Single-Sample and Robust Online Resource Allocation

2025-05-05

AI Summary

This paper studies online resource allocation under large budget constraints: given a stochastic sequence of multi-type, multi-choice requests arriving over time, we design a learnable and robust algorithm with only a single sample from each request’s distribution—a minimal prior. We propose the first single-sample algorithm based on exponential dynamic pricing, achieving a $(1-varepsilon)$-approximation to the hindsight optimal solution. Our algorithm provides three key guarantees: (1) theoretical optimality—breaking previous barriers by attaining $(1-varepsilon)$-approximation under mild large-budget assumptions; (2) strong robustness—insensitivity to outliers and value perturbations; and (3) feasibility and incentive compatibility—ensuring no resource over-allocation and truthful reporting. This resolves the robust online allocation open problem posed at SODA’22, eliminating reliance on full distributional knowledge or stringent arrival assumptions (e.g., i.i.d. or Poisson).

Technology Category

• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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 $(1-epsilon)$-approximation to the hindsight optimum, where $epsilon>0$ 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 $(1-epsilon)$-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 $(1 - epsilon)$-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.

Problem

• Achieving near-optimal online resource allocation with single-sample learnability
• Ensuring robustness against corruptions in outlier and value augmentation models
• Designing incentive-compatible pricing without requiring full distribution knowledge

Innovation

• Exponential Pricing algorithm for resource allocation
• Single sample from request distributions required
• Robust to corruptions in outlier and value models