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Beyond Dominant Resource Fairness David Parkes (Harvard) Ariel Procaccia (CMU) Nisarg Shah (CMU)

Beyond Dominant Resource Fairness David Parkes (Harvard) Ariel Procaccia (CMU) Nisarg Shah (CMU). Motivation. Allocation of multiple resources (e.g., CPU, RAM, bandwidth) Users have heterogeneous demands Today: fixed bundles (slots) Allocate slots using single resource abstraction.

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Beyond Dominant Resource Fairness David Parkes (Harvard) Ariel Procaccia (CMU) Nisarg Shah (CMU)

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  1. Beyond Dominant Resource Fairness David Parkes (Harvard) Ariel Procaccia (CMU) Nisarg Shah (CMU)

  2. Motivation • Allocation of multiple resources (e.g., CPU, RAM, bandwidth) • Users have heterogeneous demands • Today: fixed bundles (slots) • Allocate slots using single resource abstraction

  3. The DRF mechanism • Assume proportional demands (a.k.a. Leontief preferences) • Example: • User wishes to execute multiple instances of a job that requires 2 CPU and 1 RAM • Indifferent between 5 CPU and 2 RAM, and 4 CPU and 2 GB • Happier with 4.2+2.1 • Dominant resource fairness [Ghodsi et al. 2011]: equalize largest shares

  4. DRF animated User 1 alloc. User 2 alloc. Total alloc.

  5. Properties of DRF • Pareto optimality • Envy freeness: users do not want to swap allocations • Sharing incentives (a.k.a. fair share, proportionality, IR): users receive at least as much value as an equal split • Strategyproofness: reporting true demands is a dominant strategy • Exciting application of fair division theory!

  6. Indivisible tasks • Demands specified as fraction of resource r that user i needs to run one instance of its task • User’s utility strictly increases with number of complete instances of task

  7. PO+SI+SP are incompatible User 1 demand User 2 demand Allocation User 1 demand User 2 demand Allocation

  8. Envy freeness • PO and EF are trivially incompatible • Need to relax the notion of envy freeness [Budish 2011, Lipton et al. 2004, Moulin and Stong 2002] • Envy freeness up to one bundle (EF1) = i does not prefer j’s after removing one copy of i’s task • Theorem: PO+EF1+SP impossible

  9. Sequential Minmax • SI+EF1+SP trivial • SI+PO+SP, EF1+PO+SP impossible • Can we achieve PO+SI+EF1? • The Sequential Minmax mechanism: allocate at each step to minimize maximum allocated share after allocation • Theorem: Mechanism is PO+SI+EF1

  10. Sequential Minmax illustrated User 1 demand User 2 demand User 1 alloc. User 2 alloc. Total alloc.

  11. Discussion • Additional results in paper • An extension of DRF to settings with possibly zero demands and endowments, which satisfies group strategyproofness • Lower bounds on social welfare maximization • Current work: dynamic fairness

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