### Abstract

We present distributed random projected gradient algorithms for Support Vector Machines (SVMs) that can be used by multiple agents connected over a time-varying network. The goal is for the agents to cooperatively find the same maximum margin hyperplane. In the primal SVM formulation, the objective function can be represented as a sum of convex functions and the constraint set is an intersection of multiple halfspaces. Each agent minimizes a local objective subject to a local constraint set. It maintains its own estimate sequence and communicates with its neighbors. More specifically, each agent calculates weighted averages of the received estimates and its own estimate, adjust the estimate by using gradient information of its local objective function and project onto a subset of its local constraint set. At each iteration, an agent considers only one halfspace since projection onto a single halfspace is easy. We also consider the convergence behavior of the algorithms and prove that all the estimates of agents converge to the same limit point in the optimal set.

Original language | English (US) |
---|---|

Article number | 6425875 |

Pages (from-to) | 5286-5291 |

Number of pages | 6 |

Journal | Unknown Journal |

DOIs | |

State | Published - 2012 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

### Cite this

*Unknown Journal*, 5286-5291. [6425875]. https://doi.org/10.1109/CDC.2012.6425875

**DrSVM : Distributed random projection algorithms for SVMs.** / Lee, Soomin; Nedich, Angelia.

Research output: Contribution to journal › Article

*Unknown Journal*, pp. 5286-5291. https://doi.org/10.1109/CDC.2012.6425875

}

TY - JOUR

T1 - DrSVM

T2 - Distributed random projection algorithms for SVMs

AU - Lee, Soomin

AU - Nedich, Angelia

PY - 2012

Y1 - 2012

N2 - We present distributed random projected gradient algorithms for Support Vector Machines (SVMs) that can be used by multiple agents connected over a time-varying network. The goal is for the agents to cooperatively find the same maximum margin hyperplane. In the primal SVM formulation, the objective function can be represented as a sum of convex functions and the constraint set is an intersection of multiple halfspaces. Each agent minimizes a local objective subject to a local constraint set. It maintains its own estimate sequence and communicates with its neighbors. More specifically, each agent calculates weighted averages of the received estimates and its own estimate, adjust the estimate by using gradient information of its local objective function and project onto a subset of its local constraint set. At each iteration, an agent considers only one halfspace since projection onto a single halfspace is easy. We also consider the convergence behavior of the algorithms and prove that all the estimates of agents converge to the same limit point in the optimal set.

AB - We present distributed random projected gradient algorithms for Support Vector Machines (SVMs) that can be used by multiple agents connected over a time-varying network. The goal is for the agents to cooperatively find the same maximum margin hyperplane. In the primal SVM formulation, the objective function can be represented as a sum of convex functions and the constraint set is an intersection of multiple halfspaces. Each agent minimizes a local objective subject to a local constraint set. It maintains its own estimate sequence and communicates with its neighbors. More specifically, each agent calculates weighted averages of the received estimates and its own estimate, adjust the estimate by using gradient information of its local objective function and project onto a subset of its local constraint set. At each iteration, an agent considers only one halfspace since projection onto a single halfspace is easy. We also consider the convergence behavior of the algorithms and prove that all the estimates of agents converge to the same limit point in the optimal set.

UR - http://www.scopus.com/inward/record.url?scp=84874236050&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84874236050&partnerID=8YFLogxK

U2 - 10.1109/CDC.2012.6425875

DO - 10.1109/CDC.2012.6425875

M3 - Article

SP - 5286

EP - 5291

JO - Scanning Electron Microscopy

JF - Scanning Electron Microscopy

SN - 0586-5581

M1 - 6425875

ER -