The internet has become the main source of data to train modern text-to-image or vision-language models, yet it is increasingly unclear whether web-scale data collection practices for training AI systems adequately respect data owners' wishes. Ignoring the owner's indication of consent around data usage not only raises ethical concerns but also has recently been elevated into lawsuits around copyright infringement cases. In this work, we aim to reveal information about data owners' consent to AI scraping and training, and study how it's expressed in DataComp, a popular dataset of 12.8 billion text-image pairs. We examine both the sample-level information, including the copyright notice, watermarking, and metadata, and the web-domain-level information, such as a site's Terms of Service (ToS) and Robots Exclusion Protocol. We estimate at least 122M of samples exhibit some indication of copyright notice in CommonPool, and find that 60% of the samples in the top 50 domains come from websites with ToS that prohibit scraping. Furthermore, we estimate 9-13% with 95% confidence interval of samples from CommonPool to contain watermarks, where existing watermark detection methods fail to capture them in high fidelity. Our holistic methods and findings show that data owners rely on various channels to convey data consent, of which current AI data collection pipelines do not entirely respect. These findings highlight the limitations of the current dataset curation/release practice and the need for a unified data consent framework taking AI purposes into consideration.

We investigate the problem of designing differentially private (DP), revenue-maximizing single item auction. Specifically, we consider broadly applicable settings in mechanism design where agents' valuation distributions are **independent**, **non-identical**, and can be either **bounded** or **unbounded**. Our goal is to design such auctions with **pure**, i.e., $(\epsilon,0)$ privacy in polynomial time. In this paper, we propose two computationally efficient auction learning framework that achieves **pure** privacy under bounded and unbounded distribution settings. These frameworks reduces the problem of privately releasing a revenue-maximizing auction to the private estimation of pre-specified quantiles. Our solutions increase the running time by polylog factors compared to the non-private version. As an application, we show how to extend our results to the multi-round online auction setting with non-myopic bidders. To our best knowledge, this paper is the first to efficiently deliver a Myerson auction with **pure** privacy and near-optimal revenue, and the first to provide such auctions for **unbounded** distributions.

Numerous online services are data-driven: the behavior of users affects the system’s parameters, and the system’s parameters affect the users’ experience of the service, which in turn affects the way users may interact with the system. For example, people may choose to use a service only for tasks that already works well, or they may choose to switch to a different service. These adaptations influence the ability of a system to learn about a population of users and tasks in order to improve its performance broadly. In this work, we analyze a class of such dynamics—where users allocate their participation amongst services to reduce the individual risk they experience, and services update their model parameters to reduce the service’s risk on their current user population. We refer to these dynamics as \emph{risk-reducing}, which cover a broad class of common model updates including gradient descent and multiplicative weights. For this general class of dynamics, we show that asymptotically stable equilibria are always segmented, with sub-populations allocated to a single learner. Under mild assumptions, the utilitarian social optimum is a stable equilibrium. In contrast to previous work, which shows that repeated risk minimization can result in representation disparity and high overall loss with a single learner (Hashimoto et al., 2018; Miller et al., 2021), we find that repeated myopic updates with multiple learners lead to better outcomes. We illustrate the phenomena via a simulated example initialized from real data.

Machine unlearning is motivated by principles of data autonomy. The premise is that a person can request to have their data's influence removed from deployed models, and those models should be updated as if they were retrained without the person's data. We show that these updates expose individuals to high-accuracy reconstruction attacks which allow the attacker to recover their data in its entirety, even when the original models are so simple that privacy risk might not otherwise have been a concern. We show how to mount a near-perfect attack on the deleted data point from linear regression models. We then generalize our attack to other loss functions and architectures, and empirically demonstrate the effectiveness of our attacks across a wide range of datasets (capturing both tabular and image data). Our work highlights that privacy risk is significant even for extremely simple model classes when individuals can request deletion of their data from the model.

This paper investigates ML systems serving a group of users, with multiple models/services, each aimed at specializing to a sub-group of users. We consider settings where upon deploying a set of services, users choose the one minimizing their personal losses and the learner iteratively learns by interacting with diverse users. Prior research shows that the outcomes of learning dynamics, which comprise both the services' adjustments and users' service selections, hinge significantly on the initial conditions. However, finding good initial conditions faces two main challenges: (i) \emph{Bandit feedback:} Typically, data on user preferences are not available before deploying services and observing user behavior; (ii) \emph{Suboptimal local solutions:} The total loss landscape (i.e., the sum of loss functions across all users and services) is not convex and gradient-based algorithms can get stuck in poor local minima. We address these challenges with a randomized algorithm to adaptively select a minimal set of users for data collection in order to initialize a set of services. Under mild assumptions on the loss functions, we prove that our initialization leads to a total loss within a factor of the \textit{globally optimal total loss,with complete user preference data}, and this factor scales logarithmically in the number of services. This result is a generalization of the well-known $k$-means++ guarantee to a broad problem class which is also of independent interest. The theory is complemented by experiments on real as well as semi-synthetic datasets.

In critical machine learning applications, ensuring fairness is essential to avoid perpetuating social inequities. In this work, we address the challenges of reducing bias and improving accuracy in data-scarce environments, where the cost of collecting labeled data prohibits the use of large, labeled datasets. In such settings, active learning promises to maximize marginal accuracy gains of small amounts of labeled data. However, existing applications of active learning for fairness fail to deliver on this, typically requiring large labeled datasets, or failing to ensure the desired fairness tolerance is met on the population distribution. To address such limitations, we introduce an innovative active learning framework that combines an exploration procedure inspired by posterior sampling with a fair classification subroutine. We demonstrate that this framework performs effectively in very data-scarce regimes, maximizing accuracy while satisfying fairness constraints with high probability. We evaluate our proposed approach using well-established real-world benchmark datasets and compare it against state-of-the-art methods, demonstrating its effectiveness in producing fair models, and improvement over existing methods.

We show how to take a regression function that is appropriately multicalibrated and efficiently post-process it into an approximately error minimizing classifier satisfying a large variety of fairness constraints. The post-processing requires no labeled data, and only a modest amount of unlabeled data and computation. The computational and sample complexity requirements of computing are comparable to the requirements for solving a single fair learning task optimally, but it can in fact be used to solve many different downstream fairness-constrained learning problems efficiently. Our post-processing method easily handles intersecting groups, generalizing prior work on post-processing regression functions to satisfy fairness constraints that only applied to disjoint groups. Our work extends recent work showing that multicalibrated regression functions are omnipredictors (i.e. can be post-processed to optimally solve unconstrained ERM problems) to constrained optimization problems.

Algorithmic audits of industry face recognition models have recently incentivized companies to diversify their data collection methods, which in turn has reduced error disparities along demographic lines, such as gender or race. We argue that it is important to understand exactly how various forms of targeted data collection mitigate performance disparities in these updated face recognition models. We propose an empirical framework to assess the impact of additional dataset collection targeted towards various racial groups. We apply our framework to three racially-annotated benchmark datasets using three standard face recognition models. Our findings empirically validate the notion that the introduction of data from the demographic group with the initially-lowest performance improves performance on that group significantly more than adding from other groups. We also observe that in all settings, the introduction of data from a previously omitted group does not harm the performance of other groups. Furthermore, investigation of feature embeddings reveals that performance increases are associated with a larger separation among images of different identities. Despite the commonalities we observe across datasets, we also find key differences: for example, in one dataset, training on one racial group generalizes well across all groups. These differences speak to the criticality of re-applying empirical evaluation methods, such as the methods in this work, when introducing new datasets or models.

In this talk, I’ll describe some recent work outlining how distribution shifts are fundamental to working with human-centric data. Some of these shifts come from attempting to "join" datasets gathered in different contexts, others may be the result of people’s preferences affecting which data they provide to which systems, and even more can arise when peoples’ preferences themselves are shaped by ML systems’ recommendations. Each of these types of shift require different modeling and analysis to more accurately predict the behavior of ML pipelines deployed in a way where they interact repeatedly with people who care about their predictions.

Membership inference attacks are designed to determine, using black box access to trained models, whether a particular example was used in training or not. Membership inference can be formalized as a hypothesis testing problem. The most effective existing attacks estimate the distribution of some test statistic (usually the model's confidence on the true label) on points that were (and were not) used in training by training many \emph{shadow models}---i.e. models of the same architecture as the model being attacked, trained on a random subsample of data. While effective, these attacks are extremely computationally expensive, especially when the model under attack is large. \footnotetext[0]{ Martin and Shuai are the lead authors, and other authors are ordered alphabetically. \{maberlop,shuat\}@amazon.com} We introduce a new class of attacks based on performing quantile regression on the distribution of confidence scores induced by the model under attack on points that are not used in training. We show that our method is competitive with state-of-the-art shadow model attacks, while requiring substantially less compute because our attack requires training only a single model. Moreover, unlike shadow model attacks, our proposed attack does not require any knowledge of the architecture of the model under attack and is therefore truly ``black-box". We show the efficacy of this approach in an extensive series of experiments on various datasets and model architectures. Our code is available at \href{https://github.com/amazon-science/quantile-mia}{github.com/amazon-science/quantile-mia.}

The remarkable attention which fair clustering has received in the last few years has resulted in a significant number of different notions of fairness. Despite the fact that these notions are well-justified, they are often motivated and studied in a disjoint manner where one fairness desideratum is considered exclusively in isolation from the others. This leaves the understanding of the relations between different fairness notions as an important open problem in fair clustering. In this paper, we take the first step in this direction. Specifically, we consider the two most prominent demographic representation fairness notions in clustering: (1) Group Fairness ($\textbf{GF}$), where the different demographic groups are supposed to have close to population-level representation in each cluster and (2) Diversity in Center Selection ($\textbf{DS}$), where the selected centers are supposed to have close to population-level representation of each group. We show that given a constant approximation algorithm for one constraint ($\textbf{GF}$ or $\textbf{DS}$ only) we can obtain a constant approximation solution that satisfies both constraints simultaneously. Interestingly, we prove that any given solution that satisfies the $\textbf{GF}$ constraint can always be post-processed at a bounded degradation to the clustering cost to additionally satisfy the $\textbf{DS}$ constraint while the same statement is not true given a solution that satisfies $\textbf{DS}$ instead. Furthermore, we show that both $\textbf{GF}$ and $\textbf{DS}$ are incompatible (having an empty feasibility set in the worst case) with a collection of other distance-based fairness notions. Finally, we carry experiments to validate our theoretical findings.

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.

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.

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 safe 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.

The design of content recommendation systems underpins many online platforms: social media feeds, online news aggregators, and audio/video hosting websites all choose how best to organize an enormous amount of content for users to consume. 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.

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.

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.

In data summarization we want to choose $k$ prototypes in order to summarize a data set. We study a setting where the data set comprises several demographic groups and we are restricted to choose $k_i$ prototypes belonging to group $i$. A common approach to the problem without the fairness constraint is to optimize a centroid-based clustering objective such as $k$-center. A natural extension then is to incorporate the fairness constraint into the clustering problem. Existing algorithms for doing so run in time super-quadratic in the size of the data set, which is in contrast to the standard $k$-center problem being approximable in linear time. In this paper, we resolve this gap by providing a simple approximation algorithm for the $k$-center problem under the fairness constraint with running time linear in the size of the data set and $k$. If the number of demographic groups is small, the approximation guarantee of our algorithm only incurs a constant-factor overhead.

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.

We study a network formation game where agents receive benefits by forming connections to other agents but also incur both direct and indirect costs from the formed connections. Specifically, once the agents have purchased their connections, an attack starts at a randomly chosen vertex in the network and spreads according to the independent cascade model with a fixed probability, destroying any infected agents. The utility or welfare of an agent in our game is defined to be the expected size of the agent's connected component post-attack minus her expenditure in forming connections. Our goal is to understand the properties of the equilibrium networks formed in this game. Our first result concerns the edge density of equilibrium networks. A network connection increases both the likelihood of remaining connected to other agents after an attack as well the likelihood of getting infected by a cascading spread of infection. We show that the latter concern primarily prevails and any equilibrium network in our game contains only $O(n\log n)$ edges where $n$ denotes the number of agents. On the other hand, there are equilibrium networks that contain $\Omega(n)$ edges showing that our edge density bound is tight up to a logarithmic factor. Our second result shows that the presence of attack and its spread through a cascade does not significantly lower social welfare as long as the network is not too dense. We show that any non-trivial equilibrium network with $O(n)$ edges has $\Theta(n^2)$ social welfare, asymptotically similar to the social welfare guarantee in the game without any attacks.

We study the problem of learning Bayesian-optimal revenue-maximizing auctions. The classical approach to maximizing revenue requires a known prior distribution on the demand of the bidders, although recent work has shown how to replace the knowledge of a prior distribution with a polynomial sample. However, in an online setting, when buyers can participate in multiple rounds, standard learning techniques are susceptible to \emph{strategic overfitting}: bidders can improve their long-term wellbeing by manipulating the trajectory of the learning algorithm in earlier rounds. For example, they may be able to strategically adjust their behavior in earlier rounds to achieve lower, more favorable future prices. Such non-truthful behavior can hinder learning and harm revenue. In this paper, we combine tools from differential privacy, mechanism design, and sample complexity to give a repeated auction that (1) learns bidder demand from past data, (2) is approximately revenue-optimal, and (3) strategically robust, as it incentivizes bidders to behave truthfully.

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 the Fair-PCA problem introduced by Samadi et al. [NeurIPS18] and the Nash Social Welfare (NSW) problem. In the Fair-PCA problem, 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 maximum reconstruction error of any one group is minimized. In NSW the goal is to maximize the product of the individual variances of the groups achieved by the common low-dimensinal space. Our main result is an exact polynomial-time algorithm for the two-criteria 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, resolving an open problem of Samadi et al.[NeurIPS18], 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 the results of several experiments indicating improved performance and generalized application of our algorithm on real-world datasets.

We study fairness in linear bandit problems. Starting from the notion of meritocratic fairness introduced in~\citeJKMR16, 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.

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. In such settings, one might like to run a ``greedy'' algorithm, which always makes the 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 in slightly perturbed environments, exploration and exploitation need not be in conflict in the linear setting.

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.

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.

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 qualifie ones [8].

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 the most prominent examples of “simple” auctions, including anonymous and non-anonymous item and bundle pricings, with either a single or multiple buyers. The first step of the framework is to show that the set of auction allocation rules have a low-dimensional representation. The second step shows that, across the subset of auctions that share the same allocations on a given set of samples, the auction revenue varies in a low-dimensional way. Our results effectively imply that whenever it is 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.

We introduce the study of fairness in multi-armed bandit problems. Our fairness definition demands that, given a pool of applicants, a worse applicant is never favored over a better one, despite a learning algorithm’s uncertainty over the true payoffs. In the classic stochastic bandits problem we provide a provably fair algorithm based on “chained” confidence intervals, and prove 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, providing a strong separation between fair and unfair learning that 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 vice versa. 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.

We study the efficiency of simple auctions in the presence of complements. Devanur et al. [2015] 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 [Feige et al. 2015], where the degree of complementarity d is captured by the maximum number of neighbours 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(d2 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(√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.

Walrasian equilibrium prices have a remarkable property: they allow each buyer to purchase a bundle of goods that she finds the most desirable, while guaranteeing that the induced allocation over all buyers will globally maximize social welfare. However, this clean story has two caveats. * First, the prices may induce indifferences. In fact, the minimal equilibrium prices necessarily induce indifferences. Accordingly, buyers may need to coordinate with one another to arrive at a socially optimal outcome---the prices alone are not sufficient to coordinate the market. * Second, although natural procedures converge to Walrasian equilibrium prices on a fixed population, in practice buyers typically observe prices without participating in a price computation process. These prices cannot be perfect Walrasian equilibrium prices, but instead somehow reflect distributional information about the market. To better understand the performance of Walrasian prices when facing these two problems, we give two results. First, we propose a mild genericity condition on valuations under which the minimal Walrasian equilibrium prices induce allocations which result in low over-demand, no matter how the buyers break ties. In fact, under genericity the over-demand of any good can be bounded by 1, which is the best possible at the minimal prices. We demonstrate our results for unit demand valuations and give an extension to matroid based valuations (MBV), conjectured to be equivalent to gross substitute valuations (GS). Second, we use techniques from learning theory to argue that the over-demand and welfare induced by a price vector converge to their expectations uniformly over the class of all price vectors, with respective sample complexity linear and quadratic in the number of goods in the market. These results make no assumption on the form of the valuation functions. These two results imply that under a mild genericity condition, the exact Walrasian equilibrium prices computed in a market are guaranteed to induce both low over-demand and high welfare when used in a new market where agents are sampled independently from the same distribution, whenever the number of agents is larger than the number of commodities in the market.

Auction theory traditionally assumes that bidders’ val- uation distributions are known to the auctioneer, such as in the celebrated, revenue-optimal Myerson auc- tion (Myerson 1981). However, this theory does not de- scribe how the auctioneer comes to possess this infor- mation. Recently work (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’ val- uation distributions from much weaker forms of obser- vations. 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.

In settings with incomplete information, players can find it difficult to coordinate to find states with good social welfare. For instance, one of the main reasons behind the recent financial crisis was found to be the lack of market transparency, which made it difficult for financial firms to accurately measure the risks and returns of their investments. Although regulators may have access to firms' investment decisions, directly reporting all firms' actions raises confiden- tiality concerns for both individuals and institutions. The natural question, therefore, is whether it is possible for the regulatory agencies to publish some information that, on one hand, helps the financial firms understand the risks of their investments better, and, at the same time, preserves the privacy of their investment decisions. More generally, when can the publication of privacy-preserving information about the state of the game improve overall outcomes such as social welfare? In this paper, we explore this question in a sequential resource-sharing game where the value gained by a player on choosing a resource depends on the number of other players who have chosen that resource in the past. Without any knowledge of the actions of the past players, the social welfare attained in this game can be arbitrarily bad. We show, however, that it is possible for the players to achieve good social welfare with the help of privacy-preserving, publicly-announced information. We model the behavior of players in this imperfect information setting in two ways -- greedy and undominated strategic behaviours, and we prove guarantees about the social welfare that certain kinds of privacy-preserving information can help attain. To achieve the social welfare guarantees, we design a counter with improved privacy guarantees under continual observation. In addition to the resource-sharing game, we study the main question for other games including sequential versions of the cut, machine-scheduling and cost-sharing games, and games where the value attained by a player on a particular action is not only a function of the actions of the past players but also of the actions of the future players.

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.

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).

We introduce single-bid auctions as a new format for combinatorial auctions. In single-bid auctions, each bidder submits a single real-valued bid for the right to buy items at a fixed price. Contrary to other simple auction formats, such as simultaneous or sequential single-item auctions, bidders can implement no-regret learning strategies for single-bid auctions in polynomial time. Price of anarchy bounds for correlated equilibria concepts in single-bid auctions therefore have more bite than their counterparts for auctions and equilibria for which learning is not known to be computationally tractable (or worse, known to be computationally intractable [Cai and Papadimitriou 2014; Dobzinski et al. 2015] this end, we show that for any subadditive valuations the social welfare at equilibrium is an O(log 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 Nash equilibria and no-regret learning outcomes in both Bayesian and complete information settings 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.

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 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 joint-differential privacy, under which it is known that asymptotically optimal allocations can be computed in two sided markets [Hsu et al. STOC 2014]. We therefore consider a further relaxation that we call marginal-differential privacy --which promises, informally, that the privacy of every agent i is protected from every other agent j ≠ 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.

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.

It is well known that strategic behavior in elections is essentially unavoidable; we therefore ask: how bad can the rational outcome be? We answer this question via the notion of the price of anarchy, using the scores of alternatives as a proxy for their quality and bounding the ratio between the score of the optimal alternative and the score of the winning alternative in Nash equilibrium. Specifically, we are interested in Nash equilibria that are obtained via sequences of rational strategic moves. Focusing on three common voting rules — plurality, veto, and Borda — we provide very positive results for plurality and very negative results for Borda, and place veto in the middle of this spectrum.

We consider the problem of selecting fair divisions of a heterogeneous divisible good among a set of agents. Recent work (Cohler et al., AAAI 2011) focused on designing algorithms for computing maxsum—social welfare maximizing—allocations under the fairness notion of envy-freeness. Maxsum allocations can also be found under alternative notions such as equitability. In this paper, we examine the properties of these allocations. In particular, We provide conditions for when maxsum envy-free or equitable allocations are Pareto optimal and give examples where fairness with Pareto optimality is not possible. We also prove that maxsum envy-free allocations have weakly greater welfare than maxsum equitable allocations when agents have structured valuations, and we derive an approximate version of this inequality for general valuations.

Abstract. Several recent security-typed programming languages allow programmers to express and enforce authorization policies governing access to controlled resources. Policies are expressed as propositions in an authorization logic, and enforced by a type system that requires each access to a sensitive resource to be accompanied by a proof. The securitytyped languages described in the literature, such as Aura and PCML5, have been presented as new, stand-alone language designs. In this paper, we instead show how to embed a security-typed programming language within an existing dependently typed programming language, Agda. This language-design strategy allows us to inherit both the metatheoretic results, such as type safety, and the implementation of the host language. Our embedding consists of the following ingredients: First, we represent the syntax and proofs of an authorization logic, Garg and Pfenning’s BL0, using dependent types. Second, we implement a proof search procedure, based on a focused sequent calculus, to ease the burden of constructing proofs. Third, we define an indexed monad of computations on behalf of a principal, with proof-carrying primitive operations. Our work shows that a dependently typed language can be used to prototype a security-typed language, and contributes to the growing body of literature on using dependently typed languages to construct domain-specific type systems. 1