  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\left(\min \left(\kappa^{0.5},
\kappa/n^{0.5},\kappa^{1.5}/n\right)\right)$ where $\kappa$ 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 trade-off 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.
