  We explore the class of problems where a central planner needs to select a
subset of agents, each with different quality and cost. The planner wants to
maximize its utility while ensuring that the average quality of the selected
agents is above a certain threshold. When the agents' quality is known, we
formulate our problem as an integer linear program (ILP) and propose a
deterministic algorithm, namely \dpss\ that provides an exact solution to our
ILP.
  We then consider the setting when the qualities of the agents are unknown. We
model this as a Multi-Arm Bandit (MAB) problem and propose \newalgo\ to learn
the qualities over multiple rounds. We show that after a certain number of
rounds, $\tau$, \newalgo\ outputs a subset of agents that satisfy the average
quality constraint with a high probability. Next, we provide bounds on $\tau$
and prove that after $\tau$ rounds, the algorithm incurs a regret of $O(\ln
T)$, where $T$ is the total number of rounds. We further illustrate the
efficacy of \newalgo\ through simulations.
  To overcome the computational limitations of \dpss, we propose a
polynomial-time greedy algorithm, namely \greedy, that provides an approximate
solution to our ILP. We also compare the performance of \dpss\ and \greedy\
through experiments.

Machine Learning