arXiv subjects

Jamie Morgenstern

Publications and source records attributed to Jamie Morgenstern.

At least 55 records · Page 3Linked to original sources

arXiv2019

Guarantees for Spectral Clustering with Fairness Constraints

Given the widespread popularity of spectral clustering (SC) for partitioning graph data, we study a version of constrained SC in which we try to incorporate the fairness notion proposed by Chierichetti et al. (2017). According to this notion, a clustering is fair if every demographic group is approximately proportionally represented in each cluster. To this end, we develop variants of both normalized and unnormalized constrained SC and show that they help find fairer clusterings on both synthetic and real data. We also provide a rigorous theoretical analysis of our algorithms on a natural variant of the stochastic block model, where $h$ groups have strong inter-group connectivity, but also exhibit a "natural" clustering structure which is fair. We prove that our algorithms can recover this fair clustering with high probability.

stat.ML↗

arXiv2019

Predictive Inequity in Object Detection

In this work, we investigate whether state-of-the-art object detection systems have equitable predictive performance on pedestrians with different skin tones. This work is motivated by many recent examples of ML and vision systems displaying higher error rates for certain demographic groups than others. We annotate an existing large scale dataset which contains pedestrians, BDD100K, with Fitzpatrick skin tones in ranges [1-3] or [4-6]. We then provide an in-depth comparative analysis of performance between these two skin tone groupings, finding that neither time of day nor occlusion explain this behavior, suggesting this disparity is not merely the result of pedestrians in the 4-6 range appearing in more difficult scenes for detection. We investigate to what extent time of day, occlusion, and reweighting the supervised loss during training affect this predictive bias.

cs.CV↗

arXiv2018

The Price of Fair PCA: One Extra Dimension

We investigate whether the standard dimensionality reduction technique of PCA inadvertently produces data representations with different fidelity for two different populations. We show on several real-world data sets, PCA has higher reconstruction error on population A than on B (for example, women versus men or lower- versus higher-educated individuals). This can happen even when the data set has a similar number of samples from A and B. This motivates our study of dimensionality reduction techniques which maintain similar fidelity for A and B. We define the notion of Fair PCA and give a polynomial-time algorithm for finding a low dimensional representation of the data which is nearly-optimal with respect to this measure. Finally, we show on real-world data sets that our algorithm can be used to efficiently generate a fair low dimensional representation of the data.

cs.LG↗

arXiv2018

A Smoothed Analysis of the Greedy Algorithm for the Linear Contextual Bandit Problem

Bandit learning is characterized by the tension between long-term exploration and short-term exploitation. However, as has recently been noted, in settings in which the choices of the learning algorithm correspond to important decisions about individual people (such as criminal recidivism prediction, lending, and sequential drug trials), exploration corresponds to explicitly sacrificing the well-being of one individual for the potential future benefit of others. This raises a fairness concern. In such settings, one might like to run a "greedy" algorithm, which always makes the (myopically) optimal decision for the individuals at hand - but doing this can result in a catastrophic failure to learn. In this paper, we consider the linear contextual bandit problem and revisit the performance of the greedy algorithm. We give a smoothed analysis, showing that even when contexts may be chosen by an adversary, small perturbations of the adversary's choices suffice for the algorithm to achieve "no regret", perhaps (depending on the specifics of the setting) with a constant amount of initial training data. This suggests that "generically" (i.e. in slightly perturbed environments), exploration and exploitation need not be in conflict in the linear setting.

cs.LG↗

arXiv2017

Fairness in Reinforcement Learning

We initiate the study of fairness in reinforcement learning, where the actions of a learning algorithm may affect its environment and future rewards. Our fairness constraint requires that an algorithm never prefers one action over another if the long-term (discounted) reward of choosing the latter action is higher. Our first result is negative: despite the fact that fairness is consistent with the optimal policy, any learning algorithm satisfying fairness must take time exponential in the number of states to achieve non-trivial approximation to the optimal policy. We then provide a provably fair polynomial time algorithm under an approximate notion of fairness, thus establishing an exponential gap between exact and approximate fairness

cs.LG↗

arXiv2017

Fair Algorithms for Infinite and Contextual Bandits

We study fairness in linear bandit problems. Starting from the notion of meritocratic fairness introduced in Joseph et al. [2016], we carry out a more refined analysis of a more general problem, achieving better performance guarantees with fewer modelling assumptions on the number and structure of available choices as well as the number selected. We also analyze the previously-unstudied question of fairness in infinite linear bandit problems, obtaining instance-dependent regret upper bounds as well as lower bounds demonstrating that this instance-dependence is necessary. The result is a framework for meritocratic fairness in an online linear setting that is substantially more powerful, general, and realistic than the current state of the art.

cs.LG↗

arXiv2017

A Convex Framework for Fair Regression

We introduce a flexible family of fairness regularizers for (linear and logistic) regression problems. These regularizers all enjoy convexity, permitting fast optimization, and they span the rang from notions of group fairness to strong individual fairness. By varying the weight on the fairness regularizer, we can compute the efficient frontier of the accuracy-fairness trade-off on any given dataset, and we measure the severity of this trade-off via a numerical quantity we call the Price of Fairness (PoF). The centerpiece of our results is an extensive comparative study of the PoF across six different datasets in which fairness is a primary consideration.

cs.LG↗

arXiv2017

Fairness Incentives for Myopic Agents

We consider settings in which we wish to incentivize myopic agents (such as Airbnb landlords, who may emphasize short-term profits and property safety) to treat arriving clients fairly, in order to prevent overall discrimination against individuals or groups. We model such settings in both classical and contextual bandit models in which the myopic agents maximize rewards according to current empirical averages, but are also amenable to exogenous payments that may cause them to alter their choices. Our notion of fairness asks that more qualified individuals are never (probabilistically) preferred over less qualified ones [Joseph et al]. We investigate whether it is possible to design inexpensive {subsidy} or payment schemes for a principal to motivate myopic agents to play fairly in all or almost all rounds. When the principal has full information about the state of the myopic agents, we show it is possible to induce fair play on every round with a subsidy scheme of total cost $o(T)$ (for the classic setting with $k$ arms, $\tilde{O}(\sqrt{k^3T})$, and for the $d$-dimensional linear contextual setting $\tilde{O}(d\sqrt{k^3 T})$). If the principal has much more limited information (as might often be the case for an external regulator or watchdog), and only observes the number of rounds in which members from each of the $k$ groups were selected, but not the empirical estimates maintained by the myopic agent, the design of such a scheme becomes more complex. We show both positive and negative results in the classic and linear bandit settings by upper and lower bounding the cost of fair subsidy schemes.

cs.GT↗

arXiv2016

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.

cs.GT↗

arXiv2016

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

cs.LG↗

arXiv2016

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.

cs.GT↗

arXiv2016

Do Prices Coordinate Markets?

Walrasian equilibrium prices can be said to coordinate markets: They support a welfare optimal allocation in which each buyer is buying bundle of goods that is individually most preferred. However, this clean story has two caveats. First, the prices alone are not sufficient to coordinate the market, and buyers may need to select among their most preferred bundles in a coordinated way to find a feasible allocation. Second, we don't in practice expect to encounter exact equilibrium prices tailored to the market, but instead only approximate prices, somehow encoding "distributional" information about the market. How well do prices work to coordinate markets when tie-breaking is not coordinated, and they encode only distributional information? We answer this question. First, we provide a genericity condition such that for buyers with Matroid Based Valuations, overdemand with respect to equilibrium prices is at most 1, independent of the supply of goods, even when tie-breaking is done in an uncoordinated fashion. Second, we provide learning-theoretic results that show that such prices are robust to changing the buyers in the market, so long as all buyers are sampled from the same (unknown) distribution.

cs.GT↗

arXiv2016

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).

cs.LG↗

arXiv2015

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.

cs.GT↗

arXiv2015

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.

cs.GT↗

arXiv2014

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.

cs.GT↗

arXiv2014

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.

cs.GT↗

arXiv2014

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).

cs.GT↗