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
Synchronous vs. Asynchronous Updates
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- Delay-Tolerant Distributed Stochastic Gradient Descent, Xiangru Lian, Ce Zhang, Cho-Jui Hsieh, Kai-Wei Chang, Inderjit S. Dhillon, 2015 Advances in Neural Information Processing Systems (NeurIPS 28), Vol. 48 (Proceedings of Machine Learning Research) - This paper provides theoretical convergence analysis for asynchronous SGD, specifically addressing the impact of gradient staleness and proposing delay-tolerant algorithms.
- Stale Synchronous Parallel Distributed Machine Learning, Qirong Ho, James Cipar, Henggang Cui, Seunghak Lee, Jin Kyu Kim, Phillip B. Gibbons, Garth A Gibson, Greg Ganger, Eric P Xing, 2013 Advances in Neural Information Processing Systems 26, Vol. 26 (Neural Information Processing Systems (NIPS)) - This paper introduces the Stale Synchronous Parallel (SSP) paradigm, a hybrid approach that balances the benefits of synchronous and asynchronous updates by allowing a bounded amount of staleness.
- Distributed Deep Learning: A Guide to the State-of-the-Art, Tal Ben-Nun, Torsten Hoefler, 2019 Communications of the ACM, Vol. 62 (Association for Computing Machinery (ACM)) DOI: 10.1145/3291040 - This survey provides a comprehensive overview of distributed deep learning techniques, including detailed discussions on synchronous and asynchronous training strategies, communication patterns, and their trade-offs.