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Register a new userFair Resource Allocation for Demands with Sharp Lower Tail Inequalities
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Added by
Jittat Fakcharoenphol
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We consider a fairness problem in resource allocation where multiple groups demand resources from a common source with the total fixed amount. The general model was introduced by Elzayn et al. [FAT*19]. We follow Donahue and Kleinberg [FAT*20] who considered the case when the demand distribution is known. We show that for many common demand distributions that satisfy sharp lower tail inequalities, a natural allocation that provides resources proportional to each groups average demand performs very well. More specifically, this natural allocation is approximately fair and efficient (i.e., it provides near maximum utilization). We also show that, when small amount of unfairness is allowed, the Price of Fairness (PoF), in this case, is close to 1.
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The $alpha$-fair resource allocation problem has received remarkable attention and has been studied in numerous application fields. Several algorithms have been proposed in the context of $alpha$-fair resource sharing to distributively compute its value. However, little work has been done on its structural properties. In this work, we present a lower bound for the optimal solution of the weighted $alpha$-fair resource allocation problem and compare it with existing propositions in the literature. Our derivations rely on a localization property verified by optimization problems with separable objective that permit one to better exploit their local structures. We give a local version of the well-known midpoint domination axiom used to axiomatically build the Nash Bargaining Solution (or proportionally fair resource allocation problem). Moreover, we show how our lower bound can improve the performances of a distributed algorithm based on the Alternating Directions Method of Multipliers (ADMM). The evaluation of the algorithm shows that our lower bound can considerably reduce its convergence time up to two orders of magnitude compared to when the bound is not used at all or is simply looser.
We consider the problem of dividing limited resources between a set of agents arriving sequentially with unknown (stochastic) utilities. Our goal is to find a fair allocation - one that is simultaneously Pareto-efficient and envy-free. When all utilities are known upfront, the above desiderata are simultaneously achievable (and efficiently computable) for a large class of utility functions. In a sequential setting, however, no policy can guarantee these desiderata simultaneously for all possible utility realizations. A natural online fair allocation objective is to minimize the deviation of each agents final allocation from their fair allocation in hindsight. This translates into simultaneous guarantees for both Pareto-efficiency and envy-freeness. However, the resulting dynamic program has state-space which is exponential in the number of agents. We propose a simple policy, HopeOnline, that instead aims to `match the ex-post fair allocation vector using the current available resources and `predicted histogram of future utilities. We demonstrate the effectiveness of our policy compared to other heurstics on a dataset inspired by mobile food-bank allocations.
We consider the problem of fairly allocating indivisible public goods. We model the public goods as elements with feasibility constraints on what subsets of elements can be chosen, and assume that agents have additive utilities across elements. Our model generalizes existing frameworks such as fair public decision making and participatory budgeting. We study a groupwise fairness notion called the core, which generalizes well-studied notions of proportionality and Pareto efficiency, and requires that each subset of agents must receive an outcome that is fair relative to its size. In contrast to the case of divisible public goods (where fractional allocations are permitted), the core is not guaranteed to exist when allocating indivisible public goods. Our primary contributions are the notion of an additive approximation to the core (with a tiny multiplicative loss), and polynomial time algorithms that achieve a small additive approximation, where the additive factor is relative to the largest utility of an agent for an element. If the feasibility constraints define a matroid, we show an additive approximation of 2. A similar approach yields a constant additive bound when the feasibility constraints define a matching. More generally, if the feasibility constraints define an arbitrary packing polytope with mild restrictions, we show an additive guarantee that is logarithmic in the width of the polytope. Our algorithms are based on variants of the convex program for maximizing the Nash social welfare, but differ significantly from previous work in how it is used. Our guarantees are meaningful even when there are fewer elements than the number of agents. As far as we are aware, our work is the first to approximate the core in indivisible settings.
Settings such as lending and policing can be modeled by a centralized agent allocating a resource (loans or police officers) amongst several groups, in order to maximize some objective (loans given that are repaid or criminals that are apprehended). Often in such problems fairness is also a concern. A natural notion of fairness, based on general principles of equality of opportunity, asks that conditional on an individual being a candidate for the resource, the probability of actually receiving it is approximately independent of the individuals group. In lending this means that equally creditworthy individuals in different racial groups have roughly equal chances of receiving a loan. In policing it means that two individuals committing the same crime in different districts would have roughly equal chances of being arrested. We formalize this fairness notion for allocation problems and investigate its algorithmic consequences. Our main technical results include an efficient learning algorithm that converges to an optimal fair allocation even when the frequency of candidates (creditworthy individuals or criminals) in each group is unknown. The algorithm operates in a censored feedback model in which only the number of candidates who received the resource in a given allocation can be observed, rather than the true number of candidates. This models the fact that we do not learn the creditworthiness of individuals we do not give loans to nor learn about crimes committed if the police presence in a district is low. As an application of our framework, we consider the predictive policing problem. The learning algorithm is trained on arrest data gathered from its own deployments on previous days, resulting in a potential feedback loop that our algorithm provably overcomes. We empirically investigate the performance of our algorithm on the Philadelphia Crime Incidents dataset.
As Communication Service Providers (CSPs) adopt the Network Function Virtualization (NFV) paradigm, they need to transition their network function capacity to a virtualized infrastructure with different Network Functions running on a set of heterogeneous servers. This abstract describes a novel technique for allocating server resources (compute, storage and network) for a given set of Virtual Network Function (VNF) requirements. Our approach helps the telco providers decide the most effective way to run several VNFs on servers with different performance characteristics. Our analysis of prior VNF performance characterization on heterogeneous/different server resource allocations shows that the ability to arbitrarily create many VNFs among different servers resource allocations leads to a comparative advantage among servers. We propose a VNF resource allocation method called COMPARE that maximizes the total throughput of the system by formulating this resource allocation problem as a comparative advantage problem among heterogeneous servers. There several applications for using the VNF resource allocation from COMPARE including transitioning current Telco deployments to NFV based solutions and providing initial VNF placement for Service Function Chain (SFC) provisioning.
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