Mathematics for AI and Machine Learning

Foundations for modern AI and machine learning

SDE Continuous Optimization Limit

Chapter 19 Dynamics & diffusion

Chapter 19: Stochastic Differential Equations — SDEs as Limits of Optimization Algorithms

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SDE Continuous Optimization Limit — animated GIF preview
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SDE Continuous Optimization Limit — high-resolution mind-map icon

From the book

Chapter 19: Stochastic Differential Equations. In the chapter mind map this icon labels SDEs as Limits of Optim Algos. The discussion below is excerpted and lightly edited from § SDEs as Limits of Optimization Algorithms in Mathematics for AI and Machine Learning.

Itô calculus, SDEs, and continuous-time stochastic processes

What this drawing shows

What you see. Green discrete optimization steps fixed; purple continuous SDE path grows from the last iterate toward the continuous-time limit.

In the mind map. Chapter 19 — SDEs as Limits of Optim Algos. See From the book above for definitions, figures, and worked examples.

Where to read next

Open Chapter 19 companion →

Read the full definitions, figures, and worked examples in Chapter 19: Stochastic Differential Equations — see the mind-map node SDEs as Limits of Optim Algos.