  We study an online resource allocation problem under uncertainty about demand
and about the reward of each type of demand (agents) for the resource. Even
though dealing with demand uncertainty in resource allocation problems has been
the topic of many papers in the literature, the challenge of not knowing
rewards has been barely explored. The lack of knowledge about agents' rewards
is inspired by the problem of allocating units of a new resource (e.g., newly
developed vaccines or drugs) with unknown effectiveness/value. For such
settings, we assume that we can \emph{test} the market before the allocation
period starts. During the test period, we sample each agent in the market with
probability $p$. We study how to optimally exploit the \emph{sample
information} in our online resource allocation problem under adversarial
arrival processes. We present an asymptotically optimal algorithm that achieves
$1-\Theta(1/(p\sqrt{m}))$ competitive ratio, where $m$ is the number of
available units of the resource. By characterizing an upper bound on the
competitive ratio of any randomized and deterministic algorithm, we show that
our competitive ratio of $1-\Theta(1/(p\sqrt{m}))$ is tight for any $p
=\omega(1/\sqrt{m})$. That asymptotic optimality is possible with sample
information highlights the significant advantage of running a test period for
new resources. We demonstrate the efficacy of our proposed algorithm using a
dataset that contains the number of COVID-19 related hospitalized patients
across different age groups.
