We investigate Learning from Label Proportions (LLP), a partial information setting where examples in a training set are grouped into bags, and only aggregate label values in each bag are available. Despite the partial observability, the goal is still to achieve small regret at the level of individual examples. We give results on the sample complexity of LLP under square loss, showing that our sample complexity is essentially optimal. From an algorithmic viewpoint, we rely on carefully designed variants of Empirical Risk Minimization, and Stochastic Gradient Descent algorithms, combined with ad hoc variance reduction techniques. On one hand, our theoretical results improve in important ways on the existing literature on LLP, specifically in the way the sample complexity depends on the bag size. On the other hand, we validate our algorithmic solutions on several datasets, demonstrating improved empirical performance (better accuracy for less samples) against recent baselines.

The analysis of the privacy properties of Privacy-Preserving Ads APIs is an area of research that has received strong interest from academics, industry, and regulators.Despite this interest, the empirical study of these methods is severely hindered by the lack of publicly available data.Reliable empirical analysis of the privacy properties of an API, in fact, requires access to a dataset consisting of realistic API outputs for a large collection of users; however, privacy concerns prevent the general release of such data to the public.In this work, we address this problem by developing a novel methodology to construct synthetic API outputs that are simultaneously realistic enough to enable accurate study and provide strong privacy protections.We focus on one of the Privacy-Preserving Ads APIs: the Topics API, part of Google Chrome's Privacy Sandbox, which enables interest-based advertising without relying on third-party cookies.We developed a methodology to generate a differentially-private dataset that closely matches the re-identification risk properties of the real Topics API data.The use of differential privacy provides strong theoretical bounds on the leakage of private user information from this release.Our methodology is based on first computing a large number of differentially-private statistics describing how output API traces evolve over time.Then, we design a parameterized distribution over sequences of API traces and optimize its parameters so that they closely match the statistics obtained.Finally, we create the synthetic data by drawing from this distribution.Our work is complemented by an open-source release of the anonymized dataset obtained by this methodology.We hope this will enable external researchers to analyze the API in-depth and replicate prior and future work on a realistic large-scale dataset.

In the private set union problem each user owns a bag of at most $k$ items (from some large universe of items), and we are interested in computing the union of the items in the bags of all of the users. This is trivial without privacy, but a differentially private algorithm must be careful about reporting items contained in only a small number of bags. We consider differentially private algorithms that always report a subset of the union, and define the utility of an algorithm to be the expected size of the subset that it reports. Because the achievable utility varies significantly with the dataset, we introduce the *utility ratio*, which normalizes utility by a dataset-specific upper bound and characterizes a mechanism by its lowest normalized utility across all datasets. We then develop algorithms with guaranteed utility ratios and complement them with bounds on the best possible utility ratio. Prior work has shown that a single algorithm can be simultaneously optimal for all datasets when $k=1$, but we show that instance-optimal algorithms do not exist when $k>1$, and characterize how performance degrades as $k$ grows. At the same time, we design a private algorithm that achieves the maximum possible utility, regardless of $k$, when the item histogram matches a prior prediction (for instance, from a previous data release) and degrades gracefully with the $L_\infty$ distance between the prediction and the actual histogram when the prediction is imperfect.

We propose reconstruction advantage measures to audit label privatization mechanisms. A reconstruction advantage measure quantifies the increase in an attacker's ability to infer the true label of an unlabeled example when provided with a private version of the labels in a dataset (e.g., aggregate of labels from different users or noisy labels output by randomized response), compared to an attacker that only observes the feature vectors, but may have prior knowledge of the correlation between features and labels. We consider two such auditing measures: one additive, and on multiplicative. These cover previous approaches taken in the literature on empirical auditing and differential privacy. These measures allow us to place a variety of proposed privatization schemes---some differentially private, some not---on the same footing. We analyze these measures theoretically under a distributional model which, we claim, encapsulates reasonable adversarial settings. We also quantify their behavior empirically on real and simulated prediction tasks. Across a range of experimental settings, we find that differentially private schemes dominate or match the privacy-utility tradeoff of more heuristic approaches.

Algorithms often have tunable parameters that impact performance metrics such as runtime and solution quality. For many algorithms used in practice, no parameter settings admit meaningful worst-case bounds, so the parameters are made available for the user to tune. Alternatively, parameters may be tuned implicitly within the proof of a worst-case approximation ratio or runtime bound. Worst-case instances, however, may be rare or nonexistent in practice. A growing body of research has demonstrated that a data-driven approach to parameter tuning can lead to significant improvements in performance. This approach uses a training set of problem instances sampled from an unknown, application-specific distribution and returns a parameter setting with strong average performance on the training set. We provide techniques for deriving generalization guarantees that bound the difference between the algorithm’s average performance over the training set and its expected performance on the unknown distribution. Our results apply no matter how the parameters are tuned, be it via an automated or manual approach. The challenge is that for many types of algorithms, performance is a volatile function of the parameters: slightly perturbing the parameters can cause a large change in behavior. Prior research [e.g., 12 , 16 , 20 , 62 ] has proved generalization bounds by employing case-by-case analyses of greedy algorithms, clustering algorithms, integer programming algorithms, and selling mechanisms. We streamline these analyses with a general theorem that applies whenever an algorithm’s performance is a piecewise-constant, piecewise-linear, or—more generally— piecewise-structured function of its parameters. Our results, which are tight up to logarithmic factors in the worst case, also imply novel bounds for configuring dynamic programming algorithms from computational biology.

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and non-convex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction problems. Tree search algorithms come with a variety of tunable parameters that are notoriously challenging to tune by hand. A growing body of research has demonstrated the power of using a data-driven approach to automatically optimize the parameters of tree search algorithms. These techniques use a training set of integer programs sampled from an application-specific instance distribution to find a parameter setting that has strong average performance over the training set. However, with too few samples, a parameter setting may have strong average performance on the training set but poor expected performance on future integer programs from the same application. Our main contribution is to provide the first sample complexity guarantees for tree search parameter tuning. These guarantees bound the number of samples sufficient to ensure that the average performance of tree search over the samples nearly matches its future expected performance on the unknown instance distribution. In particular, the parameters we analyze weight scoring rules used for variable selection. Proving these guarantees is challenging because tree size is a volatile function of these parameters: we prove that, for any discretization (uniform or not) of the parameter space, there exists a distribution over integer programs such that every parameter setting in the discretization results in a tree with exponential expected size, yet there exist parameter settings between the discretized points that result in trees of constant size. In addition, we provide data-dependent guarantees that depend on the volatility of these tree-size functions: our guarantees improve if the tree-size functions can be well approximated by simpler functions. Finally, via experiments, we illustrate that learning an optimal weighting of scoring rules reduces tree size.

We propose a new definition of instance optimality for differentially private estimation algorithms. Our definition requires an optimal algorithm to compete, simultaneously for every dataset $D$, with the best private benchmark algorithm that (a) knows $D$ in advance and (b) is evaluated by its worst-case performance on large subsets of $D$. That is, the benchmark algorithm need not perform well when potentially extreme points are added to $D$; it only has to handle the removal of a small number of real data points that already exist. This makes our benchmark significantly stronger than those proposed in prior work. We nevertheless show, for real-valued datasets, how to construct private algorithms that achieve our notion of instance optimality when estimating a broad class of dataset properties, including means, quantiles, and $\ell_p$-norm minimizers. For means in particular, we provide a detailed analysis and show that our algorithm simultaneously matches or exceeds the asymptotic performance of existing algorithms under a range of distributional assumptions.

When applying differential privacy to sensitive data, we can often improve performance using external information such as other sensitive data, public data, or human priors. We propose to use the learning-augmented algorithms (or algorithms with predictions) framework---previously applied largely to improve time complexity or competitive ratios---as a powerful way of designing and analyzing privacy-preserving methods that can take advantage of such external information to improve utility. This idea is instantiated on the important task of multiple quantile release, for which we derive error guarantees that scale with a natural measure of prediction quality while (almost) recovering state-of-the-art prediction-independent guarantees. Our analysis enjoys several advantages, including minimal assumptions about the data, a natural way of adding robustness, and the provision of useful surrogate losses for two novel ''meta'' algorithms that learn predictions from other (potentially sensitive) data. We conclude with experiments on challenging tasks demonstrating that learning predictions across one or more instances can lead to large error reductions while preserving privacy.

We consider the problem of Learning from Label Proportions (LLP), a weakly supervised classification setup where instances are grouped into i.i.d. “bags”, and only the frequency of class labels at each bag is available. Albeit, the objective of the learner is to achieve low task loss at an individual instance level. Here we propose EASYLLP, a flexible and simple-to-implement debiasing approach based on aggregate labels, which operates on arbitrary loss functions. Our technique allows us to accurately estimate the expected loss of an arbitrary model at an individual level. We elucidate the differences between our method and standard methods based on label proportion matching, in terms of applicability and optimality conditions. We showcase the flexibility of our approach compared to alternatives by applying our method to popular learning frameworks, like Empirical Risk Minimization (ERM) and Stochastic Gradient Descent (SGD) with provable guarantees on instance level performance. Finally, we validate our theoretical results on multiple datasets, empirically illustrating the conditions under which our algorithm is expected to perform better or worse than previous LLP approaches

Existing work on differentially private linear regression typically assumes that end users can precisely set data bounds or algorithmic hyperparameters. End users often struggle to meet these requirements without directly examining the data (and violating privacy). Recent work has attempted to develop solutions that shift these burdens from users to algorithms, but they struggle to provide utility as the feature dimension grows. This work extends these algorithms to higher-dimensional problems by introducing a differentially private feature selection method based on Kendall rank correlation. We prove a utility guarantee for the setting where features are normally distributed and conduct experiments across 25 datasets. We find that adding this private feature selection step before regression significantly broadens the applicability of ``plug-and-play'' private linear regression algorithms at little additional cost to privacy, computation, or decision-making by the end user.

Compact user representations (such as embeddings) form the backbone of personalization services. In this work, we present a new theoretical framework to measure re-identification risk in such user representations. Our framework, based on hypothesis testing, formally bounds the probability that an attacker may be able to obtain the identity of a user from their representation. As an application, we show how our framework is general enough to model important real-world applications such as the Chrome's Topics API for interest-based advertising. We complement our theoretical bounds by showing provably good attack algorithms for re-identification that we use to estimate the re-identification risk in the Topics API. We believe this work provides a rigorous and interpretable notion of re-identification risk and a framework to measure it that can be used to inform real-world applications.

In this paper we initiate the study of financial asset design with fairness as an explicit goal. We consider a variation on the classical problem of optimal portfolio design. In our setting, an individual consumer is specified by her risk tolerance, which corresponds to the variance in returns she is willing to accept in exchange for higher expected returns. We must design a (small) collection of portfolios and assign each consumer to a portfolio at lower or approximately equal risk than her tolerance. Fairness is imposed by demanding that the portfolios designed do not discriminate (in terms of expected returns) against less wealthy clients (or other specified protected groups).

Algorithms often have tunable parameters that impact performance metrics such as runtime and solution quality. For many algorithms used in practice, no parameter settings admit meaningful worst-case bounds, so the parameters are made available for the user to tune. Alternatively, parameters may be tuned implicitly within the proof of a worst-case guarantee. Worst-case instances, however, may be rare or nonexistent in practice. A growing body of research has demonstrated that data-driven algorithm design can lead to significant improvements in performance. This approach uses a training set of problem instances sampled from an unknown, application-specific distribution and returns a parameter setting with strong average performance on the training set.

Optimization in the presence of sharp (non-Lipschitz), unpredictable (w.r.t. time and amount) changes is a challenging and largely unexplored problem of great significance. We consider the class of piecewise Lipschitz functions, which is the most general online setting considered in the literature for the problem, and arises naturally in various combinatorial algorithm selection problems where utility functions can have sharp discontinuities. The usual performance metric of ‘static’ regret minimizes the gap between the payoff accumulated and that of the best fixed point for the entire duration, and thus fails to capture changing environments. Shifting regret is a useful alternative, which allows for up to $s$ environment {\it shifts}. In this work we provide an $O(\sqrt{sdT\log T}+sT^{1-\beta})$ regret bound for $\beta$-dispersed functions, where $\beta$ roughly quantifies the rate at which discontinuities appear in the utility functions in expectation (typically $\beta\ge1/2$ in problems of practical interest \cite{2019arXiv190409014B,balcan2018dispersion}). We also present a lower bound tight up to sub-logarithmic factors. We further obtain improved bounds when selecting from a small pool of experts. We empirically demonstrate a key application of our algorithms to online clustering problems on popular benchmarks.

The covariance matrix of a dataset is a fundamental statistic that can be used for calculating optimum regression weights as well as in many other learning and data analysis settings. For datasets containing private user information, we often want to estimate the covariance matrix in a way that preserves differential privacy. While there are known methods for privately computing the covariance matrix, they all have one of two major shortcomings. Some, like the Gaussian mechanism, only guarantee (epsilon, delta)-differential privacy, leaving a non-trivial probability of privacy failure. Others give strong epsilon-differential privacy guarantees, but are impractical, requiring complicated sampling schemes, and tend to perform poorly on real data. In this work we propose a new epsilon-differentially private algorithm for computing the covariance matrix of a dataset that addresses both of these limitations. We show that it has lower error than existing state-of-the-art approaches, both analytically and empirically. In addition, the algorithm is significantly less complicated than other methods and can be efficiently implemented with rejection sampling.

In classic fair division problems such as cake cutting and rent division, envy-freeness requires that each individual (weakly) prefer his allocation to anyone else's. On a conceptual level, we argue that envy-freeness also provides a compelling notion of fairness for classification tasks, especially when individuals have heterogeneous preferences. Our technical focus is the generalizability of envy-free classification, i.e., understanding whether a classifier that is envy free on a sample would be almost envy free with respect to the underlying distribution with high probability. Our main result establishes that a small sample is sufficient to achieve such guarantees, when the classifier in question is a mixture of deterministic classifiers that belong to a family of low Natarajan dimension.

A crucial problem in modern data science is data-driven algorithm design, where the goal is to choose the best algorithm, or algorithm parameters, for a specific application domain. In practice, we often optimize over a parametric algorithm family, searching for parameters with high performance on a collection of typical problem instances. While effective in practice, these procedures generally have not come with provable guarantees. A recent line of work initiated by a seminal paper of Gupta and Roughgarden (2017) analyzes application-specific algorithm selection from a theoretical perspective. We progress this research direction in several important settings. We provide upper and lower bounds on regret for algorithm selection in online settings, where problems arrive sequentially and we must choose parameters online. We also consider differentially private algorithm selection, where the goal is to find good parameters for a set of problems without divulging too much sensitive information contained therein. We analyze several important parameterized families of algorithms, including SDP-rounding schemes for problems formulated as integer quadratic programs as well as greedy techniques for several canonical subset selection problems. The cost function that measures an algorithm's performance is often a volatile piecewise Lipschitz function of its parameters, since a small change to the parameters can lead to a cascade of different decisions made by the algorithm. We present general techniques for optimizing the sum or average of piecewise Lipschitz functions when the underlying functions satisfy a sufficient and general condition called dispersion. Intuitively, a set of piecewise Lipschitz functions is dispersed if no small region contains many of the functions' discontinuities. Using dispersion, we improve over the best-known online learning regret bounds for a variety problems, prove regret bounds for problems not previously studied, and provide matching regret lower bounds. In the private optimization setting, we show how to optimize performance while preserving privacy for several important problems, providing matching upper and lower bounds on performance loss due to privacy preservation. Though algorithm selection is our primary motivation, we believe the notion of dispersion may be of independent interest. Therefore, we present our results for the more general problem of optimizing piecewise Lipschitz functions. Finally, we uncover dispersion in domains beyond algorithm selection, namely, auction design and pricing, providing online and privacy guarantees for these problems as well.

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial problems. These algorithms recursively partition the search space to find an optimal solution. To keep the tree small, it is crucial to carefully decide, when expanding a tree node, which variable to branch on at that node to partition the remaining space. Many partitioning techniques have been proposed, but no theory describes which is optimal. We show how to use machine learning to determine an optimal weighting of any set of partitioning procedures for the instance distribution at hand using samples. Via theory and experiments, we show that learning to branch is both practical and hugely beneficial.

Algorithms for clustering points in metric spaces is a long-studied area of research. Clustering has seen a multitude of work both theoretically, in understanding the approximation guarantees possible for many objective functions such as k-median and k-means clustering, and experimentally, in finding the fastest algorithms and seeding procedures for Lloyd's algorithm. The performance of a given clustering algorithm depends on the specific application at hand, and this may not be known up front. For example, a "typical instance" may vary depending on the application, and different clustering heuristics perform differently depending on the instance. In this paper, we define an infinite family of algorithms generalizing Lloyd's algorithm, with one parameter controlling the the initialization procedure, and another parameter controlling the local search procedure. This family of algorithms includes the celebrated k-means++ algorithm, as well as the classic farthest-first traversal algorithm. We design efficient learning algorithms which receive samples from an application-specific distribution over clustering instances and learn a near-optimal clustering algorithm from the class. We show the best parameters vary significantly across datasets such as MNIST, CIFAR, and mixtures of Gaussians. Our learned algorithms never perform worse than k-means++, and on some datasets we see significant improvements.

We present a new perspective on the popular multi-class algorithmic techniques of one-vs-all and error correcting output codes. Rather than studying the behavior of these techniques for supervised learning, we establish a connection between the success of these methods and the existence of label-efficient learning procedures. We show that in both the realizable and agnostic cases, if output codes are successful at learning from labeled data, they implicitly assume structure on how the classes are related. By making that structure explicit, we design learning algorithms to recover the classes with low label complexity. We provide results for the commonly studied cases of one-vs-all learning and when the codewords of the classes are well separated. We additionally consider the more challenging case where the codewords are not well separated, but satisfy a boundary features condition that captures the natural intuition that every bit of the codewords should be significant.

In distributed machine learning, data is dispatched to multiple machines for processing. Motivated by the fact that similar data points often belong to the same or similar classes, and more generally, classification rules of high accuracy tend to be “locally simple but globally complex” (Vapnik and Bottou, 1993), we propose data dependent dispatching that takes advantage of such structure. We present an in-depth analysis of this model, providing new algorithms with provable worst-case guarantees, analysis proving existing scalable heuristics perform well in natural non worst-case conditions, and techniques for extending a dispatching rule from a small sample to the entire distribution. We overcome novel technical challenges to satisfy important conditions for accurate distributed learning, including fault tolerance and balancedness. We empirically compare our approach with baselines based on random partitioning, balanced partition trees, and locality sensitive hashing, showing that we achieve significantly higher accuracy on both synthetic and real world image and advertising datasets. We also demonstrate that our technique strongly scales with the available computing power.

We study the problem of clustering sensitive data while preserving the privacy of individuals represented in the dataset, which has broad applications in practical machine learning and data analysis tasks. Although the problem has been widely studied in the context of low-dimensional, discrete spaces, much remains unknown concerning private clustering in high-dimensional Euclidean spaces $\mathbb{R}^d$. In this work, we give differentially private and efficient algorithms achieving strong guarantees for $k$-means and $k$-median clustering when $d=\Omega(\mathsf{polylog}(n))$. Our algorithm achieves clustering loss at most $\log^3(n)\mathsf{OPT}+\mathsf{poly}(\log n,d,k)$, advancing the state-of-the-art result of $\sqrt{d}\mathsf{OPT}+\mathsf{poly}(\log n,d^d,k^d)$. We also study the case where the data points are $s$-sparse and show that the clustering loss can scale logarithmically with $d$, i.e., $\log^3(n)\mathsf{OPT}+\mathsf{poly}(\log n,\log d,k,s)$. Experiments on both synthetic and real datasets verify the effectiveness of the proposed method.

In this paper we consider online learning in finite Markov decision processes (MDPs) with changing cost sequences under full and bandit-information. We propose to view this problem as an instance of online linear optimization. We propose two methods for this problem: MD^2 (mirror descent with approximate projections) and the continuous exponential weights algorithm with Dikin walks. We provide a rigorous complexity analysis of these techniques, while providing near-optimal regret-bounds (in particular, we take into account the computational costs of performing approximate projections in MD^2). In the case of full-information feedback, our results complement existing ones. In the case of bandit-information feedback we consider the online stochastic shortest path problem, a special case of the above MDP problems, and manage to improve the existing results by removing the previous restrictive assumption that the state-visitation probabilities are uniformly bounded away from zero under all policies.

Pointing to indicate direction or position is one of the intuitive communication mechanisms used by humans in all life stages. Our aim is to develop a natural human-robot command interface using pointing gestures for human-robot interaction (HRI). We propose an interface based on the Kinect sensor for selecting by pointing (SEPO) in a 3D real-world situation, where the user points to a target object or location and the interface returns the 3D position coordinates of the target. Through our interface we perform three experiments to study precision and accuracy of human pointing in typical household scenarios: pointing to a “wall”, pointing to a “table”, and pointing to a “floor”. Our results prove that the proposed SEPO interface enables users to point and select objects with an average 3D position accuracy of 9:6 cm in household situations.