Gradient Descent for Resource Allocation with Packet Loss*

Abstract

This paper studies the effect of packet loss during the application of the weighted gradient descent to solve a resource allocation problem with piecewise quadratic cost functions in a multi-agent system. We define two performance metrics that measure, respectively, the deviation from the constraint and the error on the expected cost function. We derive upper bounds on both metrics: both bounds are proportional to the difference between the initial cost function and the cost function evaluated at the minimizer. Then, we extend the analysis of the constraint violation to open multi-agent systems where agents are replaced: based on a preliminary result and simulations we show that the combination of replacements and losses makes the constraint violation error diverge with time.