On the Dual Gradient Descent Method for the Resource Allocation Problem in Multiagent Systems

We consider a sequence of block-separable convex programming problems describing the resource allocation in multiagent systems. We construct several iterative algorithms for setting the resource prices. Under various assumptions about the utility functions and resource constraints, we obtain estimates for the average deviation (regret) of the objective function from the optimal value and the constraint residuals. Here the average is understood as the expectation for independent identically distributed data and as the time average in the online optimization problem. The analysis of the problem is carried out by online optimization methods and duality theory. The algorithms considered use the information concerning the difference between the total demand and supply that is generated by agents’ reactions to prices and corresponds to the constraint residuals.