
      -5.000000
    

    

      13
      13
      13_0
      COMPLETED
      MBM
      335.722888
      -5.000000
      1.484998
    

    

      14
      14
      14_0
      COMPLETED
      MBM
      250.000000
      -5.000000
      -5.000000
    

    

      15
      15
      15_0
      COMPLETED
      MBM
      530.000000
      -5.000000
      5.000000
    

    

      16
      16
      16_0
      COMPLETED
      MBM
      189.451491
      -4.425598
      -4.970557
    

    

      17
      17
      17_0
      COMPLETED
      MBM
      105.038123
      -2.896620
      -0.074709
    

    

      18
      18
      18_0
      COMPLETED
      MBM
      71.895360
      -3.380211
      1.453249
    

    

      19
      19
      19_0
      COMPLETED
      MBM
      90.346464
      0.677539
      3.576455
    

    

      20
      20
      20_0
      COMPLETED
      MBM
      238.493157
      -3.253807
      5.000000
    

    

      21
      21
      21_0
      COMPLETED
      MBM
      219.768158
      0.717192
      -3.390997
    

    

      22
      22
      22_0
      COMPLETED
      MBM
      141.188293
      -1.497899
      -1.676488
    

    

      23
      23
      23_0
      COMPLETED
      MBM
      260.516785
      -1.989265
      5.000000
    

    

      24
      24
      24_0
      COMPLETED
      MBM
      97.171966
      -3.165345
      0.562693
    

    

      25
      25
      25_0
      COMPLETED
      MBM
      185.103993
      -4.562655
      -1.069194
    

    

      26
      26
      26_0
      COMPLETED
      MBM
      156.788150
      0.973625
      4.130264
    

    

      27
      27
      27_0
      COMPLETED
      MBM
      183.716137
      -3.910927
      4.597795
    

    

      28
      28
      28_0
      COMPLETED
      MBM
      78.688735
      -3.767511
      1.865900
    

    

      29
      29
      29_0
      COMPLETED
      MBM
      69.527386
      -1.238337
      2.087124
    

    

      30
      30
      30_0
      COMPLETED
      MBM
      242.038240
      0.370831
      4.566838
    

    

      31
      31
      31_0
      COMPLETED
      MBM
      119.086940
      0.515086
      1.136697
    

    

      32
      32
      32_0
      COMPLETED
      MBM
      14.335789
      -3.401320
      3.045053
    

    

      33
      33
      33_0
      COMPLETED
      MBM
      19.794878
      -2.007575
      2.754078
    

    

      34
      34
      34_0
      COMPLETED
      MBM
      50.767975
      1.182725
      2.484993
    

    

      35
      35
      35_0
      COMPLETED
      MBM
      54.316963
      -0.859376
      3.095207
    

    

      36
      36
      36_0
      COMPLETED
      MBM
      9.815705
      -3.882716
      -2.829839
    

    

      37
      37
      37_0
      COMPLETED
      MBM
      3.955424
      -3.130026
      3.075887
    

    

      38
      38
      38_0
      COMPLETED
      MBM
      24.637874
      -3.572554
      3.079422
    

    

      39
      39
      39_0
      COMPLETED
      MBM
      68.255421
      -0.370660
      2.617325
    

  







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.