Learning Packing and Covering from Samples

We consider a multiple-choice mixed packing and covering problem in the online setting: at each timestep $t$, the algorithm faces a collection of $K$ choices. Each choice consumes some resources, and gives some benefits; both resources and benefits are $d$-dimensional vectors. We would like to make a choice for each timestep, such that we use at most $B$ units of each resource, and we get at least $B$ units of each kind of benefit. Among its many applications, this general problem captures the question of load-balancing on unrelated machines, where the choices are allocations of jobs to machines.