🇺🇸🇮🇱 Ph.D. EE | Author | Fractional CTO | LLM, Generative ai, radar signal processing and Machine vision researcher | expert witness | Unapologetically Jewish, American patriot, Zionist and Israeli 🇺🇸 🇮🇱
In optimization, Newton's method is renowned for its quadratic convergence, largely due to its optimal step size determined by the Hessian matrix. Unlike gradient descent, which simplifies the step size to a single coefficient, alpha, through line search, Newton's method utilizes the full Hessian matrix. This difference is crucial. In Newton's method, the step size is a matrix that captures the curvature of the objective function, enabling faster and more accurate convergence. However, when we use gradient descent, we collapse this matrix into a scalar coefficient, which degrades performance and slows down convergence. This degeneration from a matrix to a scalar is what costs us efficiency. While calculating the Hessian can be computationally intensive, leading to the use of quasi-Newton methods like BFGS, understanding the fundamental advantage of Newton's method in maintaining a matrix step size can guide better optimization practices. How do you approach the trade-off between computational feasibility and convergence speed in your optimization tasks? Let's discuss the strategies and experiences that have worked best for you. PS if the content brought you value please share with someone who can benefit from it. If not, please tell me how can I improve my content. #Optimization #NewtonMethod #MachineLearning #GradientDescent #DataScience #AI #Algorithm #Performance #Convergence #BFGS
