arXiv subjects

Vasilis Syrgkanis

Publications and source records attributed to Vasilis Syrgkanis.

At least 91 records · Page 5Linked to original sources

arXiv2020

Learning and Efficiency in Games with Dynamic Population

We study the quality of outcomes in repeated games when the population of players is dynamically changing and participants use learning algorithms to adapt to the changing environment. Game theory classically considers Nash equilibria of one-shot games, while in practice many games are played repeatedly, and in such games players often use algorithmic tools to learn to play in the given environment. Most previous work on learning in repeated games assumes that the population playing the game is static over time. We analyze the efficiency of repeated games in dynamically changing environments, motivated by application domains such as Internet ad-auctions and packet routing. We prove that, in many classes of games, if players choose their strategies in a way that guarantees low adaptive regret, then high social welfare is ensured, even under very frequent changes. In fact, in large markets learning players achieve asymptotically optimal social welfare despite high turnover. Previous work has only showed that high welfare is guaranteed for learning outcomes in static environments. Our work extends these results to more realistic settings when participation is drastically evolving over time.

cs.GT↗

arXiv2020

Accurate Inference for Adaptive Linear Models

Estimators computed from adaptively collected data do not behave like their non-adaptive brethren. Rather, the sequential dependence of the collection policy can lead to severe distributional biases that persist even in the infinite data limit. We develop a general method -- $\mathbf{W}$-decorrelation -- for transforming the bias of adaptive linear regression estimators into variance. The method uses only coarse-grained information about the data collection policy and does not need access to propensity scores or exact knowledge of the policy. We bound the finite-sample bias and variance of the $\mathbf{W}$-estimator and develop asymptotically correct confidence intervals based on a novel martingale central limit theorem. We then demonstrate the empirical benefits of the generic $\mathbf{W}$-decorrelation procedure in two different adaptive data settings: the multi-armed bandit and the autoregressive time series.

stat.ML↗

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.

cs.LG↗

arXiv2019

Low-Rank Bandit Methods for High-Dimensional Dynamic Pricing

We consider dynamic pricing with many products under an evolving but low-dimensional demand model. Assuming the temporal variation in cross-elasticities exhibits low-rank structure based on fixed (latent) features of the products, we show that the revenue maximization problem reduces to an online bandit convex optimization with side information given by the observed demands. We design dynamic pricing algorithms whose revenue approaches that of the best fixed price vector in hindsight, at a rate that only depends on the intrinsic rank of the demand model and not the number of products. Our approach applies a bandit convex optimization algorithm in a projected low-dimensional space spanned by the latent product features, while simultaneously learning this span via online singular value decomposition of a carefully-crafted matrix containing the observed demands.

cs.LG↗

arXiv2019

Oracle-Efficient Online Learning and Auction Design

We consider the design of computationally efficient online learning algorithms in an adversarial setting in which the learner has access to an offline optimization oracle. We present an algorithm called Generalized Follow-the-Perturbed-Leader and provide conditions under which it is oracle-efficient while achieving vanishing regret. Our results make significant progress on an open problem raised by Hazan and Koren, who showed that oracle-efficient algorithms do not exist in general and asked whether one can identify properties under which oracle-efficient online learning may be possible. Our auction-design framework considers an auctioneer learning an optimal auction for a sequence of adversarially selected valuations with the goal of achieving revenue that is almost as good as the optimal auction in hindsight, among a class of auctions. We give oracle-efficient learning results for: (1) VCG auctions with bidder-specific reserves in single-parameter settings, (2) envy-free item pricing in multi-item auctions, and (3) s-level auctions of Morgenstern and Roughgarden for single-item settings. The last result leads to an approximation of the overall optimal Myerson auction when bidders' valuations are drawn according to a fast-mixing Markov process, extending prior work that only gave such guarantees for the i.i.d. setting. Finally, we derive various extensions, including: (1) oracle-efficient algorithms for the contextual learning setting in which the learner has access to side information (such as bidder demographics), (2) learning with approximate oracles such as those based on Maximal-in-Range algorithms, and (3) no-regret bidding in simultaneous auctions, resolving an open problem of Daskalakis and Syrgkanis.

cs.LG↗

arXiv2019

Semi-Parametric Efficient Policy Learning with Continuous Actions

We consider off-policy evaluation and optimization with continuous action spaces. We focus on observational data where the data collection policy is unknown and needs to be estimated. We take a semi-parametric approach where the value function takes a known parametric form in the treatment, but we are agnostic on how it depends on the observed contexts. We propose a doubly robust off-policy estimate for this setting and show that off-policy optimization based on this estimate is robust to estimation errors of the policy function or the regression model. Our results also apply if the model does not satisfy our semi-parametric form, but rather we measure regret in terms of the best projection of the true value function to this functional space. Our work extends prior approaches of policy optimization from observational data that only considered discrete actions. We provide an experimental evaluation of our method in a synthetic data example motivated by optimal personalized pricing and costly resource allocation.

econ.EM↗

arXiv2019

Non-Parametric Inference Adaptive to Intrinsic Dimension

We consider non-parametric estimation and inference of conditional moment models in high dimensions. We show that even when the dimension $D$ of the conditioning variable is larger than the sample size $n$, estimation and inference is feasible as long as the distribution of the conditioning variable has small intrinsic dimension $d$, as measured by locally low doubling measures. Our estimation is based on a sub-sampled ensemble of the $k$-nearest neighbors ($k$-NN) $Z$-estimator. We show that if the intrinsic dimension of the covariate distribution is equal to $d$, then the finite sample estimation error of our estimator is of order $n^{-1/(d+2)}$ and our estimate is $n^{1/(d+2)}$-asymptotically normal, irrespective of $D$. The sub-sampling size required for achieving these results depends on the unknown intrinsic dimension $d$. We propose an adaptive data-driven approach for choosing this parameter and prove that it achieves the desired rates. We discuss extensions and applications to heterogeneous treatment effect estimation.

cs.LG↗

arXiv2019

Machine Learning Estimation of Heterogeneous Treatment Effects with Instruments

We consider the estimation of heterogeneous treatment effects with arbitrary machine learning methods in the presence of unobserved confounders with the aid of a valid instrument. Such settings arise in A/B tests with an intent-to-treat structure, where the experimenter randomizes over which user will receive a recommendation to take an action, and we are interested in the effect of the downstream action. We develop a statistical learning approach to the estimation of heterogeneous effects, reducing the problem to the minimization of an appropriate loss function that depends on a set of auxiliary models (each corresponding to a separate prediction task). The reduction enables the use of all recent algorithmic advances (e.g. neural nets, forests). We show that the estimated effect model is robust to estimation errors in the auxiliary models, by showing that the loss satisfies a Neyman orthogonality criterion. Our approach can be used to estimate projections of the true effect model on simpler hypothesis spaces. When these spaces are parametric, then the parameter estimates are asymptotically normal, which enables construction of confidence sets. We applied our method to estimate the effect of membership on downstream webpage engagement on TripAdvisor, using as an instrument an intent-to-treat A/B test among 4 million TripAdvisor users, where some users received an easier membership sign-up process. We also validate our method on synthetic data and on public datasets for the effects of schooling on income.

econ.EM↗

arXiv2019

Bayesian Incentive-Compatible Bandit Exploration

Individual decision-makers consume information revealed by the previous decision makers, and produce information that may help in future decisions. This phenomenon is common in a wide range of scenarios in the Internet economy, as well as in other domains such as medical decisions. Each decision-maker would individually prefer to "exploit": select an action with the highest expected reward given her current information. At the same time, each decision-maker would prefer previous decision-makers to "explore", producing information about the rewards of various actions. A social planner, by means of carefully designed information disclosure, can incentivize the agents to balance the exploration and exploitation so as to maximize social welfare. We formulate this problem as a multi-armed bandit problem (and various generalizations thereof) under incentive-compatibility constraints induced by the agents' Bayesian priors. We design an incentive-compatible bandit algorithm for the social planner whose regret is asymptotically optimal among all bandit algorithms (incentive-compatible or not). Further, we provide a black-box reduction from an arbitrary multi-arm bandit algorithm to an incentive-compatible one, with only a constant multiplicative increase in regret. This reduction works for very general bandit setting that incorporate contexts and arbitrary auxiliary feedback.

cs.GT↗

arXiv2018

Optimal Data Acquisition for Statistical Estimation

We consider a data analyst's problem of purchasing data from strategic agents to compute an unbiased estimate of a statistic of interest. Agents incur private costs to reveal their data and the costs can be arbitrarily correlated with their data. Once revealed, data are verifiable. This paper focuses on linear unbiased estimators. We design an individually rational and incentive compatible mechanism that optimizes the worst-case mean-squared error of the estimation, where the worst-case is over the unknown correlation between costs and data, subject to a budget constraint in expectation. We characterize the form of the optimal mechanism in closed-form. We further extend our results to acquiring data for estimating a parameter in regression analysis, where private costs can correlate with the values of the dependent variable but not with the values of the independent variables.

cs.GT↗

arXiv2018

Orthogonal Machine Learning: Power and Limitations

Double machine learning provides $\sqrt{n}$-consistent estimates of parameters of interest even when high-dimensional or nonparametric nuisance parameters are estimated at an $n^{-1/4}$ rate. The key is to employ Neyman-orthogonal moment equations which are first-order insensitive to perturbations in the nuisance parameters. We show that the $n^{-1/4}$ requirement can be improved to $n^{-1/(2k+2)}$ by employing a $k$-th order notion of orthogonality that grants robustness to more complex or higher-dimensional nuisance parameters. In the partially linear regression setting popular in causal inference, we show that we can construct second-order orthogonal moments if and only if the treatment residual is not normally distributed. Our proof relies on Stein's lemma and may be of independent interest. We conclude by demonstrating the robustness benefits of an explicit doubly-orthogonal estimation procedure for treatment effect.

cs.LG↗

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.

stat.ML↗

arXiv2018

Learning to Bid Without Knowing your Value

We address online learning in complex auction settings, such as sponsored search auctions, where the value of the bidder is unknown to her, evolving in an arbitrary manner and observed only if the bidder wins an allocation. We leverage the structure of the utility of the bidder and the partial feedback that bidders typically receive in auctions, in order to provide algorithms with regret rates against the best fixed bid in hindsight, that are exponentially faster in convergence in terms of dependence on the action space, than what would have been derived by applying a generic bandit algorithm and almost equivalent to what would have been achieved in the full information setting. Our results are enabled by analyzing a new online learning setting with outcome-based feedback, which generalizes learning with feedback graphs. We provide an online learning algorithm for this setting, of independent interest, with regret that grows only logarithmically with the number of actions and linearly only in the number of potential outcomes (the latter being very small in most auction settings). Last but not least, we show that our algorithm outperforms the bandit approach experimentally and that this performance is robust to dropping some of our theoretical assumptions or introducing noise in the feedback that the bidder receives.

cs.GT↗

arXiv2018

Optimal and Myopic Information Acquisition

We consider the problem of optimal dynamic information acquisition from many correlated information sources. Each period, the decision-maker jointly takes an action and allocates a fixed number of observations across the available sources. His payoff depends on the actions taken and on an unknown state. In the canonical setting of jointly normal information sources, we show that the optimal dynamic information acquisition rule proceeds myopically after finitely many periods. If signals are acquired in large blocks each period, then the optimal rule turns out to be myopic from period 1. These results demonstrate the possibility of robust and "simple" optimal information acquisition, and simplify the analysis of dynamic information acquisition in a widely used informational environment.

cs.GT↗

arXiv2018

Adversarial Generalized Method of Moments

We provide an approach for learning deep neural net representations of models described via conditional moment restrictions. Conditional moment restrictions are widely used, as they are the language by which social scientists describe the assumptions they make to enable causal inference. We formulate the problem of estimating the underling model as a zero-sum game between a modeler and an adversary and apply adversarial training. Our approach is similar in nature to Generative Adversarial Networks (GAN), though here the modeler is learning a representation of a function that satisfies a continuum of moment conditions and the adversary is identifying violating moments. We outline ways of constructing effective adversaries in practice, including kernels centered by k-means clustering, and random forests. We examine the practical performance of our approach in the setting of non-parametric instrumental variable regression.

econ.EM↗

arXiv2018

Inference on Auctions with Weak Assumptions on Information

Given a sample of bids from independent auctions, this paper examines the question of inference on auction fundamentals (e.g. valuation distributions, welfare measures) under weak assumptions on information structure. The question is important as it allows us to learn about the valuation distribution in a robust way, i.e., without assuming that a particular information structure holds across observations. We leverage the recent contributions of \cite{Bergemann2013} in the robust mechanism design literature that exploit the link between Bayesian Correlated Equilibria and Bayesian Nash Equilibria in incomplete information games to construct an econometrics framework for learning about auction fundamentals using observed data on bids. We showcase our construction of identified sets in private value and common value auctions. Our approach for constructing these sets inherits the computational simplicity of solving for correlated equilibria: checking whether a particular valuation distribution belongs to the identified set is as simple as determining whether a {\it linear} program is feasible. A similar linear program can be used to construct the identified set on various welfare measures and counterfactual objects. For inference and to summarize statistical uncertainty, we propose novel finite sample methods using tail inequalities that are used to construct confidence regions on sets. We also highlight methods based on Bayesian bootstrap and subsampling. A set of Monte Carlo experiments show adequate finite sample properties of our inference procedures. We illustrate our methods using data from OCS auctions.

econ.EM↗

arXiv2018

Expert identification of visual primitives used by CNNs during mammogram classification

This work interprets the internal representations of deep neural networks trained for classification of diseased tissue in 2D mammograms. We propose an expert-in-the-loop interpretation method to label the behavior of internal units in convolutional neural networks (CNNs). Expert radiologists identify that the visual patterns detected by the units are correlated with meaningful medical phenomena such as mass tissue and calcificated vessels. We demonstrate that several trained CNN models are able to produce explanatory descriptions to support the final classification decisions. We view this as an important first step toward interpreting the internal representations of medical classification CNNs and explaining their predictions.

cs.CV↗

arXiv2018

Training GANs with Optimism

We address the issue of limit cycling behavior in training Generative Adversarial Networks and propose the use of Optimistic Mirror Decent (OMD) for training Wasserstein GANs. Recent theoretical results have shown that optimistic mirror decent (OMD) can enjoy faster regret rates in the context of zero-sum games. WGANs is exactly a context of solving a zero-sum game with simultaneous no-regret dynamics. Moreover, we show that optimistic mirror decent addresses the limit cycling problem in training WGANs. We formally show that in the case of bi-linear zero-sum games the last iterate of OMD dynamics converges to an equilibrium, in contrast to GD dynamics which are bound to cycle. We also portray the huge qualitative difference between GD and OMD dynamics with toy examples, even when GD is modified with many adaptations proposed in the recent literature, such as gradient penalty or momentum. We apply OMD WGAN training to a bioinformatics problem of generating DNA sequences. We observe that models trained with OMD achieve consistently smaller KL divergence with respect to the true underlying distribution, than models trained with GD variants. Finally, we introduce a new algorithm, Optimistic Adam, which is an optimistic variant of Adam. We apply it to WGAN training on CIFAR10 and observe improved performance in terms of inception score as compared to Adam.

cs.LG↗