Advanced Optimization Techniques for Machine Learning
Chapter 1: Foundations of Optimization in Machine Learning
Revisiting Gradient Descent Variants
The Role of Convexity
Understanding Loss Surfaces
Convergence Analysis Fundamentals
Challenges in Non-Convex Optimization
Numerical Stability Considerations
Practice: Analyzing Convergence Behavior
Chapter 2: Second-Order Optimization Methods
Newton's Method: Theory and Derivation
The Hessian Matrix: Computation and Properties
Challenges with Newton's Method
Quasi-Newton Methods: Approximating the Hessian
BFGS Algorithm Explained
Limited-memory BFGS (L-BFGS)
Trust Region Methods
Hands-on Practical: Implementing L-BFGS
Chapter 3: Adaptive Learning Rate Algorithms
Limitations of Fixed Learning Rates
AdaGrad: Adapting Rates Based on Past Gradients
RMSprop: Addressing AdaGrad's Diminishing Rates
Adam: Combining Momentum and RMSprop
Adamax and Nadam Variants
AMSGrad: Improving Adam's Convergence
Understanding Learning Rate Schedules
Hands-on Practical: Comparing Adaptive Optimizers
Chapter 4: Optimization for Large-Scale Datasets
Stochastic Gradient Descent Revisited: Variance Reduction
Stochastic Average Gradient (SAG)
Stochastic Variance Reduced Gradient (SVRG)
Mini-batch Gradient Descent Trade-offs
Asynchronous Stochastic Gradient Descent
Data Parallelism Strategies
Hands-on Practical: Implementing SVRG
Chapter 5: Distributed Optimization Strategies
Motivation for Distributed Training
Parameter Server Architectures
Synchronous vs. Asynchronous Updates
Communication Bottlenecks and Strategies
All-Reduce Algorithms
Federated Learning Optimization Principles
Hands-on Practical: Simulating Distributed SGD
Chapter 6: Optimization Challenges in Deep Learning
Characteristics of Deep Learning Loss Landscapes
Impact of Network Architecture on Optimization
Normalization Techniques and Optimization
Gradient Clipping and Explosion/Vanishing Gradients
Initialization Strategies and Their Effect
Regularization Methods as Implicit Optimization
Practice: Tuning Optimizers for Deep Networks
Chapter 7: Advanced and Specialized Optimization Topics
Constrained Optimization Fundamentals
Lagrangian Duality and KKT Conditions
Projected Gradient Methods
Derivative-Free Optimization Overview
Bayesian Optimization for Hyperparameter Tuning
Optimization for Reinforcement Learning Policies
Practice: Implementing Projected Gradient Descent
Bayesian Optimization for Hyperparameter Tuning
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- Practical Bayesian Optimization of Machine Learning Algorithms, Jasper Snoek, Hugo Larochelle, and Ryan P. Adams, 2012 Advances in Neural Information Processing Systems (NIPS 25), Vol. 4 (Curran Associates, Inc.) DOI: 10.48550/arXiv.1206.2944 - A foundational paper on applying Bayesian Optimization specifically to the tuning of machine learning hyperparameters, using Gaussian Processes.
- Gaussian Processes for Machine Learning, Carl Edward Rasmussen and Christopher K. I. Williams, 2006 (The MIT Press) - The authoritative textbook for a comprehensive understanding of Gaussian Processes, which are fundamental to many Bayesian Optimization surrogate models.
- Taking the Human Out of the Loop: A Review of Bayesian Optimization, Bob Shahriari, Kevin Swersky, Ziyu Wang, Ryan P. Adams, and Nando de Freitas, 2016 Proceedings of the IEEE, Vol. 104 (IEEE) DOI: 10.1109/JPROC.2015.2494218 - A comprehensive review article that surveys the theory, applications, and challenges of Bayesian Optimization across various domains.