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
Communication Bottlenecks and Strategies
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- Deep Gradient Compression: Reducing the Communication Bandwidth for Distributed Training, Yujun Lin, Song Han, Huizi Mao, Yu Wang, William J. Dally, 2018 ICLR 2018 DOI: 10.48550/arXiv.1712.01887 - This paper introduces deep gradient compression techniques that combine sparsification, quantization, and gradient accumulation to significantly reduce communication overhead in distributed deep learning without losing accuracy.
- Horovod: Fast and Easy Distributed Deep Learning in TensorFlow, Alexander Sergeev, Mike Del Balso, 2018 arXiv preprint arXiv:1802.05799 DOI: 10.48550/arXiv.1802.05799 - This paper presents Horovod, a distributed training framework that uses optimized All-Reduce operations for efficient gradient synchronization, offering significant speedups and ease of use for distributed deep learning.
- Local SGD: Distributed SGD with Non-convex Optimization Guarantees, Sebastian U. Stich, 2018 Advances in Neural Information Processing Systems (NeurIPS), Vol. 31 (NeurIPS) DOI: 10.5591/978-1-57766-324-4.neurips2018.0 - This paper provides theoretical guarantees for Local SGD (periodic averaging) in non-convex optimization, demonstrating its effectiveness in reducing communication frequency while maintaining convergence properties.
- Dive into Deep Learning, Aston Zhang, Zack C. Lipton, Mu Li, Alex Smola, 2024 (Cambridge University Press) - This online textbook offers a detailed chapter on distributed training, covering synchronous and asynchronous methods, communication patterns, and strategies for improving efficiency, providing practical and theoretical foundations.