arXiv subjects

Zhiwei Steven Wu

Publications and source records attributed to Zhiwei Steven Wu.

At least 145 records · Page 8Linked to original sources

arXiv2020

Structured Linear Contextual Bandits: A Sharp and Geometric Smoothed Analysis

Bandit learning algorithms typically involve the balance of exploration and exploitation. However, in many practical applications, worst-case scenarios needing systematic exploration are seldom encountered. In this work, we consider a smoothed setting for structured linear contextual bandits where the adversarial contexts are perturbed by Gaussian noise and the unknown parameter $θ^*$ has structure, e.g., sparsity, group sparsity, low rank, etc. We propose simple greedy algorithms for both the single- and multi-parameter (i.e., different parameter for each context) settings and provide a unified regret analysis for $θ^*$ with any assumed structure. The regret bounds are expressed in terms of geometric quantities such as Gaussian widths associated with the structure of $θ^*$. We also obtain sharper regret bounds compared to earlier work for the unstructured $θ^*$ setting as a consequence of our improved analysis. We show there is implicit exploration in the smoothed setting where a simple greedy algorithm works.

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arXiv2020

Learn to Expect the Unexpected: Probably Approximately Correct Domain Generalization

Domain generalization is the problem of machine learning when the training data and the test data come from different data domains. We present a simple theoretical model of learning to generalize across domains in which there is a meta-distribution over data distributions, and those data distributions may even have different supports. In our model, the training data given to a learning algorithm consists of multiple datasets each from a single domain drawn in turn from the meta-distribution. We study this model in three different problem settings---a multi-domain Massart noise setting, a decision tree multi-dataset setting, and a feature selection setting, and find that computationally efficient, polynomial-sample domain generalization is possible in each. Experiments demonstrate that our feature selection algorithm indeed ignores spurious correlations and improves generalization.

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arXiv2019

Random Quadratic Forms with Dependence: Applications to Restricted Isometry and Beyond

Several important families of computational and statistical results in machine learning and randomized algorithms rely on uniform bounds on quadratic forms of random vectors or matrices. Such results include the Johnson-Lindenstrauss (J-L) Lemma, the Restricted Isometry Property (RIP), randomized sketching algorithms, and approximate linear algebra. The existing results critically depend on statistical independence, e.g., independent entries for random vectors, independent rows for random matrices, etc., which prevent their usage in dependent or adaptive modeling settings. In this paper, we show that such independence is in fact not needed for such results which continue to hold under fairly general dependence structures. In particular, we present uniform bounds on random quadratic forms of stochastic processes which are conditionally independent and sub-Gaussian given another (latent) process. Our setup allows general dependencies of the stochastic process on the history of the latent process and the latent process to be influenced by realizations of the stochastic process. The results are thus applicable to adaptive modeling settings and also allows for sequential design of random vectors and matrices. We also discuss stochastic process based forms of J-L, RIP, and sketching, to illustrate the generality of the results.

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arXiv2019

Locally Private Gaussian Estimation

We study a basic private estimation problem: each of $n$ users draws a single i.i.d. sample from an unknown Gaussian distribution, and the goal is to estimate the mean of this Gaussian distribution while satisfying local differential privacy for each user. Informally, local differential privacy requires that each data point is individually and independently privatized before it is passed to a learning algorithm. Locally private Gaussian estimation is therefore difficult because the data domain is unbounded: users may draw arbitrarily different inputs, but local differential privacy nonetheless mandates that different users have (worst-case) similar privatized output distributions. We provide both adaptive two-round solutions and nonadaptive one-round solutions for locally private Gaussian estimation. We then partially match these upper bounds with an information-theoretic lower bound. This lower bound shows that our accuracy guarantees are tight up to logarithmic factors for all sequentially interactive $(\varepsilon,δ)$-locally private protocols.

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arXiv2019

Orthogonal Random Forest for Causal Inference

We propose the orthogonal random forest, an algorithm that combines Neyman-orthogonality to reduce sensitivity with respect to estimation error of nuisance parameters with generalized random forests (Athey et al., 2017)--a flexible non-parametric method for statistical estimation of conditional moment models using random forests. We provide a consistency rate and establish asymptotic normality for our estimator. We show that under mild assumptions on the consistency rate of the nuisance estimator, we can achieve the same error rate as an oracle with a priori knowledge of these nuisance parameters. We show that when the nuisance functions have a locally sparse parametrization, then a local $\ell_1$-penalized regression achieves the required rate. We apply our method to estimate heterogeneous treatment effects from observational data with discrete treatments or continuous treatments, and we show that, unlike prior work, our method provably allows to control for a high-dimensional set of variables under standard sparsity conditions. We also provide a comprehensive empirical evaluation of our algorithm on both synthetic and real data.

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arXiv2019

Distributed Training with Heterogeneous Data: Bridging Median- and Mean-Based Algorithms

Recently, there is a growing interest in the study of median-based algorithms for distributed non-convex optimization. Two prominent such algorithms include signSGD with majority vote, an effective approach for communication reduction via 1-bit compression on the local gradients, and medianSGD, an algorithm recently proposed to ensure robustness against Byzantine workers. The convergence analyses for these algorithms critically rely on the assumption that all the distributed data are drawn iid from the same distribution. However, in applications such as Federated Learning, the data across different nodes or machines can be inherently heterogeneous, which violates such an iid assumption. This work analyzes signSGD and medianSGD in distributed settings with heterogeneous data. We show that these algorithms are non-convergent whenever there is some disparity between the expected median and mean over the local gradients. To overcome this gap, we provide a novel gradient correction mechanism that perturbs the local gradients with noise, together with a series results that provable close the gap between mean and median of the gradients. The proposed methods largely preserve nice properties of these methods, such as the low per-iteration communication complexity of signSGD, and further enjoy global convergence to stationary solutions. Our perturbation technique can be of independent interest when one wishes to estimate mean through a median estimator.

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arXiv2019

Fair Regression: Quantitative Definitions and Reduction-based Algorithms

In this paper, we study the prediction of a real-valued target, such as a risk score or recidivism rate, while guaranteeing a quantitative notion of fairness with respect to a protected attribute such as gender or race. We call this class of problems \emph{fair regression}. We propose general schemes for fair regression under two notions of fairness: (1) statistical parity, which asks that the prediction be statistically independent of the protected attribute, and (2) bounded group loss, which asks that the prediction error restricted to any protected group remain below some pre-determined level. While we only study these two notions of fairness, our schemes are applicable to arbitrary Lipschitz-continuous losses, and so they encompass least-squares regression, logistic regression, quantile regression, and many other tasks. Our schemes only require access to standard risk minimization algorithms (such as standard classification or least-squares regression) while providing theoretical guarantees on the optimality and fairness of the obtained solutions. In addition to analyzing theoretical properties of our schemes, we empirically demonstrate their ability to uncover fairness--accuracy frontiers on several standard datasets.

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arXiv2019

The Perils of Exploration under Competition: A Computational Modeling Approach

We empirically study the interplay between exploration and competition. Systems that learn from interactions with users often engage in exploration: making potentially suboptimal decisions in order to acquire new information for future decisions. However, when multiple systems are competing for the same market of users, exploration may hurt a system's reputation in the near term, with adverse competitive effects. In particular, a system may enter a "death spiral", when the short-term reputation cost decreases the number of users for the system to learn from, which degrades its performance relative to competition and further decreases its market share. We ask whether better exploration algorithms are incentivized under competition. We run extensive numerical experiments in a stylized duopoly model in which two firms deploy multi-armed bandit algorithms and compete for myopic users. We find that duopoly and monopoly tend to favor a primitive "greedy algorithm" that does not explore and leads to low consumer welfare, whereas a temporary monopoly (a duopoly with an early entrant) may incentivize better bandit algorithms and lead to higher consumer welfare. Our findings shed light on the first-mover advantage in the digital economy by exploring the role that data can play as a barrier to entry in online markets.

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arXiv2019

Locally Private Bayesian Inference for Count Models

We present a general method for privacy-preserving Bayesian inference in Poisson factorization, a broad class of models that includes some of the most widely used models in the social sciences. Our method satisfies limited precision local privacy, a generalization of local differential privacy, which we introduce to formulate privacy guarantees appropriate for sparse count data. We develop an MCMC algorithm that approximates the locally private posterior over model parameters given data that has been locally privatized by the geometric mechanism (Ghosh et al., 2012). Our solution is based on two insights: 1) a novel reinterpretation of the geometric mechanism in terms of the Skellam distribution (Skellam, 1946) and 2) a general theorem that relates the Skellam to the Bessel distribution (Yuan & Kalbfleisch, 2000). We demonstrate our method in two case studies on real-world email data in which we show that our method consistently outperforms the commonly-used naive approach, obtaining higher quality topics in text and more accurate link prediction in networks. On some tasks, our privacy-preserving method even outperforms non-private inference which conditions on the true data.

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arXiv2019

Bayesian Exploration with Heterogeneous Agents

It is common in recommendation systems that users both consume and produce information as they make strategic choices under uncertainty. While a social planner would balance "exploration" and "exploitation" using a multi-armed bandit algorithm, users' incentives may tilt this balance in favor of exploitation. We consider Bayesian Exploration: a simple model in which the recommendation system (the "principal") controls the information flow to the users (the "agents") and strives to incentivize exploration via information asymmetry. A single round of this model is a version of a well-known "Bayesian Persuasion game" from [Kamenica and Gentzkow]. We allow heterogeneous users, relaxing a major assumption from prior work that users have the same preferences from one time step to another. The goal is now to learn the best personalized recommendations. One particular challenge is that it may be impossible to incentivize some of the user types to take some of the actions, no matter what the principal does or how much time she has. We consider several versions of the model, depending on whether and when the user types are reported to the principal, and design a near-optimal "recommendation policy" for each version. We also investigate how the model choice and the diversity of user types impact the set of actions that can possibly be "explored" by each type.

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arXiv2018

Privacy-Preserving Distributed Deep Learning for Clinical Data

Deep learning with medical data often requires larger samples sizes than are available at single providers. While data sharing among institutions is desirable to train more accurate and sophisticated models, it can lead to severe privacy concerns due the sensitive nature of the data. This problem has motivated a number of studies on distributed training of neural networks that do not require direct sharing of the training data. However, simple distributed training does not offer provable privacy guarantees to satisfy technical safe standards and may reveal information about the underlying patients. We present a method to train neural networks for clinical data in a distributed fashion under differential privacy. We demonstrate these methods on two datasets that include information from multiple independent sites, the eICU collaborative Research Database and The Cancer Genome Atlas.

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arXiv2018

Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness

The most prevalent notions of fairness in machine learning are statistical definitions: they fix a small collection of pre-defined groups, and then ask for parity of some statistic of the classifier across these groups. Constraints of this form are susceptible to intentional or inadvertent "fairness gerrymandering", in which a classifier appears to be fair on each individual group, but badly violates the fairness constraint on one or more structured subgroups defined over the protected attributes. We propose instead to demand statistical notions of fairness across exponentially (or infinitely) many subgroups, defined by a structured class of functions over the protected attributes. This interpolates between statistical definitions of fairness and recently proposed individual notions of fairness, but raises several computational challenges. It is no longer clear how to audit a fixed classifier to see if it satisfies such a strong definition of fairness. We prove that the computational problem of auditing subgroup fairness for both equality of false positive rates and statistical parity is equivalent to the problem of weak agnostic learning, which means it is computationally hard in the worst case, even for simple structured subclasses. We then derive two algorithms that provably converge to the best fair classifier, given access to oracles which can solve the agnostic learning problem. The algorithms are based on a formulation of subgroup fairness as a two-player zero-sum game between a Learner and an Auditor. Our first algorithm provably converges in a polynomial number of steps. Our second algorithm enjoys only provably asymptotic convergence, but has the merit of simplicity and faster per-step computation. We implement the simpler algorithm using linear regression as a heuristic oracle, and show that we can effectively both audit and learn fair classifiers on real datasets.

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arXiv2018

How to Use Heuristics for Differential Privacy

We develop theory for using heuristics to solve computationally hard problems in differential privacy. Heuristic approaches have enjoyed tremendous success in machine learning, for which performance can be empirically evaluated. However, privacy guarantees cannot be evaluated empirically, and must be proven --- without making heuristic assumptions. We show that learning problems over broad classes of functions can be solved privately and efficiently, assuming the existence of a non-private oracle for solving the same problem. Our first algorithm yields a privacy guarantee that is contingent on the correctness of the oracle. We then give a reduction which applies to a class of heuristics which we call certifiable, which allows us to convert oracle-dependent privacy guarantees to worst-case privacy guarantee that hold even when the heuristic standing in for the oracle might fail in adversarial ways. Finally, we consider a broad class of functions that includes most classes of simple boolean functions studied in the PAC learning literature, including conjunctions, disjunctions, parities, and discrete halfspaces. We show that there is an efficient algorithm for privately constructing synthetic data for any such class, given a non-private learning oracle. This in particular gives the first oracle-efficient algorithm for privately generating synthetic data for contingency tables. The most intriguing question left open by our work is whether or not every problem that can be solved differentially privately can be privately solved with an oracle-efficient algorithm. While we do not resolve this, we give a barrier result that suggests that any generic oracle-efficient reduction must fall outside of a natural class of algorithms (which includes the algorithms given in this paper).

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arXiv2018

An Empirical Study of Rich Subgroup Fairness for Machine Learning

Kearns et al. [2018] recently proposed a notion of rich subgroup fairness intended to bridge the gap between statistical and individual notions of fairness. Rich subgroup fairness picks a statistical fairness constraint (say, equalizing false positive rates across protected groups), but then asks that this constraint hold over an exponentially or infinitely large collection of subgroups defined by a class of functions with bounded VC dimension. They give an algorithm guaranteed to learn subject to this constraint, under the condition that it has access to oracles for perfectly learning absent a fairness constraint. In this paper, we undertake an extensive empirical evaluation of the algorithm of Kearns et al. On four real datasets for which fairness is a concern, we investigate the basic convergence of the algorithm when instantiated with fast heuristics in place of learning oracles, measure the tradeoffs between fairness and accuracy, and compare this approach with the recent algorithm of Agarwal et al. [2018], which implements weaker and more traditional marginal fairness constraints defined by individual protected attributes. We find that in general, the Kearns et al. algorithm converges quickly, large gains in fairness can be obtained with mild costs to accuracy, and that optimizing accuracy subject only to marginal fairness leads to classifiers with substantial subgroup unfairness. We also provide a number of analyses and visualizations of the dynamics and behavior of the Kearns et al. algorithm. Overall we find this algorithm to be effective on real data, and rich subgroup fairness to be a viable notion in practice.

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arXiv2018

Semiparametric Contextual Bandits

This paper studies semiparametric contextual bandits, a generalization of the linear stochastic bandit problem where the reward for an action is modeled as a linear function of known action features confounded by an non-linear action-independent term. We design new algorithms that achieve $\tilde{O}(d\sqrt{T})$ regret over $T$ rounds, when the linear function is $d$-dimensional, which matches the best known bounds for the simpler unconfounded case and improves on a recent result of Greenewald et al. (2017). Via an empirical evaluation, we show that our algorithms outperform prior approaches when there are non-linear confounding effects on the rewards. Technically, our algorithms use a new reward estimator inspired by doubly-robust approaches and our proofs require new concentration inequalities for self-normalized martingales.

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arXiv2018

The Externalities of Exploration and How Data Diversity Helps Exploitation

Online learning algorithms, widely used to power search and content optimization on the web, must balance exploration and exploitation, potentially sacrificing the experience of current users for information that will lead to better decisions in the future. Recently, concerns have been raised about whether the process of exploration could be viewed as unfair, placing too much burden on certain individuals or groups. Motivated by these concerns, we initiate the study of the externalities of exploration - the undesirable side effects that the presence of one party may impose on another - under the linear contextual bandits model. We introduce the notion of a group externality, measuring the extent to which the presence of one population of users impacts the rewards of another. We show that this impact can in some cases be negative, and that, in a certain sense, no algorithm can avoid it. We then study externalities at the individual level, interpreting the act of exploration as an externality imposed on the current user of a system by future users. This drives us to ask under what conditions inherent diversity in the data makes explicit exploration unnecessary. We build on a recent line of work on the smoothed analysis of the greedy algorithm that always chooses the action that currently looks optimal, improving on prior results to show that a greedy approach almost matches the best possible Bayesian regret rate of any other algorithm on the same problem instance whenever the diversity conditions hold, and that this regret is at most $\tilde{O}(T^{1/3})$. Returning to group-level effects, we show that under the same conditions, negative group externalities essentially vanish under the greedy algorithm. Together, our results uncover a sharp contrast between the high externalities that exist in the worst case, and the ability to remove all externalities if the data is sufficiently diverse.

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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.

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arXiv2017

Competing Bandits: Learning under Competition

Most modern systems strive to learn from interactions with users, and many engage in exploration: making potentially suboptimal choices for the sake of acquiring new information. We initiate a study of the interplay between exploration and competition--how such systems balance the exploration for learning and the competition for users. Here the users play three distinct roles: they are customers that generate revenue, they are sources of data for learning, and they are self-interested agents which choose among the competing systems. In our model, we consider competition between two multi-armed bandit algorithms faced with the same bandit instance. Users arrive one by one and choose among the two algorithms, so that each algorithm makes progress if and only if it is chosen. We ask whether and to what extent competition incentivizes the adoption of better bandit algorithms. We investigate this issue for several models of user response, as we vary the degree of rationality and competitiveness in the model. Our findings are closely related to the "competition vs. innovation" relationship, a well-studied theme in economics.

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