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Course10610146647 lectures

Distributed Optimization and Machine Learning

Prof. Mayank Baranwal · IIT Bombay

Start with lecture 1 At NPTEL

About

Centralized access to information and its subsequent processing is often computationally prohibitive over large networks due to communication overhead and the scale of the problem. Consequently, such systems rely on control and optimization algorithms that are fully distributed or even decentralized in nature. This course will provide a comprehensive overview of design and analysis of distributed optimization algorithms and their applications to machine learning. The aim is to revisit classical control and optimization algorithms for centralized optimization and discuss how these can be extended to distributed setting to accommodate the effects of communication constraints, network topology, computational resources, and robustness. Topics include graph theory, iterative methods for convex problems, synchronous and asynchronous setups, consensus algorithms, and distributed machine learning. We will also explore some recent literature in this area that exploits control theory for design of accelerated distributed optimization algorithms.

Intended audience: MTech and PhD students in broad areas of optimization and data science

Prerequisites: A background in convex optimization and differential equations is preferred

Lectures

Week 1.1: Introduction to Distributed Optimization

  1. Lecture 1: Introduction to optimization YouTube
  2. Lecture 2: Analyzing optimization algorithms in continuous time domain YouTube
  3. Lecture 3: Course Outline YouTube
  4. Lecture 4: Basics of optimization problems YouTube
  5. Lecture 5: Convex sets and Convex functions YouTube

Week 2.1: Strong Convexity and Its Implications

  1. Lecture 6: Strictly and strongly convex functions YouTube
  2. Lecture 7: Implications of strong convexity YouTube
  3. Lecture 8: Primal and dual optimization problems YouTube

Week 3

  1. Lecture 9: Slaters condition YouTube
  2. Lecture 10: Analysis of gradient descent algorithm YouTube
  3. Lecture 11: KKT conditions YouTube

Week 4

  1. Lecture 12: Acceleration under strong convexity YouTube
  2. Lecture 13: Accelerate the convergence even further YouTube
  3. Lecture 14: Stability theory YouTube
  4. Lecture 15: Connections to optimization problems YouTube

Week 5

  1. Lecture 16: Exponential stability YouTube
  2. Lecture 17: Bregman Divergance YouTube
  3. Lecture 18: Rescaled Gradient Flow YouTube

Week 6

  1. Lecture 19: Advanced Results on PL inequality: Part 1 YouTube
  2. Lecture 20: Advanced Results on PL inequality: Part 2 YouTube
  3. Lecture 21: Constrained Optimization Problem YouTube
  4. Lecture 22: Augmented Lagrangian YouTube

Week 7

  1. Lecture 23: Method of Multipliers YouTube
  2. Lecture 24: Dual Ascent and Dual Decomposition YouTube
  3. Lecture 25: ADMM Algorithm YouTube

Week 8

  1. Lecture 26: Basics of Graph Theory YouTube
  2. Lecture 27: Basics of Graph Theory-2 YouTube
  3. Lecture 28: Consensus and Average Consensus YouTube
  4. Lecture 29: Consensus and Average Consensus-2 YouTube

Week 9

  1. Lecture 30: Consensus Algorithms YouTube
  2. Lecture 31: Consensus Algorithms-Fixed time YouTube
  3. Lecture 32: Distributed Economic Dispatch Problem YouTube
  4. Lecture 33: Algorithm for Uncapacitated EDP YouTube
  5. Lecture 34: Capacitated EDP YouTube

Week 10

  1. Lecture 35: Algorithms for Distributed Optimization YouTube
  2. Lecture 36: Algorithms for Distributed Optimization-2 YouTube
  3. Lecture 37: Continuous-time Distributed Optimization Algorithms YouTube
  4. Lecture 38: Introduction to Neural Networks YouTube
  5. Lecture 39: Large Scale Machine Learning YouTube

Week 11

  1. Lecture 40: Decentralized Stochastic Gradient Descent YouTube
  2. Lecture 41: Decentralized Stochastic Gradient Descent -2 YouTube
  3. Lecture 42: Introduction to Federated Learning YouTube
  4. Lecture 43: FedAvg Algorithm YouTube
  5. Lecture 44: Convergence Analysis of FL YouTube

Week 12

  1. Lecture 45: Sources of Computational Heterogenity in FL YouTube
  2. Lecture 46: Objective Inconsistency Problem YouTube
  3. Lecture 47: General Update Rule YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Bombay
Department
Computer Science and Engineering
Teacher
Prof. Mayank Baranwal
Level
Graduate
Language
English
Subjects
Computer science, Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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