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3 cards from this section. Quick, good the night before a test.
What is the primary goal of gradient-based methods?
Think about what 'optima' can mean in optimization.
Define what a learning rate (α) is in the context of optimization.
Consider how it affects how quickly you might reach the optimum.
What does the learning rate (α) do in the Gradient Descent method?
Think of it as the amount of progress you make in each update.
True or False: Stochastic Gradient Descent uses the entire dataset to compute gradients.
Reflect on how SGD is defined.
Consider a function f(x) = x^2 + 4x + 4. Use Gradient Descent with a learning rate of 0.1 to find the minimum starting from x = 0. Show your calculations through two iterations.
Calculate the gradient before each move and adjust accordingly.
Use Newton’s method to optimize the function f(x) = x^2 - 2x + 1. Confirm you find a minimum and demonstrate the Hessian's role.
Identify the critical points and compute second derivatives dynamically.
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