8 · Hyperparameter Optimisation & Model Selection · Hyperparameter Optimisation

Successive Halving and Hyperband

Multi-fidelity methods begin with many candidates at a small resource budget and allocate more epochs/data to strong candidates, reducing wasted training. The important practical question is not only how the technique is defined, but what assumptions it introduces, which data are allowed to influence it, and how its effect should be validated on unseen evidence.

Reference lessonPython exampleVisual explanation

Intuition first

What this concept means in practice

The practical value of Successive Halving and Hyperband comes from understanding both the transformation and the boundary around it: what information is allowed to enter, what assumption is being made, and how you know the result is still valid after the transformation.

A beginner-friendly way to reason about it is to start with a tiny case where the correct result can be checked independently. Once the mechanism is clear, scale the exact same reasoning to larger tables, pipelines or models.

PurposeUse when partial training performance is predictive of final performance.

MechanismStart many configurations with a small resource budget, discard weak ones, and progressively allocate more epochs/data to survivors.

EvidenceInspect intermediate and final output; compare with an independent expectation.

Main cautionEarly rankings can be unreliable for slow-starting models; choose the fidelity/resource carefully.

Mechanism

Trace the operation from input to decision

Start many configurations with a small resource budget, discard weak ones, and progressively allocate more epochs/data to survivors.

1Input→

2Apply rule→

3Inspect state→

4Validate→

5Use result

Key rule

many cheap trials → few expensive trials

Visual explanation

Make the structure visible

The interactive view uses a concept-specific plot when the topic maps naturally to one; otherwise it uses a workflow view instead of leaving a broken placeholder.

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Practical example

Where you would use it

Train 81 configs for 1 epoch, retain 27 for 3 epochs, then 9 for 9 epochs, and so on.

Use when

Use when partial training performance is predictive of final performance.

Pitfall

What can make the result misleading

Watch out

Early rankings can be unreliable for slow-starting models; choose the fidelity/resource carefully.

A useful diagnostic question is: Could the same code still run successfully if the analytical assumption were wrong? If yes, add an explicit validation check rather than relying on execution success.

Implementation

Miniature Python example

Keep the example small enough that you can inspect each stage manually.

Python

# Purpose: demonstrate Successive Halving and Hyperband with a small, inspectable example.
# Follow the comments and printed stages to connect each operation with its result.
# Import the library or helper used in this example.
# Step 1 — Import only the named objects needed by the following steps, keeping dependencies explicit.
from sklearn.datasets import make_classification
# Import the library or helper used in this example.
# Step 2 — Import only the named objects needed by the following steps, keeping dependencies explicit.
from sklearn.linear_model import LogisticRegression
# Import the library or helper used in this example.
# Step 3 — Import only the named objects needed by the following steps, keeping dependencies explicit.
from sklearn.model_selection import GridSearchCV

# Store this intermediate value with a descriptive name for the next step.
# Step 4 — Compute the right-hand expression and store its result in `X,y` for the next step.
X,y = make_classification(n_samples=80,n_features=5,n_informative=3,random_state=7)
# Print this intermediate result so you can verify the workflow step by step.
# Step 5 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 1 · Data:", X.shape, "positive rate:", round(y.mean(),2))
# Store this intermediate value with a descriptive name for the next step.
# Step 6 — Instantiate `search` with the chosen algorithm/configuration before fitting it to data.
search = GridSearchCV(LogisticRegression(max_iter=500), {"C":[0.1,1,10]}, cv=4, scoring="accuracy")
# Fit only on the training data so the model learns from allowed information.
# Step 7 — Fit the model or transformer, learning its parameters from the supplied training data.
search.fit(X,y)
# Print this intermediate result so you can verify the workflow step by step.
# Step 8 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 2 · Tried C values:", search.param_grid["C"])
# Print this intermediate result so you can verify the workflow step by step.
# Step 9 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 3 · Best C:", search.best_params_["C"])
# Print this intermediate result so you can verify the workflow step by step.
# Step 10 — Display the current value explicitly so the result/state can be inspected during execution.
print("STEP 3 · Best CV accuracy:", round(search.best_score_,3))

Expected / illustrative output

STEP 1 · Data: (80, 5) positive rate: 0.5
STEP 2 · Tried C values: [0.1, 1, 10]
STEP 3 · Best C: 0.1
STEP 3 · Best CV accuracy: 0.925

Implementation checklist

Before you move on

Can you state what data or object enters the operation?
Can you explain what changes and what must remain invariant?
Have you checked the result on a tiny case you can verify independently?
Have you considered the main failure mode described above?
Can the operation be reproduced from code/formulas and documented assumptions?