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Jamie Morgenstern

Jamie Morgenstern appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Computer Science and Game TheoryMachine LearningData Structures and AlgorithmsArtificial IntelligenceComputational Engineering, Finance, and ScienceDiscrete Mathematicseess.SYInformation Retrievalmath.OCPopulations and EvolutionSocial and Information NetworksSystems and Control

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Published work

24 published item(s)

preprint2026arXiv

Instance-Adaptive Online Multicalibration

We study online multicalibration beyond the worst-case. We give a single, efficient algorithm which dynamically interpolates between benign and worst-case sequences by adaptively refining a dyadic grid of prediction values. Its error is controlled by the number of leaves in the refinement tree. Our analysis recovers the known $\widetilde O(T^{2/3})$ worst-case-optimal rate for online multicalibration, while simultaneously automatically adapting to easier instances: in the marginal stochastic setting it obtains a rate of $\widetilde O(\sqrt T)$, and for piecewise-stationary means with $J$ segments its rate is $\widetilde O(\sqrt{JT})$. More generally, the rate depends on a threshold-complexity measure of the predictable mean process relative to the group family. We show that this dependence is tight up to logarithmic factors.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Active Learning with Safety Constraints

Active learning methods have shown great promise in reducing the number of samples necessary for learning. As automated learning systems are adopted into real-time, real-world decision-making pipelines, it is increasingly important that such algorithms are designed with safety in mind. In this work we investigate the complexity of learning the best safe decision in interactive environments. We reduce this problem to a constrained linear bandits problem, where our goal is to find the best arm satisfying certain (unknown) safety constraints. We propose an adaptive experimental design-based algorithm, which we show efficiently trades off between the difficulty of showing an arm is unsafe vs suboptimal. To our knowledge, our results are the first on best-arm identification in linear bandits with safety constraints. In practice, we demonstrate that this approach performs well on synthetic and real world datasets.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Active Sampling for Min-Max Fairness

We propose simple active sampling and reweighting strategies for optimizing min-max fairness that can be applied to any classification or regression model learned via loss minimization. The key intuition behind our approach is to use at each timestep a datapoint from the group that is worst off under the current model for updating the model. The ease of implementation and the generality of our robust formulation make it an attractive option for improving model performance on disadvantaged groups. For convex learning problems, such as linear or logistic regression, we provide a fine-grained analysis, proving the rate of convergence to a min-max fair solution.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Competition Alleviates Present Bias in Task Completion

We build upon recent work [Kleinberg and Oren, 2014, Kleinberg et al., 2016, 2017] that considers present biased agents, who place more weight on costs they must incur now than costs they will incur in the future. They consider a graph theoretic model where agents must complete a task and show that present biased agents can take exponentially more expensive paths than optimal. We propose a theoretical model that adds competition into the mix -- two agents compete to finish a task first. We show that, in a wide range of settings, a small amount of competition can alleviate the harms of present bias. This can help explain why biased agents may not perform so poorly in naturally competitive settings, and can guide task designers on how to protect present biased agents from harm. Our work thus paints a more positive picture than much of the existing literature on present bias.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Individual Preference Stability for Clustering

In this paper, we propose a natural notion of individual preference (IP) stability for clustering, which asks that every data point, on average, is closer to the points in its own cluster than to the points in any other cluster. Our notion can be motivated from several perspectives, including game theory and algorithmic fairness. We study several questions related to our proposed notion. We first show that deciding whether a given data set allows for an IP-stable clustering in general is NP-hard. As a result, we explore the design of efficient algorithms for finding IP-stable clusterings in some restricted metric spaces. We present a polytime algorithm to find a clustering satisfying exact IP-stability on the real line, and an efficient algorithm to find an IP-stable 2-clustering for a tree metric. We also consider relaxing the stability constraint, i.e., every data point should not be too far from its own cluster compared to any other cluster. For this case, we provide polytime algorithms with different guarantees. We evaluate some of our algorithms and several standard clustering approaches on real data sets.

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preprint2022arXiv

Optimal Spend Rate Estimation and Pacing for Ad Campaigns with Budgets

Online ad platforms offer budget management tools for advertisers that aim to maximize the number of conversions given a budget constraint. As the volume of impressions, conversion rates and prices vary over time, these budget management systems learn a spend plan (to find the optimal distribution of budget over time) and run a pacing algorithm which follows the spend plan. This paper considers two models for impressions and competition that varies with time: a) an episodic model which exhibits stationarity in each episode, but each episode can be arbitrarily different from the next, and b) a model where the distributions of prices and values change slowly over time. We present the first learning theoretic guarantees on both the accuracy of spend plans and the resulting end-to-end budget management system. We present four main results: 1) for the episodic setting we give sample complexity bounds for the spend rate prediction problem: given $n$ samples from each episode, with high probability we have $|\widehatρ_e - ρ_e| \leq \tilde{O}(\frac{1}{n^{1/3}})$ where $ρ_e$ is the optimal spend rate for the episode, $\widehatρ_e$ is the estimate from our algorithm, 2) we extend the algorithm of Balseiro and Gur (2017) to operate on varying, approximate spend rates and show that the resulting combined system of optimal spend rate estimation and online pacing algorithm for episodic settings has regret that vanishes in number of historic samples $n$ and the number of rounds $T$, 3) for non-episodic but slowly-changing distributions we show that the same approach approximates the optimal bidding strategy up to a factor dependent on the rate-of-change of the distributions and 4) we provide experiments showing that our algorithm outperforms both static spend plans and non-pacing across a wide variety of settings.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Preference Dynamics Under Personalized Recommendations

Many projects (both practical and academic) have designed algorithms to match users to content they will enjoy under the assumption that user's preferences and opinions do not change with the content they see. Evidence suggests that individuals' preferences are directly shaped by what content they see -- radicalization, rabbit holes, polarization, and boredom are all example phenomena of preferences affected by content. Polarization in particular can occur even in ecosystems with "mass media," where no personalization takes place, as recently explored in a natural model of preference dynamics by~\citet{hkazla2019geometric} and~\citet{gaitonde2021polarization}. If all users' preferences are drawn towards content they already like, or are repelled from content they already dislike, uniform consumption of media leads to a population of heterogeneous preferences converging towards only two poles. In this work, we explore whether some phenomenon akin to polarization occurs when users receive \emph{personalized} content recommendations. We use a similar model of preference dynamics, where an individual's preferences move towards content the consume and enjoy, and away from content they consume and dislike. We show that standard user reward maximization is an almost trivial goal in such an environment (a large class of simple algorithms will achieve only constant regret). A more interesting objective, then, is to understand under what conditions a recommendation algorithm can ensure stationarity of user's preferences. We show how to design a content recommendations which can achieve approximate stationarity, under mild conditions on the set of available content, when a user's preferences are known, and how one can learn enough about a user's preferences to implement such a strategy even when user preferences are initially unknown.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Evaluating Fairness of Machine Learning Models Under Uncertain and Incomplete Information

Training and evaluation of fair classifiers is a challenging problem. This is partly due to the fact that most fairness metrics of interest depend on both the sensitive attribute information and label information of the data points. In many scenarios it is not possible to collect large datasets with such information. An alternate approach that is commonly used is to separately train an attribute classifier on data with sensitive attribute information, and then use it later in the ML pipeline to evaluate the bias of a given classifier. While such decoupling helps alleviate the problem of demographic scarcity, it raises several natural questions such as: how should the attribute classifier be trained?, and how should one use a given attribute classifier for accurate bias estimation? In this work we study this question from both theoretical and empirical perspectives. We first experimentally demonstrate that the test accuracy of the attribute classifier is not always correlated with its effectiveness in bias estimation for a downstream model. In order to further investigate this phenomenon, we analyze an idealized theoretical model and characterize the structure of the optimal classifier. Our analysis has surprising and counter-intuitive implications where in certain regimes one might want to distribute the error of the attribute classifier as unevenly as possible among the different subgroups. Based on our analysis we develop heuristics for both training and using attribute classifiers for bias estimation in the data scarce regime. We empirically demonstrate the effectiveness of our approach on real and simulated data.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

A Notion of Individual Fairness for Clustering

A common distinction in fair machine learning, in particular in fair classification, is between group fairness and individual fairness. In the context of clustering, group fairness has been studied extensively in recent years; however, individual fairness for clustering has hardly been explored. In this paper, we propose a natural notion of individual fairness for clustering. Our notion asks that every data point, on average, is closer to the points in its own cluster than to the points in any other cluster. We study several questions related to our proposed notion of individual fairness. On the negative side, we show that deciding whether a given data set allows for such an individually fair clustering in general is NP-hard. On the positive side, for the special case of a data set lying on the real line, we propose an efficient dynamic programming approach to find an individually fair clustering. For general data sets, we investigate heuristics aimed at minimizing the number of individual fairness violations and compare them to standard clustering approaches on real data sets.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Diversity and Inclusion Metrics in Subset Selection

The ethical concept of fairness has recently been applied in machine learning (ML) settings to describe a wide range of constraints and objectives. When considering the relevance of ethical concepts to subset selection problems, the concepts of diversity and inclusion are additionally applicable in order to create outputs that account for social power and access differentials. We introduce metrics based on these concepts, which can be applied together, separately, and in tandem with additional fairness constraints. Results from human subject experiments lend support to the proposed criteria. Social choice methods can additionally be leveraged to aggregate and choose preferable sets, and we detail how these may be applied.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Equalized odds postprocessing under imperfect group information

Most approaches aiming to ensure a model's fairness with respect to a protected attribute (such as gender or race) assume to know the true value of the attribute for every data point. In this paper, we ask to what extent fairness interventions can be effective even when only imperfect information about the protected attribute is available. In particular, we study the prominent equalized odds postprocessing method of Hardt et al. (2016) under a perturbation of the attribute. We identify conditions on the perturbation that guarantee that the bias of a classifier is reduced even by running equalized odds with the perturbed attribute. We also study the error of the resulting classifier. We empirically observe that under our identified conditions most often the error does not suffer from a perturbation of the protected attribute. For a special case, we formally prove this observation to be true.

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preprint2020arXiv

Multi-Criteria Dimensionality Reduction with Applications to Fairness

Dimensionality reduction is a classical technique widely used for data analysis. One foundational instantiation is Principal Component Analysis (PCA), which minimizes the average reconstruction error. In this paper, we introduce the "multi-criteria dimensionality reduction" problem where we are given multiple objectives that need to be optimized simultaneously. As an application, our model captures several fairness criteria for dimensionality reduction such as our novel Fair-PCA problem and the Nash Social Welfare (NSW) problem. In Fair-PCA, the input data is divided into $k$ groups, and the goal is to find a single $d$-dimensional representation for all groups for which the minimum variance of any one group is maximized. In NSW, the goal is to maximize the product of the individual variances of the groups achieved by the common low-dimensional space. Our main result is an exact polynomial-time algorithm for the two-criterion dimensionality reduction problem when the two criteria are increasing concave functions. As an application of this result, we obtain a polynomial time algorithm for Fair-PCA for $k=2$ groups and a polynomial time algorithm for NSW objective for $k=2$ groups. We also give approximation algorithms for $k>2$. Our technical contribution in the above results is to prove new low-rank properties of extreme point solutions to semi-definite programs. We conclude with experiments indicating the effectiveness of algorithms based on extreme point solutions of semi-definite programs on several real-world data sets.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Fairness in Learning: Classic and Contextual Bandits

We introduce the study of fairness in multi-armed bandit problems. Our fairness definition can be interpreted as demanding that given a pool of applicants (say, for college admission or mortgages), a worse applicant is never favored over a better one, despite a learning algorithm's uncertainty over the true payoffs. We prove results of two types. First, in the important special case of the classic stochastic bandits problem (i.e., in which there are no contexts), we provide a provably fair algorithm based on "chained" confidence intervals, and provide a cumulative regret bound with a cubic dependence on the number of arms. We further show that any fair algorithm must have such a dependence. When combined with regret bounds for standard non-fair algorithms such as UCB, this proves a strong separation between fair and unfair learning, which extends to the general contextual case. In the general contextual case, we prove a tight connection between fairness and the KWIK (Knows What It Knows) learning model: a KWIK algorithm for a class of functions can be transformed into a provably fair contextual bandit algorithm, and conversely any fair contextual bandit algorithm can be transformed into a KWIK learning algorithm. This tight connection allows us to provide a provably fair algorithm for the linear contextual bandit problem with a polynomial dependence on the dimension, and to show (for a different class of functions) a worst-case exponential gap in regret between fair and non-fair learning algorithms

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Learning Simple Auctions

We present a general framework for proving polynomial sample complexity bounds for the problem of learning from samples the best auction in a class of "simple" auctions. Our framework captures all of the most prominent examples of "simple" auctions, including anonymous and non-anonymous item and bundle pricings, with either a single or multiple buyers. The technique we propose is to break the analysis of auctions into two natural pieces. First, one shows that the set of allocation rules have large amounts of structure; second, fixing an allocation on a sample, one shows that the set of auctions agreeing with this allocation on that sample have revenue functions with low dimensionality. Our results effectively imply that whenever it's possible to compute a near-optimal simple auction with a known prior, it is also possible to compute such an auction with an unknown prior (given a polynomial number of samples).

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preprint2016arXiv

Simple Mechanisms For Agents With Complements

We study the efficiency of simple auctions in the presence of complements. [DMSW15] introduced the single-bid auction, and showed that it has a price of anarchy (PoA) of $O(\log m)$ for complement-free (i.e., subadditive) valuations. Prior to our work, no non-trivial upper bound on the PoA of single bid auctions was known for valuations exhibiting complements. We introduce a hierarchy over valuations, where levels of the hierarchy correspond to the degree of complementarity, and the PoA of the single bid auction degrades gracefully with the level of the hierarchy. This hierarchy is a refinement of the Maximum over Positive Hypergraphs (MPH) hierarchy [FFIILS15], where the degree of complementarity $d$ is captured by the maximum number of neighbors of a node in the positive hypergraph representation. We show that the price of anarchy of the single bid auction for valuations of level $d$ of the hierarchy is $O(d^2 \log(m/d))$, where $m$ is the number of items. We also establish an improved upper bound of $O(d \log m)$ for a subclass where every hyperedge in the positive hypergraph representation is of size at most 2 (but the degree is still $d$). Finally, we show that randomizing between the single bid auction and the grand bundle auction has a price of anarchy of at most $O(\sqrt{m})$ for general valuations. All of our results are derived via the smoothness framework, thus extend to coarse-correlated equilibria and to Bayes Nash equilibria.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Strategic Network Formation with Attack and Immunization

Strategic network formation arises where agents receive benefit from connections to other agents, but also incur costs for forming links. We consider a new network formation game that incorporates an adversarial attack, as well as immunization against attack. An agent's benefit is the expected size of her connected component post-attack, and agents may also choose to immunize themselves from attack at some additional cost. Our framework is a stylized model of settings where reachability rather than centrality is the primary concern and vertices vulnerable to attacks may reduce risk via costly measures. In the reachability benefit model without attack or immunization, the set of equilibria is the empty graph and any tree. The introduction of attack and immunization changes the game dramatically; new equilibrium topologies emerge, some more sparse and some more dense than trees. We show that, under a mild assumption on the adversary, every equilibrium network with $n$ agents contains at most $2n-4$ edges for $n\geq 4$. So despite permitting topologies denser than trees, the amount of overbuilding is limited. We also show that attack and immunization don't significantly erode social welfare: every non-trivial equilibrium with respect to several adversaries has welfare at least as that of any equilibrium in the attack-free model. We complement our theory with simulations demonstrating fast convergence of a new bounded rationality dynamic which generalizes linkstable best response but is considerably more powerful in our game. The simulations further elucidate the wide variety of asymmetric equilibria and demonstrate topological consequences of the dynamics e.g. heavy-tailed degree distributions. Finally, we report on a behavioral experiment on our game with over 100 participants, where despite the complexity of the game, the resulting network was surprisingly close to equilibrium.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Private Pareto Optimal Exchange

We consider the problem of implementing an individually rational, asymptotically Pareto optimal allocation in a barter-exchange economy where agents are endowed with goods and have preferences over the goods of others, but may not use money as a medium of exchange. Because one of the most important instantiations of such economies is kidney exchange -- where the "input"to the problem consists of sensitive patient medical records -- we ask to what extent such exchanges can be carried out while providing formal privacy guarantees to the participants. We show that individually rational allocations cannot achieve any non-trivial approximation to Pareto optimality if carried out under the constraint of differential privacy -- or even the relaxation of \emph{joint} differential privacy, under which it is known that asymptotically optimal allocations can be computed in two-sided markets, where there is a distinction between buyers and sellers and we are concerned only with privacy of the buyers~\citep{Matching}. We therefore consider a further relaxation that we call \emph{marginal} differential privacy -- which promises, informally, that the privacy of every agent $i$ is protected from every other agent $j \neq i$ so long as $j$ does not collude or share allocation information with other agents. We show that, under marginal differential privacy, it is possible to compute an individually rational and asymptotically Pareto optimal allocation in such exchange economies.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

The Pseudo-Dimension of Near-Optimal Auctions

This paper develops a general approach, rooted in statistical learning theory, to learning an approximately revenue-maximizing auction from data. We introduce $t$-level auctions to interpolate between simple auctions, such as welfare maximization with reserve prices, and optimal auctions, thereby balancing the competing demands of expressivity and simplicity. We prove that such auctions have small representation error, in the sense that for every product distribution $F$ over bidders' valuations, there exists a $t$-level auction with small $t$ and expected revenue close to optimal. We show that the set of $t$-level auctions has modest pseudo-dimension (for polynomial $t$) and therefore leads to small learning error. One consequence of our results is that, in arbitrary single-parameter settings, one can learn a mechanism with expected revenue arbitrarily close to optimal from a polynomial number of samples.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Approximately Stable, School Optimal, and Student-Truthful Many-to-One Matchings (via Differential Privacy)

We present a mechanism for computing asymptotically stable school optimal matchings, while guaranteeing that it is an asymptotic dominant strategy for every student to report their true preferences to the mechanism. Our main tool in this endeavor is differential privacy: we give an algorithm that coordinates a stable matching using differentially private signals, which lead to our truthfulness guarantee. This is the first setting in which it is known how to achieve nontrivial truthfulness guarantees for students when computing school optimal matchings, assuming worst- case preferences (for schools and students) in large markets.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Learning Valuation Distributions from Partial Observation

Auction theory traditionally assumes that bidders' valuation distributions are known to the auctioneer, such as in the celebrated, revenue-optimal Myerson auction. However, this theory does not describe how the auctioneer comes to possess this information. Recently, Cole and Roughgarden [2014] showed that an approximation based on a finite sample of independent draws from each bidder's distribution is sufficient to produce a near-optimal auction. In this work, we consider the problem of learning bidders' valuation distributions from much weaker forms of observations. Specifically, we consider a setting where there is a repeated, sealed-bid auction with $n$ bidders, but all we observe for each round is who won, but not how much they bid or paid. We can also participate (i.e., submit a bid) ourselves, and observe when we win. From this information, our goal is to (approximately) recover the inherently recoverable part of the underlying bid distributions. We also consider extensions where different subsets of bidders participate in each round, and where bidders' valuations have a common-value component added to their independent private values.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Learning What's going on: reconstructing preferences and priorities from opaque transactions

We consider a setting where $n$ buyers, with combinatorial preferences over $m$ items, and a seller, running a priority-based allocation mechanism, repeatedly interact. Our goal, from observing limited information about the results of these interactions, is to reconstruct both the preferences of the buyers and the mechanism of the seller. More specifically, we consider an online setting where at each stage, a subset of the buyers arrive and are allocated items, according to some unknown priority that the seller has among the buyers. Our learning algorithm observes only which buyers arrive and the allocation produced (or some function of the allocation, such as just which buyers received positive utility and which did not), and its goal is to predict the outcome for future subsets of buyers. For this task, the learning algorithm needs to reconstruct both the priority among the buyers and the preferences of each buyer. We derive mistake bound algorithms for additive, unit-demand and single minded buyers. We also consider the case where buyers' utilities for a fixed bundle can change between stages due to different (observed) prices. Our algorithms are efficient both in computation time and in the maximum number of mistakes (both polynomial in the number of buyers and items).

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preprint2014arXiv

Privacy-Preserving Public Information for Sequential Games

In settings with incomplete information, players can find it difficult to coordinate to find states with good social welfare. For example, in financial settings, if a collection of financial firms have limited information about each other's strategies, some large number of them may choose the same high-risk investment in hopes of high returns. While this might be acceptable in some cases, the economy can be hurt badly if many firms make investments in the same risky market segment and it fails. One reason why many firms might end up choosing the same segment is that they do not have information about other firms' investments (imperfect information may lead to `bad' game states). Directly reporting all players' investments, however, raises confidentiality concerns for both individuals and institutions. In this paper, we explore whether information about the game-state can be publicly announced in a manner that maintains the privacy of the actions of the players, and still suffices to deter players from reaching bad game-states. We show that in many games of interest, it is possible for players to avoid these bad states with the help of privacy-preserving, publicly-announced information. We model behavior of players in this imperfect information setting in two ways -- greedy and undominated strategic behaviours, and we prove guarantees on social welfare that certain kinds of privacy-preserving information can help attain. Furthermore, we design a counter with improved privacy guarantees under continual observation.

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preprint2013arXiv

Draft Auctions

We introduce draft auctions, which is a sequential auction format where at each iteration players bid for the right to buy items at a fixed price. We show that draft auctions offer an exponential improvement in social welfare at equilibrium over sequential item auctions where predetermined items are auctioned at each time step. Specifically, we show that for any subadditive valuation the social welfare at equilibrium is an $O(\log^2(m))$-approximation to the optimal social welfare, where $m$ is the number of items. We also provide tighter approximation results for several subclasses. Our welfare guarantees hold for Bayes-Nash equilibria and for no-regret learning outcomes, via the smooth-mechanism framework. Of independent interest, our techniques show that in a combinatorial auction setting, efficiency guarantees of a mechanism via smoothness for a very restricted class of cardinality valuations, extend with a small degradation, to subadditive valuations, the largest complement-free class of valuations. Variants of draft auctions have been used in practice and have been experimentally shown to outperform other auctions. Our results provide a theoretical justification.

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preprint2012arXiv

Additive Approximation for Near-Perfect Phylogeny Construction

We study the problem of constructing phylogenetic trees for a given set of species. The problem is formulated as that of finding a minimum Steiner tree on $n$ points over the Boolean hypercube of dimension $d$. It is known that an optimal tree can be found in linear time if the given dataset has a perfect phylogeny, i.e. cost of the optimal phylogeny is exactly $d$. Moreover, if the data has a near-perfect phylogeny, i.e. the cost of the optimal Steiner tree is $d+q$, it is known that an exact solution can be found in running time which is polynomial in the number of species and $d$, yet exponential in $q$. In this work, we give a polynomial-time algorithm (in both $d$ and $q$) that finds a phylogenetic tree of cost $d+O(q^2)$. This provides the best guarantees known - namely, a $(1+o(1))$-approximation - for the case $\log(d) \ll q \ll \sqrt{d}$, broadening the range of settings for which near-optimal solutions can be efficiently found. We also discuss the motivation and reasoning for studying such additive approximations.

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