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This is a medium difficulty Machine Learning question, commonly asked during Technical Screen rounds at Uber.

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This question is commonly asked for Machine Learning Engineer candidates at Uber during technical interviews.

Implement 1D convex minimization in Python

Quick Overview

An Uber Machine Learning Engineer technical-screen question on derivative-free 1D convex optimization: minimize a black-box convex function on a closed interval using only function evaluations. It tests method selection (golden-section vs ternary search), stopping criteria and tolerances, function-evaluation and time/space complexity analysis, and robust handling of flat regions, boundary optima, noisy evaluations, and numerical precision.

Question

Implement, in Python, an algorithm that minimizes a 1D black-box convex function F(x) over a closed interval [a, b]. Assume F is convex (hence unimodal) on [a, b], gradients are unavailable, and you may use only function evaluations.

Your answer should address all of the following:

Method selection and justification. Choose an appropriate derivative-free method (e.g., golden-section search or ternary search) and justify the choice, especially with respect to the number of function evaluations each requires.
Stopping criteria and tolerances. Specify your stopping rules (absolute/relative tolerance on the bracket width, an optional function-value tolerance, and a maximum-iteration / evaluation-budget guardrail).
Complexity and function-evaluation count. Analyze time and space complexity and the number of function evaluations needed to reach a given tolerance.
Robustness to edge cases. Explain how you handle:
- non-strict convexity and flat regions,
- boundary optima (the minimum at a or b ),
- noisy function evaluations,
- numerical precision near machine epsilon, and invalid inputs.
Working code. Provide a complete, runnable implementation.
Testing and verification. Explain how you would test and verify correctness.

Quick Overview

Question

Your answer should address all of the following:

Method selection and justification. Choose an appropriate derivative-free method (e.g., golden-section search or ternary search) and justify the choice, especially with respect to the number of function evaluations each requires.
Stopping criteria and tolerances. Specify your stopping rules (absolute/relative tolerance on the bracket width, an optional function-value tolerance, and a maximum-iteration / evaluation-budget guardrail).
Complexity and function-evaluation count. Analyze time and space complexity and the number of function evaluations needed to reach a given tolerance.
Robustness to edge cases. Explain how you handle:
- non-strict convexity and flat regions,
- boundary optima (the minimum at a or b ),
- noisy function evaluations,
- numerical precision near machine epsilon, and invalid inputs.
Working code. Provide a complete, runnable implementation.
Testing and verification. Explain how you would test and verify correctness.

Implement 1D convex minimization in Python

Quick Overview

Question

Solution

Submit Your Answer

Implement 1D convex minimization in Python

Quick Overview

Question

Solution

Submit Your Answer