Adam Optimizer deeply explained by Understanding Local Minimum – Day 40

Introduction to Optimization Concepts Understanding Local Minimum, Global Minimum, and Gradient Descent in Optimization In optimization problems, especially in machine learning and deep learning, concepts like local minima, global minima, and gradient descent are central to how algorithms find optimal solutions. Let’s break down these concepts: 1. Local Minimum vs. Global Minimum Local Minimum: This is a point in the optimization landscape where the function value is lower than the surrounding points, but it might not be the lowest possible value overall. It’s “locally” the best solution, but there might be a better solution elsewhere in the space. Global Minimum: This is the point where the function attains the lowest possible value across the entire optimization landscape. It’s the “best” solution globally. When using gradient-based methods like gradient descent, the goal is to minimize a loss (or cost) function. If the function has multiple minima, we want to find the global minimum, but sometimes the algorithm might get stuck in a local minimum. 2. Why Are Local Minima Considered “Bad”? Local minima are generally considered problematic because: They might not represent the best (i.e., lowest) solution. If a gradient-based optimization algorithm, like gradient descent, falls into a local minimum, it…