SC-1: A Hands-on Approach for Implementing Stochastic Optimization Algorithms from Scratch (Day 1)

Gradient descent (GD) is a well-known first order optimization method, which uses the gradient of the loss function, along with a step-size (or learning rate), to iteratively update the solution. When the loss (cost) function is dependent on datasets with large cardinality, such in cases typically associated with deep learning (DL), GD becomes impractical. In this scenario, stochastic GD (SGD), which uses a noisy gradient approximation (computed over a random fraction of the dataset), has become crucial. There exits several variants/improvements over the “vanilla” SGD, such RMSprop, Adagrad, Adadelta, Adam, Nadam, etc., which are usually given as black-boxes by most of DL’s libraries (TensorFlow, PyTorch, MXNet, etc.). The primary objective of this course is to combined the essential theoretical aspects related to SGD and variants, along with hands on experience to program in Python, from scratch (i.e. not based on DL’s libraries such as TensorFlow, PyTorch, MXNet) the SGD along with the RMSprop, Adagrad, Adadelta, Adam and Nadam algorithms and to test their performance using the MNIST and CIFAR-10 datasets for shallow networks (consisting of up to two ReLU layers and a Softmax as the last layer).