  In this paper, we study a novel Stochastic Network Utility Maximization (NUM)
problem where the utilities of agents are unknown. The utility of each agent
depends on the amount of resource it receives from a network
operator/controller. The operator desires to do a resource allocation that
maximizes the expected total utility of the network. We consider threshold type
utility functions where each agent gets non-zero utility if the amount of
resource it receives is higher than a certain threshold. Otherwise, its utility
is zero (hard real-time). We pose this NUM setup with unknown utilities as a
regret 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 this
problem setting as a bandit setting where feedback obtained in each round
depends on the resource allocated to the agents. We propose algorithms for this
novel setting using ideas from Multiple-Play Multi-Armed Bandits and
Combinatorial Semi-Bandits. We show that the proposed algorithm is optimal when
all agents have the same utility. We validate the performance guarantees of our
proposed algorithms through numerical experiments.
