# Truth and Regret in Online Scheduling

## TL;DR

This paper develops a truthful online scheduling mechanism for cloud resources that competes with a family of near-optimal algorithms, achieving low regret and truthfulness even with unknown job lengths.

## Contribution

It introduces a method to compete against a family of online scheduling mechanisms with guaranteed regret bounds, ensuring truthfulness and optimality in worst-case scenarios.

## Key findings

- Mechanism achieves near-optimal regret in worst-case settings.
- Ensures truthfulness when mechanisms in the family are truthful.
- Adapts to non-clairvoyant settings with unknown job lengths.

## Abstract

We consider a scheduling problem where a cloud service provider has multiple units of a resource available over time. Selfish clients submit jobs, each with an arrival time, deadline, length, and value. The service provider's goal is to implement a truthful online mechanism for scheduling jobs so as to maximize the social welfare of the schedule. Recent work shows that under a stochastic assumption on job arrivals, there is a single-parameter family of mechanisms that achieves near-optimal social welfare. We show that given any such family of near-optimal online mechanisms, there exists an online mechanism that in the worst case performs nearly as well as the best of the given mechanisms. Our mechanism is truthful whenever the mechanisms in the given family are truthful and prompt, and achieves optimal (within constant factors) regret. We model the problem of competing against a family of online scheduling mechanisms as one of learning from expert advice. A primary challenge is that any scheduling decisions we make affect not only the payoff at the current step, but also the resource availability and payoffs in future steps. Furthermore, switching from one algorithm (a.k.a. expert) to another in an online fashion is challenging both because it requires synchronization with the state of the latter algorithm as well as because it affects the incentive structure of the algorithms. We further show how to adapt our algorithm to a non-clairvoyant setting where job lengths are unknown until jobs are run to completion. Once again, in this setting, we obtain truthfulness along with asymptotically optimal regret (within poly-logarithmic factors).