# A Distributed Quasi-Newton Algorithm for Empirical Risk Minimization with Nonsmooth Regularization

@article{Lee2018ADQ, title={A Distributed Quasi-Newton Algorithm for Empirical Risk Minimization with Nonsmooth Regularization}, author={Ching-pei Lee and Cong Han Lim and Stephen J. Wright}, journal={Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery \& Data Mining}, year={2018} }

We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this problem either do not work well in the distributed setting or work only for specific regularizers. Our algorithm uses successive quadratic approximations, and we describe how to maintain an approximation of the Hessian and solve subproblems efficiently in a…

## 21 Citations

### A Distributed Quasi-Newton Algorithm for Primal and Dual Regularized Empirical Risk Minimization

- Computer ScienceArXiv
- 2019

A communication- and computation-efficient distributed optimization algorithm using second-order information for solving empirical risk minimization (ERM) problems with a nonsmooth regularization term that enjoys global linear convergence for a broad range of non-strongly convex problems that includes the most commonly used ERMs, thus requiring lower communication complexity.

### DAve-QN: A Distributed Averaged Quasi-Newton Method with Local Superlinear Convergence Rate

- Computer Science, MathematicsAISTATS
- 2020

A distributed asynchronous quasi-Newton algorithm that can achieve superlinear convergence guarantees is developed, believed to be the first distributed asynchronous algorithm with super linear convergence guarantees to be developed.

### Partial-Quasi-Newton Methods: Efficient Algorithms for Minimax Optimization Problems with Unbalanced Dimensionality

- Computer ScienceKDD
- 2022

A novel second-order optimization algorithm, called Partial-Quasi-Newton (PQN) method, which takes the advantage of unbalanced structure in the problem to establish the Hessian estimate efficiently and theoretically proves the PQN method converges to the saddle point faster than existing minimax optimization algorithms.

### A Linearly Convergent Proximal Gradient Algorithm for Decentralized Optimization

- Computer Science, MathematicsNeurIPS
- 2019

This work designs a proximal gradient decentralized algorithm whose fixed point coincides with the desired minimizer and provides a concise proof that establishes its linear convergence.

### Successive Quadratic Approximation for Regularized Optimization

- Computer Science
- 2018

This work presents global analysis of the iteration complexity of inexact successive quadratic approximation methods, showing that it is sufficient to obtain an inexact solution of the subproblem to fixed multiplicative precision in order to guarantee the same order of convergence rate as the exact version.

### Inexact Successive quadratic approximation for regularized optimization

- Mathematics, Computer ScienceComput. Optim. Appl.
- 2019

This work presents global analysis of the iteration complexity of inexact successive quadratic approximation methods, showing that an inexact solution of the subproblem that is within a fixed multiplicative precision of optimality suffices to guarantee the same order of convergence rate as the exact version of the method.

### A Distributed Second-Order Algorithm You Can Trust

- Computer ScienceICML
- 2018

A new algorithm for distributed training of generalized linear models that only requires the computation of diagonal blocks of the Hessian matrix on the individual workers and dynamically adapts the auxiliary model to compensate for modeling errors is presented.

### CoCoA: A General Framework for Communication-Efficient Distributed Optimization

- Computer ScienceJ. Mach. Learn. Res.
- 2017

This work presents a general-purpose framework for distributed computing environments, CoCoA, that has an efficient communication scheme and is applicable to a wide variety of problems in machine learning and signal processing, and extends the framework to cover general non-strongly-convex regularizers, including L1-regularized problems like lasso.

### Robust Distributed Accelerated Stochastic Gradient Methods for Multi-Agent Networks

- Computer ScienceArXiv
- 2019

A framework which allows to choose the stepsize and the momentum parameters of these algorithms in a way to optimize performance by systematically trading off the bias, variance, robustness to gradient noise and dependence to network effects is developed.

### L-DQN: An Asynchronous Limited-Memory Distributed Quasi-Newton Method

- Computer Science2021 60th IEEE Conference on Decision and Control (CDC)
- 2021

This work proposes a distributed algorithm for solving empirical risk minimization problems, called L-DQN, under the master/worker communication model, which is the first distributed quasi-Newton method with provable global linear convergence guarantees in the asynchronous setting where delays between nodes are present.

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