Single-Sample and Robust Online Resource Allocation
Rohan Ghuge, Sahil Singla, Yifan Wang
TL;DR
The paper tackles online resource allocation with multiple scarce resources under budgets by addressing unknown, non-identical request distributions and robustness to outliers. It introduces Exponential Pricing, a posted-pricing scheme whose resource prices grow exponentially with overuse, enabling a $(1-\epsilon)$-approximation to the hindsight optimum whenever budgets are sufficiently large. A key advance is achieving this guarantee with only a single sample per distribution by a careful single-sample learning routine and partition-based estimation, plus an analysis that forgoes traditional no-regret with a novel zero-price no-regret perspective. The authors further demonstrate robustness to both Byzantine Secretary-type outliers and the Prophet-with-Augmentations model, preserving near-optimal welfare via discretization, restart techniques, and concentration-based arguments. Collectively, the results yield the first single-sample, robust online resource-allocation framework with posted pricing, and they imply truthful mechanisms with strong performance in practical, imperfect settings.
Abstract
Online Resource Allocation problem is a central problem in many areas of Computer Science, Operations Research, and Economics. In this problem, we sequentially receive $n$ stochastic requests for $m$ kinds of shared resources, where each request can be satisfied in multiple ways, consuming different amounts of resources and generating different values. The goal is to achieve a $(1-ε)$-approximation to the hindsight optimum, where $ε>0$ is a small constant, assuming each resource has a large budget. In this paper, we investigate the learnability and robustness of online resource allocation. Our primary contribution is a novel Exponential Pricing algorithm with the following properties: 1. It requires only a \emph{single sample} from each of the $n$ request distributions to achieve a $(1-ε)$-approximation for online resource allocation with large budgets. Such an algorithm was previously unknown, even with access to polynomially many samples, as prior work either assumed full distributional knowledge or was limited to i.i.d.\,or random-order arrivals. 2. It is robust to corruptions in the outliers model and the value augmentation model. Specifically, it maintains its $(1 - ε)$-approximation guarantee under both these robustness models, resolving the open question posed in Argue, Gupta, Molinaro, and Singla (SODA'22). 3. It operates as a simple item-pricing algorithm that ensures incentive compatibility. The intuition behind our Exponential Pricing algorithm is that the price of a resource should adjust exponentially as it is overused or underused. It differs from conventional approaches that use an online learning algorithm for item pricing. This departure guarantees that the algorithm will never run out of any resource, but loses the usual no-regret properties of online learning algorithms, necessitating a new analytical approach.