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Table of contents
Chapter 1. Introduction
1.1. Basics of Convex Optimization
1.2. Designing Faster methods
1.3. Distributed Optimization Models
1.4. Standard Decentralized Approaches with Linear Convergence
Chapter 2. Accelerated Decentralized Optimization with Pairwise Updates
2.1. Introduction
2.2. Model
2.3. Algorithm
2.4. Performances
2.5. Experiments
2.6. Conclusion
Appendices
2.A. Detailed average time per iteration proof
2.B. Execution speed comparisons
2.C. Detailed rate proof
Chapter 3. Accelerated Variance-reduced decentralized stochastic optimization
3.1. Introduction
3.2. Model and notations
3.3. Related work
3.4. Optimal rates
3.5. Block Accelerated Proximal Coordinate Gradient with Arbitrary Sampling
3.6. Accelerated Decentralized Stochastic Algorithm
3.7. Local synchrony and the randomized gossip model
3.8. Experiments
3.9. Conclusion
Appendices
3.A. Accelerated Proximal Block Coordinate Descent with Arbitrary Sampling
3.B. Average Time per Iteration
3.C. Algorithm Performances
Chapter 4. Dual-Free Decentralized Algorithm with Variance Reduction
4.1. Introduction
4.2. Algorithm Design
4.3. Convergence Rate
4.4. Acceleration
4.5. Experiments
4.6. Conclusion
Appendices
4.A. Bregman Coordinate Descent
4.B. Convergence results for DVR
4.C. Catalyst acceleration
4.D. Experiments
Chapter 5. Statistically Preconditioned Accelerated Gradient Method
5.1. Introduction
5.2. Related Work
5.3. The SPAG Algorithm
5.4. Bounding the Relative Condition Number
5.5. Experiments
5.6. Conclusion
5.7. Statistical Preconditioning with other Bregman algorithms
Appendices
5.A. Convergence Analysis of SPAG
5.B. Concentration of Hessians
5.C. Experiment Setting and Additional Results
Chapter 6. Quantifying the natural differential privacy guarantees of gossip protocols
6.1. Introduction
6.2. Background and Related Work
6.3. A Model of Differential Privacy for Gossip Protocols
6.4. Extreme Privacy Cases
6.5. Privacy vs. Speed Trade-offs
6.6. Empirical Evaluation
6.7. Concluding Remarks
Appendices
6.A. Model Extensions
6.B. Delayed Start Gossip
6.C. Detailed Proofs
6.D. Challenges of Private Gossip for General Graphs
Conclusion and Research Directions
Summary of the thesis
Perspectives
Bibliography
