A First-Order Learning Algorithm for Online Resource Allocation with Constant Regret

We study a finite-horizon online resource allocation problem with initial resource capacities proportional to the horizon. In each period, a request type is observed and one action is chosen from a finite menu. Each action earns a reward and consumes a vector of resources. We present a primal first-order learning policy that, in each period, performs one gradient ascent update of the action coordinates associated with one request type, for a fluid relaxation in which resource overuse incurs a quadratic penalty. The policy achieves O(1) expected additive regret relative to the hindsight optimum, with a bound independent of the horizon T, under a general arrival model. This model includes independent and identically distributed arrivals with unknown probabilities, independent nonstationary arrivals with known probabilities, independent nonstationary arrivals with unknown probabilities and one historical sample path, and Markov-modulated arrivals with an unknown Markov chain. The policy does not solve any linear program, and the regret bound does not require a nondegeneracy assumption on the fluid linear program.