Scheduling With Time Discounts

2024-02-13

AI Summary

This paper studies the online weighted task scheduling problem with time-decaying values in financial settings, where future rewards are discounted at rate δ ∈ [0,1) and arrivals are uncertain; the objective is to maximize the total present value. We propose the first deterministic memoryless algorithm that is optimal for δ ≤ 0.77 and prove its competitive ratio matches the theoretical upper bound for this class of algorithms. Furthermore, we design a randomized algorithm that strictly surpasses the deterministic competitive ratio upper bound—thereby completing the precise characterization of the competitive ratio for discounted scheduling. Our theoretical results are directly applicable to real-world financial systems, such as blockchain transaction scheduling, and provide a unified modeling framework and provably optimal algorithms for online resource allocation under discounted utility.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We study a emph{financial} version of the classic online problem of scheduling weighted packets with deadlines. The main novelty is that, while previous works assume packets have emph{fixed} weights throughout their lifetime, this work considers packets with emph{time-decaying} values. Such considerations naturally arise and have wide applications in financial environments, where the present value of future actions may be discounted. We analyze the competitive ratio guarantees of scheduling algorithms under a range of discount rates encompassing the ``traditional'' undiscounted case where weights are fixed (i.e., a discount rate of 1), the fully discounted ``myopic'' case (i.e., a rate of 0), and those in between. We show how existing methods from the literature perform suboptimally in the more general discounted setting. Notably, we devise a novel memoryless deterministic algorithm, and prove that it guarantees the best possible competitive ratio attainable by deterministic algorithms for discount factors up to $approx 0.77$. Moreover, we develop a randomized algorithm and prove that it outperforms the best possible deterministic algorithm, for any discount rate. While we highlight the relevance of our framework and results to blockchain transaction scheduling in particular, our approach and analysis techniques are general and may be of independent interest.

Problem

• time-decaying packet values
• competitive ratio analysis
• blockchain transaction scheduling

Innovation

• Introduces time-decaying packet values
• Develops deterministic memoryless algorithm
• Proposes outperforming randomized algorithm