A/B testing model versions in MLOps - Time & Space Complexity

Time Complexity: A/B testing model versions

O(n)

Understanding Time Complexity

We want to understand how the time to run A/B testing grows as we increase the number of users or model versions.

How does the system handle more users or more models in terms of time?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

# Distribute users to model versions
for user in users:
    model_version = select_model_version(user)
    prediction = model_version.predict(user.data)
    log_result(user.id, model_version.id, prediction)

# Aggregate results
results = aggregate_logs()
    

This code assigns each user to a model version, gets a prediction, logs it, and then aggregates results.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Loop over all users to get predictions and log results.
• How many times: Once per user, so number of users (n) times.

How Execution Grows With Input

As the number of users grows, the time to process grows roughly the same amount.

Input Size (n)	Approx. Operations
10	10 predictions and logs
100	100 predictions and logs
1000	1000 predictions and logs

Pattern observation: Doubling users roughly doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time grows linearly with the number of users tested.

Common Mistake

[X] Wrong: "Adding more model versions multiplies the time by the number of versions squared."

[OK] Correct: Each user is assigned to only one model version, so time grows with users, not the square of versions.

Interview Connect

Understanding how time grows with users helps you design scalable testing systems and shows you can think about real-world system limits.

Self-Check

"What if we tested every user on every model version instead of just one? How would the time complexity change?"