Online Learning Demands in Max-min Fairness (2012.08648v1)

Abstract: We describe mechanisms for the allocation of a scarce resource among multiple users in a way that is efficient, fair, and strategy-proof, but when users do not know their resource requirements. The mechanism is repeated for multiple rounds and a user's requirements can change on each round. At the end of each round, users provide feedback about the allocation they received, enabling the mechanism to learn user preferences over time. Such situations are common in the shared usage of a compute cluster among many users in an organisation, where all teams may not precisely know the amount of resources needed to execute their jobs. By understating their requirements, users will receive less than they need and consequently not achieve their goals. By overstating them, they may siphon away precious resources that could be useful to others in the organisation. We formalise this task of online learning in fair division via notions of efficiency, fairness, and strategy-proofness applicable to this setting, and study this problem under three types of feedback: when the users' observations are deterministic, when they are stochastic and follow a parametric model, and when they are stochastic and nonparametric. We derive mechanisms inspired by the classical max-min fairness procedure that achieve these requisites, and quantify the extent to which they are achieved via asymptotic rates. We corroborate these insights with an experimental evaluation on synthetic problems and a web-serving task.

• The paper introduces a mechanism design that ensures efficient, fair, and strategy-proof resource allocation under uncertain user demands.
• It employs an online learning framework where allocation decisions are refined over rounds using deterministic and stochastic feedback.
• Experimental validation on synthetic problems and web-serving tasks demonstrates the practical effectiveness and scalability of the proposed approach.

The paper "Online Learning Demands in Max-min Fairness" discusses mechanisms for fairly and efficiently allocating scarce resources among multiple users when those users do not fully know their specific resource requirements. This scenario is exemplified by the shared usage of a compute cluster within an organization, where users must request resources without perfect information about their actual needs.

Key Contributions

1. Mechanism Design: The paper introduces mechanisms for resource allocation that are efficient, fair (following max-min fairness principles), and strategy-proof. It means that users cannot gain an advantage by misrepresenting their resource needs, and the allocation is done in a way that aims to equalize the minimum satisfaction across users.
2. Online Learning Framework: The problem is set up as an online learning task where resource demands can change over multiple rounds, and users provide feedback about the allocation at the end of each round. This feedback helps the mechanism learn user preferences dynamically.
3. Three Feedback Types:
   • Deterministic Observations: Users' feedback is precise and predictable.
   • Stochastic Parametric Model: Users' feedback follows a probabilistic model with known parameters.
   • Stochastic Nonparametric: Users' feedback is probabilistic but not confined to any specific parametric form.
4. Asymptotic Analysis: The paper derives mechanisms modeled after max-min fairness that achieve efficiency, fairness, and strategy-proofness. The authors provide asymptotic rates to quantify how well these mechanisms perform, particularly as the number of rounds increases.
5. Experimental Validation: The proposed mechanisms are tested on synthetic problems and a web-serving task to demonstrate their practical effectiveness. These experiments corroborate the theoretical insights, showing that the mechanisms can adapt successfully to dynamic and uncertain user demands while maintaining fair and efficient allocations.

Significance

This research is significant because it addresses the practical and common problem of resource allocation in environments where users lack precise knowledge of their needs. By employing a learning-based approach, the mechanisms adapt over time, improving their ability to meet users' actual requirements while ensuring fairness and preventing strategic manipulation. Such mechanisms are particularly relevant in shared computing environments and other multi-user systems where resource allocation efficiency and fairness are crucial.