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In this paper, we study a novel Stochastic Network Utility Maximization (NUM)problem where the utilities of agents are unknown. The utility of each agentdepends on the amount of resource it receives from a networkoperator/controller. The operator desires to do a resource allocation thatmaximizes the expected total utility of the network. We consider threshold typeutility functions where each agent gets non-zero utility if the amount ofresource it receives is higher than a certain threshold. Otherwise, its utilityis zero (hard real-time). We pose this NUM setup with unknown utilities as aregret minimization problem. Our goal is to identify a policy that performs as`good' as an oracle policy that knows the utilities of agents. We model thisproblem setting as a bandit setting where feedback obtained in each rounddepends on the resource allocated to the agents. We propose algorithms for thisnovel setting using ideas from Multiple-Play Multi-Armed Bandits andCombinatorial Semi-Bandits. We show that the proposed algorithm is optimal whenall agents have the same utility. We validate the performance guarantees of ourproposed algorithms through numerical experiments.

Stochastic Network Utility Maximization with Unknown Utilities: Multi-Armed Bandits Approach