  In this paper we prove the efficacy of a simple greedy algorithm for a finite
horizon online resource allocation/matching problem, when the corresponding
static planning linear program (SPP) exhibits a non-degeneracy condition called
the general position gap (GPG). The key intuition that we formalize is that the
solution of the reward maximizing SPP is the same as a feasibility Linear
Program restricted to the optimal basic activities, and under GPG this solution
can be tracked with bounded regret by a greedy algorithm, i.e., without the
commonly used technique of periodically resolving the SPP.
  The goal of the decision maker is to combine resources (from a finite set of
resource types) into configurations (from a finite set of feasible
configurations) where each configuration is specified by the number of
resources consumed of each type and a reward. The resources are further
subdivided into three types - offline (whose quantity is known and available at
time 0), online-queueable (which arrive online and can be stored in a buffer),
and online-nonqueueable (which arrive online and must be matched on arrival or
lost). Under GRG we prove that, (i) our greedy algorithm gets bounded any-time
regret of $\mathcal{O}(1/\epsilon_0)$ for matching reward ($\epsilon_0$ is a
measure of the GPG) when no configuration contains both an online-queueable and
an online-nonqueueable resource, and (ii) $\mathcal{O}(\log t)$ expected
any-time regret otherwise (we also prove a matching lower bound). By
considering the three types of resources, our matching framework encompasses
several well-studied problems such as dynamic multi-sided matching, network
revenue management, online stochastic packing, and multiclass queueing systems.
