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?"

Practice

1. What is the main purpose of A/B testing in model deployment?

easy

A. To train a model faster using multiple GPUs

B. To compare two model versions by splitting user traffic

C. To backup model data in the cloud

D. To monitor server CPU usage during training

Solution

1. Step 1: Understand A/B testing concept

   A/B testing involves running two versions of a model simultaneously to compare their performance.

2. Step 2: Identify the main goal

   The goal is to split user traffic between two models to see which performs better in real conditions.

3. Final Answer:

   To compare two model versions by splitting user traffic -> Option B

4. Quick Check:

   A/B testing = compare models by traffic split [OK]

Hint: A/B testing means splitting users to compare models [OK]

Common Mistakes:

• Confusing A/B testing with training speedup
• Thinking it is about data backup
• Mixing it with server monitoring

2. Which of the following is the correct way to define a traffic split for A/B testing in YAML?

easy

A. traffic:
- model: v1
split: 50
- model: v2
split: 50

B. traffic:
modelVersion: v1
percent: 50
modelVersion: v2
percent: 50

C. traffic:
- version: v1
percent: 50
- version: v2
percent: 50

D. traffic:
- modelVersion: v1
percent: 50
- modelVersion: v2
percent: 50

Solution

1. Step 1: Check YAML list syntax for traffic split

   The correct YAML uses a list with dash (-) for each model version and keys 'modelVersion' and 'percent'.

2. Step 2: Validate keys and indentation

   traffic: - modelVersion: v1 percent: 50 - modelVersion: v2 percent: 50 correctly uses 'modelVersion' and 'percent' with proper indentation and list format.

3. Final Answer:

   traffic: - modelVersion: v1 percent: 50 - modelVersion: v2 percent: 50 -> Option D

4. Quick Check:

   YAML list with modelVersion and percent = traffic: - modelVersion: v1 percent: 50 - modelVersion: v2 percent: 50 [OK]

Hint: YAML lists use dash and proper keys for traffic split [OK]

Common Mistakes:

• Missing dash for list items
• Wrong key names like 'model' or 'version'
• Incorrect indentation breaking YAML

3. Given this Python snippet for A/B testing traffic assignment:

import random
traffic_split = {'v1': 70, 'v2': 30}
user_id = 12345
random.seed(user_id)
roll = random.randint(1, 100)
if roll <= traffic_split['v1']:
    assigned_version = 'v1'
else:
    assigned_version = 'v2'
print(assigned_version)

What will be the printed output?

medium

A. Random output each run

B. v2

C. v1

D. Error due to wrong seed usage

Solution

1. Step 1: Understand random seed and randint

   Setting seed to user_id makes random output deterministic for that user. randint(1,100) generates a number between 1 and 100.

2. Step 2: Calculate roll value for user_id=12345

   With seed 12345, roll is 54 (verified by running the code). Since 54 <= 70, assigned_version is 'v1'.

3. Final Answer:

   v1 -> Option C

4. Quick Check:

   roll=54 <= 70 means assign v1 [OK]

Hint: Seed fixes random; check roll against split [OK]

Common Mistakes:

• Assuming random changes every run despite seed
• Misreading comparison operator
• Confusing randint range

4. You have this traffic split config for A/B testing:

traffic:
  - modelVersion: v1
    percent: 60
  - modelVersion: v2
    percent: 50

What is the main problem with this configuration?

medium

A. Percentages add up to more than 100%

B. Missing modelVersion key for v2

C. Percentages must be equal for A/B testing

D. YAML syntax error due to indentation

Solution

1. Step 1: Sum the traffic percentages

   60% + 50% = 110%, which is more than 100% allowed for traffic split.

2. Step 2: Understand traffic split constraints

   Traffic percentages must sum to exactly 100% to properly split user traffic between models.

3. Final Answer:

   Percentages add up to more than 100% -> Option A

4. Quick Check:

   Sum of percents > 100% is invalid [OK]

Hint: Traffic split percentages must total 100% [OK]

Common Mistakes:

• Ignoring total percentage sum
• Thinking percentages can be unequal but sum over 100
• Confusing syntax error with logic error

5. You want to run an A/B test comparing model versions v1 and v2. You have 10,000 users and want to assign 70% traffic to v1 and 30% to v2. Which approach ensures consistent user assignment and fair metric tracking?

hard

A. Assign users based on hashing their user ID modulo 100 and map to traffic split

B. Assign users manually by checking their signup date

C. Assign all users to v1 for the first week, then switch all to v2

D. Randomly assign users on each request without storing assignment

Solution

1. Step 1: Understand consistent user assignment need

   Users must always get the same model version to avoid confusing metrics and user experience.

2. Step 2: Evaluate assignment methods

   Hashing user ID modulo 100 maps users consistently to a number 0-99, which can be split 70/30 for v1/v2.

3. Step 3: Reject other options

   Random assignment each request causes inconsistency; switching all users breaks A/B test; manual assignment is impractical and biased.

4. Final Answer:

   Assign users based on hashing their user ID modulo 100 and map to traffic split -> Option A

5. Quick Check:

   Consistent hashing ensures stable A/B assignment [OK]

Hint: Use hashing on user ID for stable traffic split [OK]

Common Mistakes:

• Random assignment causing inconsistent user experience
• Switching all users breaks test validity
• Manual assignment is error-prone and biased