Nisarg Shah

Beyond dominant resource fairness: extensions, limitations, and indivisibilities

We study the problem of allocating multiple resources to agents with heterogeneous demands. Technological advances such as cloud computing and data centers provide a new impetus for investigating this problem under the assumption that agents demand the resources in fixed proportions, known in economics as Leontief preferences. In a recent paper, Ghodsi et al. [2011] introduced the dominant resource fairness (DRF) mechanism, which was shown to possess highly desirable theoretical properties under Leontief preferences. We extend their results in three directions. First, we show that DRF generalizes to more expressive settings, and leverage a new technical framework to formally extend its guarantees. Second, we study the relation between social welfare and properties such as truthfulness; DRF performs poorly in terms of social welfare, but we show that this is an unavoidable shortcoming that is shared by every mechanism that satisfies one of three basic properties. Third, and most importantly, we study a realistic setting that involves indivisibilities. We chart the boundaries of the possible in this setting, contributing a new relaxed notion of fairness and providing both possibility and impossibility results.

When do noisy votes reveal the truth

A well-studied approach to the design of voting rules views them as maximum likelihood estimators; given votes that are seen as noisy estimates of a true ranking of the alternatives, the rule must reconstruct the most likely true ranking. We argue that this is too stringent a requirement, and instead ask: How many votes does a voting rule need to reconstruct the true ranking? We define the family of pairwise-majority consistent rules, and show that for all rules in this family the number of samples required from the Mallows noise model is logarithmic in the number of alternatives, and that no rule can do asymptotically better (while some rules like plurality do much worse). Taking a more normative point of view, we consider voting rules that surely return the true ranking as the number of samples tends to infinity (we call this property accuracy in the limit); this allows us to move to a higher level of abstraction. We study families of noise models that are parametrized by distance functions, and find voting rules that are accurate in the limit for all noise models in such general families. We characterize the distance functions that induce noise models for which pairwise-majority consistent rules are accurate in the limit, and provide a similar result for another novel family of position-dominance consistent rules. These characterizations capture three well-known distance functions.

The Unreasonable Fairness of Maximum Nash Welfare

The maximum Nash welfare (MNW) solution --- which selects an allocation that maximizes the product of utilities --- is known to provide outstanding fairness guarantees when allocating divisible goods. And while it seems to lose its luster when applied to indivisible goods, we show that, in fact, the MNW solution is unexpectedly, strikingly fair even in that setting. In particular, we prove that it selects allocations that are envy free up to one good --- a compelling notion that is quite elusive when coupled with economic efficiency. We also establish that the MNW solution provides a good approximation to another popular (yet possibly infeasible) fairness property, the maximin share guarantee, in theory and --- even more so --- in practice. While finding the MNW solution is computationally hard, we develop a nontrivial implementation, and demonstrate that it scales well on real data. These results lead us to believe that MNW is the ultimate solution for allocating indivisible goods, and underlie its deployment on a popular fair division website.

Osteotropic Therapy via Targeted Layer-by-Layer Nanoparticles

Current treatment options for debilitating bone diseases such as osteosarcoma, osteoporosis, and bone metastatic cancer are suboptimal and have low efficacy. New treatment options for these pathologies require targeted therapy that maximizes exposure to the diseased tissue and minimizes off-target side effects. This work investigates an approach for generating functional and targeted drug carriers specifically for treating primary osteosarcoma, a disease in which recurrence is common and the cure rate has remained around 20%. This approach utilizes the modularity of Layer-by-Layer (LbL) assembly to generate tissue-specific drug carriers for systemic administration. This is accomplished via surface modification of drug-loaded nanoparticles with an aqueous polyelectrolyte, poly(acrylic acid) (PAA), side-chain functionalized with alendronate, a potent clinically used bisphosphonate. Nanoparticles coated with PAA-alendronate are observed to bind and internalize rapidly in human osteosarcoma 143B cells. Encapsulation of doxorubicin, a front-line chemotherapeutic, in an LbL-targeted liposome demonstrates potent toxicity in vitro. Active targeting of 143B xenografts in NCR nude mice with the LbL-targeted doxorubicin liposomes promotes enhanced, prolonged tumor accumulation and significantly improved efficacy. This report represents a tunable approach towards the synthesis of drug carriers, in which LbL enables surface modification of nanoparticles for tissue-specific targeting and treatment.

Substrate Stress-Relaxation Regulates Scaffold Remodeling and Bone Formation In Vivo.

The rate of stress relaxation of adhesion substrates potently regulates cell fate and function in vitro, and in this study the authors test whether it can regulate bone formation in vivo by implanting alginate gels with differing rates of stress-relaxation carrying human mesenchymal stem cells into rat calvarial defects. After three months, the rats that received fast-relaxing hydrogels (t1/2 ≈ 50 s) show significantly more new bone growth than those that received slow-relaxing, stiffness-matched hydrogels. Strikingly, substantial bone regeneration results from rapidly relaxing hydrogels even in the absence of transplanted cells. Histological analysis reveals that the new bone formed with rapidly relaxing hydrogels is mature and accompanied by extensive matrix remodeling and hydrogel disappearance. This tissue invasion is found to be prominent after just two weeks and the ability of stress relaxation to modulate cell invasion is confirmed with in vitro analysis. These results suggest that substrate stress relaxation can mediate scaffold remodeling and thus tissue formation, giving tissue engineers a new parameter for optimizing bone regeneration.

Reliability Weighted Voting Games

We examine agent failures in weighted voting games. In our cooperative game model, R-WVG, each agent has a weight and a survival probability, and the value of an agent coalition is the probability that its surviving members would have a total weight exceeding a threshold. We propose algorithms for computing the value of a coalition, finding stable payoff allocations, and estimating the power of agents. We provide simulation results showing that on average the stability level of a game increases as the failure probabilities of the agents increase. This conforms to several recent results showing that failures increase stability in cooperative games.

Leximin Allocations in the Real World

As part of a collaboration with a major California school district, we study the problem of fairly allocating unused classrooms in public schools to charter schools. Our approach revolves around the randomized leximin mechanism. We extend previous work to the classroom allocation setting, showing that the leximin mechanism is proportional, envy-free, efficient, and group strategyproof. We also prove that the leximin mechanism provides a (worst-case) 4-approximation to the maximum number of classrooms that can possibly be allocated. Our experiments, which are based on real data, show that a nontrivial implementation of the leximin mechanism scales gracefully in terms of running time (even though the problem is intractable in theory), and performs extremely well with respect to a number of efficiency objectives. We take great pains to establish the practicability of our approach, and discuss issues related to its deployment.

Agent failures in totally balanced games and convex games

We examine the impact of independent agents failures on the solutions of cooperative games, focusing on totally balanced games and the more specific subclass of convex games. We follow the reliability extension model, recently proposed in [1] and show that a (approximately) totally balanced (or convex) game remains (approximately) totally balanced (or convex) when independent agent failures are introduced or when the failure probabilities increase. One implication of these results is that any reliability extension of a totally balanced game has a non-empty core. We propose an algorithm to compute such a core imputation with high probability. We conclude by outlining the effect of failures on non-emptiness of the core in cooperative games, especially in totally balanced games and simple games, thereby extending observations in [1].

Balanced group-labeled graphs

A group-labeled graph is a graph whose vertices and edges have been assigned labels from some abelian group. The weight of a subgraph of a group-labeled graph is the sum of the labels of the vertices and edges in the subgraph. A group-labeled graph is said to be balanced if the weight of every cycle in the graph is zero. We give a characterization of balanced group-labeled graphs that generalizes the known characterizations of balanced signed graphs and consistent marked graphs. We count the number of distinct balanced labellings of a graph by a finite abelian group @C and show that this number depends only on the order of @C and not its structure. We show that all balanced labellings of a graph can be obtained from the all-zero labeling using simple operations. Finally, we give a new constructive characterization of consistent marked graphs and markable graphs, that is, graphs that have a consistent marking with at least one negative vertex.

Peer Prediction with Heterogeneous Users

Peer prediction mechanisms incentivize agents to truthfully report their signals, in the absence of a verification mechanism, by comparing their reports with those of their peers. Prior work in this area is essentially restricted to the case of homogeneous agents, whose signal distributions are identical. This is limiting in many domains, where we would expect agents to differ in taste, judgment and reliability. Although the Correlated Agreement (CA) mechanism [30] can be extended to handle heterogeneous agents, the new challenge is with the efficient estimation of agent signal types. We solve this problem by clustering agents based on their reporting behavior, proposing a mechanism that works with clusters of agents and designing algorithms that learn such a clustering. In this way, we also connect peer prediction with the Dawid and Skene [5] literature on latent types. We retain the robustness against coordinated misreports of the CA mechanism, achieving an approximate incentive guarantee of ε-informed truthfulness. We show on real data that this incentive approximation is reasonable in practice, and even with a small number of clusters.