# D-SVM over Networked Systems with Non-Ideal Linking Conditions

arXiv: https://arxiv.org/abs/2304.06667 · HTML: https://mlsanity.com/paper/2304.06667/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 50 references that are in the map.
- First posted on arXiv 13 Apr 2023.

## Builds on (most cited first, 15 of 15)

- [Achieving Geometric Convergence for Distributed Optimization over Time-Varying Graphs](https://mlsanity.com/paper/1607.03218/) (2016)
- [ADD-OPT: Accelerated Distributed Directed Optimization](https://mlsanity.com/paper/1607.04757/) (2016)
- [Distributed support-vector-machine over dynamic balanced directed networks](https://mlsanity.com/paper/2104.00399/) (2021)
- [Distributed Convex Optimization for Continuous-Time Dynamics with Time-Varying Cost Function](https://mlsanity.com/paper/1507.04878/) (2015)
- [Decentralized Online Learning with Kernels](https://mlsanity.com/paper/1710.04062/) (2017)
- [Fast-Convergent Dynamics for Distributed Allocation of Resources Over Switching Sparse Networks with Quantized Communication Links](https://mlsanity.com/paper/2012.08181/) (2020)
- [Single-Bit Consensus with Finite-Time Convergence: Theory and Applications](https://mlsanity.com/paper/2001.00141/) (2020)
- [Decentralized Prediction-Correction Methods for Networked Time-Varying Convex Optimization](https://mlsanity.com/paper/1602.01716/) (2016)
- [Consensus-Based Distributed Estimation in the Presence of Heterogeneous, Time-Invariant Delays](https://mlsanity.com/paper/2104.00394/) (2021)
- [1st-Order Dynamics on Nonlinear Agents for Resource Allocation over Uniformly-Connected Networks](https://mlsanity.com/paper/2109.04822/) (2021)
- [Asymptotic stability of stochastic LTV systems with applications to distributed dynamic fusion](https://mlsanity.com/paper/1412.8018/) (2014)
- [A Distributed Optimization Algorithm over Time-Varying Graphs with Efficient Gradient Evaluations](https://mlsanity.com/paper/1905.11982/) (2019)
- [Distributed Optimization of Average Consensus Containment with Multiple Stationary Leaders](https://mlsanity.com/paper/2203.16451/) (2022)
- [On Arbitrary Compression for Decentralized Consensus and Stochastic Optimization over Directed Networks](https://mlsanity.com/paper/2204.08160/) (2022)
- [Linear TDOA-based Measurements for Distributed Estimation and Localized Tracking](https://mlsanity.com/paper/2204.12298/) (2022)

## Abstract (arXiv)

This paper considers distributed optimization algorithms, with application in binary classification via distributed support-vector-machines (D-SVM) over multi-agent networks subject to some link nonlinearities. The agents solve a consensus-constraint distributed optimization cooperatively via continuous-time dynamics, while the links are subject to strongly sign-preserving odd nonlinear conditions. Logarithmic quantization and clipping (saturation) are two examples of such nonlinearities. In contrast to existing literature that mostly considers ideal links and perfect information exchange over linear channels, we show how general sector-bounded models affect the convergence to the optimizer (i.e., the SVM classifier) over dynamic balanced directed networks. In general, any odd sector-bounded nonlinear mapping can be applied to our dynamics. The main challenge is to show that the proposed system dynamics always have one zero eigenvalue (associated with the consensus) and the other eigenvalues all have negative real parts. This is done by recalling arguments from matrix perturbation theory. Then, the solution is shown to converge to the agreement state under certain conditions. For example, the gradient tracking (GT) step size is tighter than the linear case by factors related to the upper/lower sector bounds. To the best of our knowledge, no existing work in distributed optimization and learning literature considers non-ideal link conditions.