
Discrete gradient descent differs qualitatively from gradient flow
We consider gradient descent on functions of the form L_1 = f and L_2 ...
read it

A frequencydomain analysis of inexact gradient descent
We study robustness properties of inexact gradient descent for strongly ...
read it

Linear Convergence of Distributed Mirror Descent with Integral Feedback for Strongly Convex Problems
Distributed optimization often requires finding the minimum of a global ...
read it

Distributed Online Optimization in Dynamic Environments Using Mirror Descent
This work addresses decentralized online optimization in nonstationary ...
read it

Optimization in Open Networks via Dual Averaging
In networks of autonomous agents (e.g., fleets of vehicles, scattered se...
read it

Surfing: Iterative optimization over incrementally trained deep networks
We investigate a sequential optimization procedure to minimize the empir...
read it

Optimal Statistical Rates for Decentralised NonParametric Regression with Linear SpeedUp
We analyse the learning performance of Distributed Gradient Descent in t...
read it
Stability of Decentralized Gradient Descent in Open MultiAgent Systems
The aim of decentralized gradient descent (DGD) is to minimize a sum of n functions held by interconnected agents. We study the stability of DGD in open contexts where agents can join or leave the system, resulting each time in the addition or the removal of their function from the global objective. Assuming all functions are smooth, strongly convex, and their minimizers all lie in a given ball, we characterize the sensitivity of the global minimizer of the sum of these functions to the removal or addition of a new function and provide bounds in O(min(κ^0.5, κ/n^0.5,κ^1.5/n)) where κ is the condition number. We also show that the states of all agents can be eventually bounded independently of the sequence of arrivals and departures. The magnitude of the bound scales with the importance of the interconnection, which also determines the accuracy of the final solution in the absence of arrival and departure, exposing thus a potential tradeoff between accuracy and sensitivity. Our analysis relies on the formulation of DGD as gradient descent on an auxiliary function. The tightness of our results is analyzed using the PESTO Toolbox.
READ FULL TEXT
Comments
There are no comments yet.