Constant Regret in Online Allocation: On the Sufficiency of a Single Historical Trace

We consider online decision-making problems where resources are allocated dynamically to a stochastic stream of requests, and decisions are made to maximize reward while satisfying a set of constraints. We propose and analyze a simple algorithm that uses only historical data, i.e., traces (sample paths) of the stochastic process. We prove that, in a large family of problems, which includes as special cases online packing and online matching, the algorithm has near-optimal performance with the minimum possible sample-complexity; in particular, it obtains constant regret with as few as one trace. The algorithm is agnostic of the generative model of arrivals; however, the results hold even under time-varying and correlated arrival processes. Finally, even in settings beyond our theoretical guarantees, our framework generates data-friendly algorithms that match and beat the performance of specialized state-of-the-art algorithms in simulations.