Adam Optimization Algorithm
Calculus & Optimization DS practice problem on Onlearn.
Difficulty: medium.
Topics: Adam Optimization Algorithm, Exponential Moving Average, Bias Correction, Second Moment Estimation, Epsilon Smoothing, Non-Stationary Objective Functions, Mathematical Optimization, Numerical Analysis, Stochastic Processes, Deep Learning Theory, Computational Statistics, First-Order Optimization Methods, Adaptive Learning Rate Schedules, Momentum-Based Acceleration, Gradient Estimation Techniques, Hyperparameter Sensitivity Analysis.
Implement the Adam (Adaptive Moment Estimation) optimization algorithm in Python. Adam is an optimization algorithm that adapts the learning rate for each parameter. Your task is to write a function adam optimizer that updates the parameters of a given function using the Adam algorithm. The function should take the following parameters: f: The objective function to be optimized grad: A function that computes the gradient of f x0: Initial parameter values learning rate: The step size (default: 0.001) beta1: Exponential decay rate for the first moment estimates (default: 0.9) beta2: Exponential decay rate for the second moment estimates (default: 0.999) epsilon: A small constant for numerical stability (default: 1e 8) num iterations: Number of iterations to run the optimizer (default: 1000) The function should return the optimized parameters.