Randomized Iterative Methods for Linear Systems: Momentum, Inexactness and Gossip
arXiv:1909.12176
Abstract
In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The need to solve optimization problems is ubiquitous in essentially all quantitative areas of human endeavor, including industry and science. In the last decade there has been a surge in the demand from practitioners, in fields such as machine learning, computer vision, artificial intelligence, signal processing and data science, for new methods able to cope with these new large scale problems. In this thesis we are focusing on the design, complexity analysis and efficient implementations of such algorithms. In particular, we are interested in the development of randomized iterative methods for solving large scale linear systems, stochastic quadratic optimization problems, the best approximation problem and quadratic optimization problems. A large part of the thesis is also devoted to the development of efficient methods for obtaining average consensus on large scale networks.
PhD Thesis, University of Edinburgh, 2019
References in corpus (10)
- Stochastic Gradient Descent for Non-smooth Optimization: Convergence Results and Optimal Averaging Schemes
- Geographic Gossip: Efficient Averaging for Sensor Networks
- Decentralized Stochastic Optimization and Gossip Algorithms with Compressed Communication
- Polynomial Filtering for Fast Convergence in Distributed Consensus
- Communication/Computation Tradeoffs in Consensus-Based Distributed Optimization
- SDNA: Stochastic Dual Newton Ascent for Empirical Risk Minimization
- Stochastic Dual Coordinate Ascent with Adaptive Probabilities
- Privacy Preserving Randomized Gossip Algorithms
- Global Convergence of Arbitrary-Block Gradient Methods for Generalized Polyak-Łojasiewicz Functions
- Reducing the variance in online optimization by transporting past gradients