Pinterest·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

Interviewed for an ML engineer role at Pinterest, got a theory question about optimization fundamentals. Pretty standard technical screen vibe, nothing too wild.

Questions Asked (1)

What are the differences between convex and nonconvex functions?

Technical Trade-offsAlgorithms & Data Structures

Author's notes

I knew the basics but fumbled a bit explaining why it actually matters for training.

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AI HintsAI Generated

Suggested Approach

Start by defining convex and nonconvex functions mathematically, then contrast their key properties such as local vs global minima and optimization implications. Emphasize why convexity is desirable in machine learning and how nonconvexity presents challenges and opportunities.

Pro tip: Relate the concepts to practical ML scenarios, like why deep learning uses nonconvex optimization despite difficulties, and mention techniques like convex relaxations or stochastic gradient descent.

1. Define Convex Functions

State that a function is convex if the line segment between any two points on the graph lies above or on the graph, mathematically f(λx + (1-λ)y) ≤ λf(x) + (1-λ)f(y) for λ in [0,1].

2. Define Nonconvex Functions

Explain that nonconvex functions do not satisfy this inequality, meaning the line segment may lie below the graph, leading to multiple local minima and a more complex landscape.

3. Compare Optimization Properties

Highlight that convex functions have a single global minimum (no local minima), making optimization easier and guarantees global optimality, while nonconvex functions can have many local minima, saddle points, and flat regions.

4. Discuss Implications in Machine Learning

Explain that convex problems (e.g., linear regression, SVMs) can be solved efficiently with guaranteed convergence, while nonconvex problems (e.g., neural networks) require heuristics like SGD and may converge to local minima but often work well in practice.

5. Mention Practical Considerations

Note that convexity is a sufficient but not necessary condition for good performance; many nonconvex models achieve state-of-the-art results, and techniques like convex relaxations or initialization strategies can help.

Key Points to Mention

Mathematical definition: f(λx + (1-λ)y) ≤ λf(x) + (1-λ)f(y) for convexity.
Convex functions have no local minima other than the global minimum.
Nonconvex functions can have multiple local minima, saddle points, and plateaus.
Convex optimization guarantees global optimality and efficient algorithms (e.g., gradient descent with convergence guarantees).
Nonconvex optimization is NP-hard in general but often solved via stochastic gradient descent and other heuristics.
Examples: Convex - linear regression, logistic regression, SVMs; Nonconvex - neural networks, k-means, matrix factorization.

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