How to Balance the Load Online When Jobs and Machines Are Both Selfish?

2024-12-30

AI Summary

This paper studies online load balancing on related machines, simultaneously addressing strategic behavior from both jobs (which may misreport their processing times) and machines (which may misreport their speeds), with the dual objectives of minimizing makespan and optimizing the ℓ_q-norm of machine loads. We propose the first online mechanism that is truthful for both jobs and machines—i.e., strategyproof in both dimensions. Our mechanism employs a speed-aware allocation policy, integrating techniques from online algorithm design and mechanism design, and provides rigorous proofs of truthfulness and competitive ratio bounds. It achieves an O(log m) competitive ratio for makespan and Õ(m^{1/q−1/q²}) for the ℓ_q-norm objective. This work overcomes prior limitations—namely, reliance on offline settings or only one-sided truthfulness—and delivers the first nontrivial solution for multi-sided incentive-compatible online scheduling.

Technology Category

• Machine Learning: Online Learning & Bandits
• Multiagent Systems: Mechanism Design
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In this paper, we study the classic optimization problem of Related Machine Online Load Balancing under the conditions of selfish machines and selfish jobs. We have $m$ related machines with varying speeds and $n$ jobs arriving online with different sizes. Our objective is to design an online truthful algorithm that minimizes the makespan while ensuring that jobs and machines report their true sizes and speeds. Previous studies in the online scenario have primarily focused on selfish jobs, beginning with the work of Aspnes et al. (JACM 1997). An $O(1)$-competitive online mechanism for selfish jobs was discovered by Feldman, Fiat, and Roytman (EC 2017). For selfish machines, truthful mechanisms have only been explored in offline settings, starting with Archer and Tardos (FOCS 2001). The best-known results are two PTAS mechanisms by Christodoulou and Kov'{a}cs (SICOMP 2013) and Epstein et al. (MOR 2016). We design an online mechanism that is truthful for both machines and jobs, achieving a competitive ratio of $O(log m)$. This is the first non-trivial two-sided truthful mechanism for online load balancing and also the first non-trivial machine-side truthful mechanism. Furthermore, we extend our mechanism to the $ell_q$ norm variant of load balancing, maintaining two-sided truthfulness with a competitive ratio of $ ilde{O}(m^{frac{1}{q}(1-frac{1}{q})})$.

Problem

• Fairness
• Efficient Allocation
• Selfish Behavior

Innovation

• Online Algorithm
• Fair Allocation
• Efficiency and Fairness in Complex Scenarios