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First-order and Stochastic Optimization Methods for Machine Learning

Master the mathematical foundations of first-order and stochastic optimization to build faster, scalable, and high-performance machine learning models for large-scale data.

(OPTIMIZE-ML.AU1) / ISBN : 979-8-90059-015-8
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About This Course

You know the algorithms—linear regression, support vector machines, neural networks—but do you know what truly powers their performance and speed? It's optimization.

This is not just another machine learning course. This intensive program dives deep into the mathematical and algorithmic core of first-order optimization methods. As datasets explode in size, traditional batch methods fail. This course is designed to equip you with the specialized knowledge to thrive in the era of large-scale machine learning by mastering stochastic optimization methods.

If you are a machine learning researcher, data scientist, or engineer serious about developing faster, more scalable, and mathematically sound AI models, this is your next step.

Skills You’ll Get

  Upon completion of this course and its hands-on LAB activities, you will be able to:

  • Implement Advanced Model Generalization: Apply foundational models (LR, SVM, NNs) and master essential regularization techniques (Lasso and Ridge) to build models with superior out-of-sample performance.
  • Establish Algorithmic Foundations: Master the theory of Convex Optimization, including Convex Sets, Convex Functions, and Lagrangian and Legendre–Fenchel Duality, forming a basis for rigorous algorithm design.
  • Drive Faster Convergence: Analyze and implement core First-Order Optimization algorithms—from Subgradient Descent to sophisticated Accelerated Gradient Descent methods and the powerful Primal–Dual Method—and perform their quantitative Convergence Analysis.
  • Scale Optimization for Big Data: Design and deploy modern Stochastic Optimization Methods and Variance-Reduced algorithms to efficiently solve Nonconvex Optimization problems and manage large-scale and Distributed Optimization environments.
Download Course Outline

1

Regularization Techniques for Generalization

  • Linear Regression
  • Logistic Regression
  • Generalized Linear Models
  • Support Vector Machines
  • Regularization, Lasso, and Ridge Regression
  • Population Risk Minimization
  • Neural Networks
  • Exercises
2

Convergence Analysis of Optimization Algorithms

  • Convex Sets
  • Convex Functions
  • Lagrange Duality
  • Legendre–Fenchel Conjugate Duality
  • Exercises
3

Deterministic Convex Optimization

  • Subgradient Descent
  • Mirror Descent
  • Accelerated Gradient Descent
  • Game Interpretation for Accelerated Gradient Descent
  • Smoothing Scheme for Nonsmooth Problems
  • Primal–Dual Method for Saddle-Point Optimization
  • Alternating Direction Method of Multipliers
  • Mirror-Prox Method for Variational Inequalities
  • Accelerated Level Method
  • Exercises
4

Stochastic Convex Optimization

  • Stochastic Mirror Descent
  • Stochastic Accelerated Gradient Descent
  • Stochastic Convex–Concave Saddle Point Problems
  • Stochastic Accelerated Primal–Dual Method
  • Stochastic Accelerated Mirror-Prox Method
  • Stochastic Block Mirror Descent Method
  • Exercises
5

Convex Finite-Sum and Distributed Optimization

  • Random Primal–Dual Gradient Method
  • Random Gradient Extrapolation Method
  • Variance-Reduced Mirror Descent
  • Variance-Reduced Accelerated Gradient Descent
  • Exercises
6

Nonconvex Optimization

  • Unconstrained Nonconvex Stochastic Optimization
  • Nonconvex Stochastic Composite Optimization
  • Nonconvex Stochastic Block Mirror Descent
  • Nonconvex Stochastic Accelerated Gradient Descent
  • Nonconvex Variance-Reduced Mirror Descent
  • Randomized Accelerated Proximal-Point Methods
  • Exercises
7

Advanced Gradient-Based Optimization

  • Conditional Gradient Method
  • Conditional Gradient Sliding Method
  • Nonconvex Conditional Gradient Method
  • Stochastic Nonconvex Conditional Gradient
  • Stochastic Nonconvex Conditional Gradient Sliding
  • Exercises
8

Operator Sliding and Decentralized Optimization

  • Gradient Sliding for Composite Optimization
  • Accelerated Gradient Sliding
  • Communication Sliding and Decentralized Optimization
  • Exercises

1

Regularization Techniques for Generalization

  • Performing Linear Regression Using OLS
  • Performing Logistic Regression for Binary Classification
  • Performing Classification Using SVM
  • Training a Neural Network Using the Adam Optimizer
2

Convergence Analysis of Optimization Algorithms

  • Exploring and Visualizing Convex Sets Using Python
  • Analyzing and Visualizing Convex Functions with Python
  • Visualizing Legendre-Fenchel Conjugate Duality
3

Deterministic Convex Optimization

  • Comparing the Convergence of Optimizers on a Loss Landscape
4

Stochastic Convex Optimization

  • Applying SMD on a Convex Function
  • Implementing the SAGD Algorithm
  • Optimizing Stochastic Convex–Concave Saddle Points
5

Convex Finite-Sum and Distributed Optimization

  • Improving Model Performance with Regularization
  • Implementing the RPDG Method on Distributed Data
  • Simulating RGE for Multi-Worker Training
6

Nonconvex Optimization

  • Solving Convex and Non-Convex Optimization Problems
  • Implementing Nonconvex Stochastic Optimization
  • Comparing Nonconvex Mirror Descent and Accelerated Gradient Descent
7

Advanced Gradient-Based Optimization

  • Implementing Conditional Gradient Algorithm
  • Implementing the SCG Algorithm
  • Fine-Tuning a Pretrained Model with Advanced Optimizers
8

Operator Sliding and Decentralized Optimization

  • Simulating Communication-Efficient Distributed Optimization
  • Applying Gradient Sliding for Composite Convex Optimization

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This course is ideal for machine learning engineers, AI researchers, and Ph.D. students who have a solid background in calculus, linear algebra, and basic machine learning, and who want to gain a deep, theoretical, and practical understanding of modern Stochastic Optimization Methods.

Understanding the underlying Convergence Analysis and complexity of First-Order Optimization algorithms allows you to select the right algorithm for the right problem, correctly tune hyperparameters (like learning rates), and even invent novel algorithms, especially when dealing with complex Nonconvex Optimization landscapes in deep learning.

Yes, the foundational methods discussed (Stochastic Gradient Descent, Mirror Descent, Acceleration, and Regularization) provide the theoretical basis for all modern adaptive optimizers like Adam. You will be able to analyze and understand why they work and how to improve them.

Absolutely. Modules 5 and 8 are dedicated to scaling up. We cover finite-sum problems, Variance-Reduced techniques (crucial for faster training), and methods for Distributed Optimization to handle data that cannot fit on a single machine.

Ready to Elevate Your ML Expertise?

  Enroll Today! Master the foundational and advanced techniques in First-Order Optimization to build the next generation of machine learning systems.

$167.99

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