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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)
Motivation • Allocation of multiple resources (e.g., CPU, RAM, bandwidth) • Users have heterogeneous demands • Today: fixed bundles (slots) • Allocate slots using single resource abstraction
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
DRF animated User 1 alloc. User 2 alloc. Total alloc.
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!
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
PO+SI+SP are incompatible User 1 demand User 2 demand Allocation User 1 demand User 2 demand Allocation
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
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
Sequential Minmax illustrated User 1 demand User 2 demand User 1 alloc. User 2 alloc. Total alloc.
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