Online Resource Allocation under Horizon Uncertainty

TL;DR

This paper develops online algorithms for resource allocation that are robust to unknown or varying request horizons, using a novel dual mirror descent approach and incorporating machine-learned horizon predictions.

Contribution

It introduces a new dual mirror descent method with time-varying target rates and provides algorithms with near-optimal performance under horizon uncertainty.

Findings

Achieves near-optimal competitive ratio growth with horizon uncertainty

Provides a fast algorithm for schedule computation of target consumption rates

Incorporates machine-learned horizon predictions to interpolate between known and unknown horizon scenarios

Abstract

We study stochastic online resource allocation: a decision maker needs to allocate limited resources to stochastically-generated sequentially-arriving requests in order to maximize reward. At each time step, requests are drawn independently from a distribution that is unknown to the decision maker. Online resource allocation and its special cases have been studied extensively in the past, but prior results crucially and universally rely on the strong assumption that the total number of requests (the horizon) is known to the decision maker in advance. In many applications, such as revenue management and online advertising, the number of requests can vary widely because of fluctuations in demand or user traffic intensity. In this work, we develop online algorithms that are robust to horizon uncertainty. In sharp contrast to the known-horizon setting, no algorithm can achieve even a constant asymptotic competitive ratio that is independent of the horizon uncertainty. We introduce a novel generalization of dual mirror descent which allows the decision maker to specify a schedule of time-varying target consumption rates, and prove corresponding performance guarantees. We go on to give a fast algorithm for computing a schedule of target consumption rates that leads to near-optimal performance in the unknown-horizon setting. In particular, our competitive ratio attains the optimal rate of growth (up to logarithmic factors) as the horizon uncertainty grows large. Finally, we also provide a way to incorporate machine-learned predictions about the horizon which interpolates between the known and unknown horizon settings.