Saddle Point
From the book
Chapter 12: Optimization Methods. In the chapter mind map this icon labels Minimax Optim: Saddle Points. The discussion below is excerpted and lightly edited from § Minimax Optimization in Mathematics for AI and Machine Learning.
where $\mathcal{V} : \Theta \times \Phi \to \mathbb{R}$ is the value function, and $\boldsymbol\theta$ and $\boldsymbol\phi$ are the optimization variables.
The minimizer (the player choosing $\boldsymbol\theta$) seeks to reduce $\mathcal{V}$, and the maximizer (the player choosing $\boldsymbol\phi$) seeks to increase it. One player's gain is the other's loss, so the setup is a zero-sum game.
What this drawing shows
What you see. Depicts a point that curves upward in one direction and downward in another, common in min-max optimization and nonconvex loss surfaces.
In the mind map. Chapter 12 — Minimax Optim: Saddle Points. See From the book above for definitions, figures, and worked examples.
Where to read next
Read the full definitions, figures, and worked examples in Chapter 12: Optimization Methods — see the mind-map node Minimax Optim: Saddle Points.
