What is Ridge Regression and how does it behave geometrically?

Ridge regression adds L2 penalty that shrinks coefficients toward zero, forming circular constraint geometry.

Ridge regression modifies the OLS objective by adding λ||β||². Geometrically, it constrains the solution space inside a hypersphere. The optimal solution occurs where elliptical contours of the loss touch the constraint boundary. This reduces variance, stabilizes coefficients, and is especially useful under multicollinearity.