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We study the problem of online prediction, in which at each time step t, an individual xt arrives, whose label we must predict. Each individual is associated with various groups, defined based on their features such as age, sex, race etc., which may intersect. Our goal is to make predictions that have regret guarantees not just overall but also simultaneously on each subsequence comprised of the members of any single group. Previous work such as [Blum & Lykouris] and [Lee et al] provide attractive regret guarantees for these problems; however, these are computationally intractable on large model classes. We show that a simple modification of the sleeping experts technique of [Blum & Lykouris] yields an efficient reduction to the wellunderstood problem of obtaining diminishing external regret absent group considerations. Our approach gives similar regret guarantees compared to [Blum & Lykouris]; however, we run in time linear in the number of groups, and are oracleefficient in the hypothesis class. This in particular implies that our algorithm is efficient whenever the number of groups is polynomially bounded and the externalregret problem can be solved efficiently, an improvement on [Blum & Lykouris]'s stronger condition that the model class must be small. Our approach can handle online linear regression and online combinatorial optimization problems like online shortest paths. Beyond providing theoretical regret bounds, we evaluate this algorithm with an extensive set of experiments on synthetic data and on two real data sets  Medical costs and the Adult income dataset, both instantiated with intersecting groups defined in terms of race, sex, and other demographic characteristics. We find that uniformly across groups, our algorithm gives substantial error improvements compared to running a standard online linear regression algorithm with no groupwise regret guarantees.more » « lessFree, publiclyaccessible full text available January 1, 2025

We present a stylized model with feedback loops for the evolution of a population's wealth over generations. Individuals have both talent and wealth: talent is a random variable distributed identically for everyone, but wealth is a random variable that is dependent on the population one is born into. Individuals then apply to a downstream agent, which we treat as a university throughout the paper (but could also represent an employer) who makes a decision about whether to admit them or not. The university does not directly observe talent or wealth, but rather a signal (representing e.g. a standardized test) that is a convex combination of both. The university knows the distributions from which an individual's type and wealth are drawn, and makes its decisions based on the posterior distribution of the applicant's characteristics conditional on their population and signal. Each population's wealth distribution at the next round then depends on the fraction of that population that was admitted by the university at the previous round. We study wealth dynamics in this model, and give conditions under which the dynamics have a single attracting fixed point (which implies population wealth inequality is transitory), and conditions under which it can have multiple attracting fixed points (which implies that population wealth inequality can be persistent). In the case in which there are multiple attracting fixed points, we study interventions aimed at eliminating or mitigating inequality, including increasing the capacity of the university to admit more people, aligning the signal generated by individuals with the preferences of the university, and making direct monetary transfers to the less wealthy population.more » « less

xisting network switches implement scheduling disciplines such as FIFO or deficit round robin that provide good utilization or fairness across flows, but do so at the expense of leaking a variety of information via timing side channels. To address this privacy breach, we propose a new scheduling mechanism for switches called indifferentfirst scheduling (IFS). A salient aspect of IFS is that it provides privacy (a notion of strong isolation) to clients that optin, while preserving the (good) performance and utilization of FIFO or round robin for clients that are satisfied with the status quo. Such a hybrid scheduling mechanism addresses the main drawback of prior proposals such as timedivision multiple access (TDMA) that provide strong isolation at the cost of low utilization and increased packet latency for all clients. We identify limitations of modern programmable switches which inhibit an implementation of IFS without compromising its privacy guarantees, and show that a version of IFS with full security can be implemented at line rate in the recently proposed pushinfirstout (PIFO) queuing architecture.more » « less

null (Ed.)We introduce the \emph{pipeline intervention} problem, defined by a layered directed acyclic graph and a set of stochastic matrices governing transitions between successive layers. The graph is a stylized model for how people from different populations are presented opportunities, eventually leading to some reward. In our model, individuals are born into an initial position (i.e. some node in the first layer of the graph) according to a fixed probability distribution, and then stochastically progress through the graph according to the transition matrices, until they reach a node in the final layer of the graph; each node in the final layer has a \emph{reward} associated with it. The pipeline intervention problem asks how to best make costly changes to the transition matrices governing people's stochastic transitions through the graph, subject to a budget constraint. We consider two objectives: social welfare maximization, and a fairnessmotivated maximin objective that seeks to maximize the value to the population (starting node) with the \emph{least} expected value. We consider two variants of the maximin objective that turn out to be distinct, depending on whether we demand a deterministic solution or allow randomization. For each objective, we give an efficient approximation algorithm (an additive FPTAS) for constant width networks. We also tightly characterize the "price of fairness" in our setting: the ratio between the highest achievable social welfare and the highest social welfare consistent with a maximin optimal solution. Finally we show that for polynomial width networks, even approximating the maximin objective to any constant factor is NP hard, even for networks with constant depth. This shows that the restriction on the width in our positive results is essential.more » « less

This paper introduces a new cryptographic primitive called a private resource allocator (PRA) that can be used to allocate resources (e.g., network bandwidth, CPUs) to a set of clients without revealing to the clients whether any other clients received resources. We give several constructions of PRAs that provide guarantees ranging from informationtheoretic to differential privacy. PRAs are useful in preventing a new class of attacks that we call allocationbased sidechannel attacks. These attacks can be used, for example, to break the privacy guarantees of anonymous messaging systems that were designed specifically to defend against sidechannel and traffic analysis attacks. Our implementation of PRAs in Alpenhorn, which is a recent anonymous messaging system, shows that PRAs increase the network resources required to start a conversation by up to 16× (can be made as low as 4×in some cases), but add no overhead once the conversation has been established.more » « less

Suppose a graph G is stochastically created by uniformly sampling vertices along a line segment and connecting each pair of vertices with a probability that is a known decreasing function of their distance. We ask if it is possible to reconstruct the actual positions of the vertices in G by only observing the generated unlabeled graph. We study this question for two natural edge probability functions — one where the probability of an edge decays exponentially with the distance and another where this probability decays only linearly. We initiate our study with the weaker goal of recovering only the order in which vertices appear on the line segment. For a segment of length n and a precision parameter δ, we show that for both exponential and linear decay edge probability functions, there is an efficient algorithm that correctly recovers (up to reflection symmetry) the order of all vertices that are at least δ apart, using only ˜ O( n / δ^2) samples (vertices). Building on this result, we then show that O( n^2 log n / δ^2) vertices (samples) are sufficient to additionally recover the location of each vertex on the line to within a precision of δ. We complement this result with an Ω( n^ 1.5 / δ ) lower bound on samples needed for reconstructing positions (even by a computationally unbounded algorithm), showing that the task of recovering positions is informationtheoretically harder than recovering the order. We give experimental results showing that our algorithm recovers the positions of almost all points with high accuracy.more » « less

We consider the problem of designing sublinear time algorithms for estimating the cost of minimum] metric traveling salesman (TSP) tour. Specifically, given access to a n × n distance matrix D that specifies pairwise distances between n points, the goal is to estimate the TSP cost by performing only sublinear (in the size of D) queries. For the closely related problem of estimating the weight of a metric minimum spanning tree (MST), it is known that for any epsilon > 0, there exists an O^~(n/epsilon^O(1))time algorithm that returns a (1+epsilon)approximate estimate of the MST cost. This result immediately implies an O^~(n/epsilon^O(1)) time algorithm to estimate the TSP cost to within a (2 + epsilon) factor for any epsilon > 0. However, no o(n^2)time algorithms are known to approximate metric TSP to a factor that is strictly better than 2. On the other hand, there were also no known barriers that rule out existence of (1 + epsilon)approximate estimation algorithms for metric TSP with O^~ (n) time for any fixed epsilon > 0. In this paper, we make progress on both algorithms and lower bounds for estimating metric TSP cost. On the algorithmic side, we first consider the graphic TSP problem where the metric D corresponds to shortest path distances in a connected unweighted undirected graph. We show that there exists an O^~(n) time algorithm that estimates the cost of graphic TSP to within a factor of (2 − epsilon_0) for some epsilon_0 > 0. This is the first sublinear cost estimation algorithm for graphic TSP that achieves an approximation factor less than 2. We also consider another wellstudied special case of metric TSP, namely, (1, 2)TSP where all distances are either 1 or 2, and give an O^~(n ^ 1.5) time algorithm to estimate optimal cost to within a factor of 1.625. Our estimation algorithms for graphic TSP as well as for (1, 2)TSP naturally lend themselves to O^~(n) space streaming algorithms that give an 11/6approximation for graphic TSP and a 1.625approximation for (1, 2)TSP. These results motivate the natural question if analogously to metric MST, for any epsilon > 0, (1 + epsilon)approximate estimates can be obtained for graphic TSP and (1, 2)TSP using O^~ (n) queries. We answer this question in the negative – there exists an epsilon_0 > 0, such that any algorithm that estimates the cost of graphic TSP ((1, 2)TSP) to within a (1 + epsilon_0)factor, necessarily requires (n^2) queries. This lower bound result highlights a sharp separation between the metric MST and metric TSP problems. Similarly to many classical approximation algorithms for TSP, our sublinear time estimation algorithms utilize subroutines for estimating the size of a maximum matching in the underlying graph. We show that this is not merely an artifact of our approach, and that for any epsilon > 0, any algorithm that estimates the cost of graphic TSP or (1, 2)TSP to within a (1 + epsilon)factor, can also be used to estimate the size of a maximum matching in a bipartite graph to within an epsilon n additive error. This connection allows us to translate known lower bounds for matching size estimation in various models to similar lower bounds for metric TSP cost estimation.more » « less