1. A computer system for an online advertising auction, comprising: a multi-armed bandit engine for learning the valuation of advertisements through sampling by scheduling the advertisements for web page placements in an online advertising auction with budget and time constraints to optimize payments for maximizing welfare of advertisers; and a storage operably coupled to the multi-armed bandit engine for storing a plurality of budgets and a plurality of bids each associated with an advertisement allocated to web page placements in the online advertising auction with budget and time constraints.