We study an online linear classification problem, in which the data is generated by strategic agents who manipulate their features in an effort to change the classification outcome. In rounds, the learner deploys a classifier, and an adversarially chosen agent arrives, possibly manipulating her features to optimally respond to the learner. The learner has no knowledge of the agents' utility functions or "real" features, which may vary widely across agents. Instead, the learner is only able to observe their "revealed preferences" -i.e. the actual manipulated feature vectors they provide. For a broad family of agent cost functions, we give a computationally efficient learning algorithm that is able to obtain diminishing "Stackelberg regret" -a form of policy regret that guarantees that the learner is obtaining loss nearly as small as that of the best classifier in hindsight, even allowing for the fact that agents will best-respond differently to the optimal classifier. 1 The particulars of the models studied in Brückner and Scheffer (2011) and Hardt et al. (2016) differ. Brückner and Scheffer model a single data generation player who manipulates the data distribution, and experiences cost equal to the squared ℓ 2 distance of his manipulation. Hardt et al. study a model in which each agent can independently manipulate his own data point, but assume that all agents experience cost as a function of the same separable cost function, known to the learner.

Investigating potential purchases is often a substantial investment under uncertainty. Standard market designs, such as simultaneous or English auctions, compound this with uncertainty about the price a bidder will have to pay in order to win. As a result they tend to confuse the process of search both by leading to wasteful information acquisition on goods that have already found a good purchaser and by discouraging needed investigations of objects, potentially eliminating all gains from trade. In contrast, we show that the Dutch auction preserves all of its properties from a standard setting without information costs because it guarantees, at the time of information acquisition, a price at which the good can be purchased. Calibrations to start-up acquisition and timber auctions suggest that in practice the social losses through poor search coordination in standard formats are an order of magnitude or two larger than the (negligible) inefficiencies arising from ex-ante bidder asymmetries. * We are grateful to conversations with Matt Gentzkow and Larry Samuelson for inspiring us to work on this project and to

Machine learning has recently enabled large advances in artificial intelligence, but these tend to be highly centralized. The large datasets required are generally proprietary; predictions are often sold on a per-query basis; and published models can quickly become out of date without effort to acquire more data and re-train them. We propose a framework for participants to collaboratively build a dataset and use smart contracts to host a continuously updated model. This model will be shared publicly on a blockchain where it can be free to use for inference. Ideal learning problems include scenarios where a model is used many times for similar input such as personal assistants, playing games, recommender systems, etc. In order to maintain the model's accuracy with respect to some test set we propose both financial and non-financial (gamified) incentive structures for providing good data. A free and open source implementation for the Ethereum blockchain is provided at https://github.com/microsoft/0xDeCA10B.

The online stochastic matching problem is a variant of online bipartite matching in which edges are labeled with probabilities. A match will "succeed" with the probability along that edge; this models, for instance, the click of a user in search advertisement. The goal is to maximize the expected number of successful matches. This problem was introduced by Mehta and Panigrahi (FOCS 2012), who focused on the case where all probabilities in the graph are equal. They gave a 0.567-competitive algorithm for vanishing probabilities, relative to a natural benchmark, leaving the general case as an open question.This paper examines the general case where the probabilities may be unequal. We take a new algorithmic approach rather than generalizing that of Mehta and Panigrahi: Our algorithm maintains, at each time, the probability that each offline vertex has succeeded thus far, and chooses assignments so as to maximize marginal contributions to these probabilities. When the algorithm does not observe the realizations of the edges, this approach gives a 0.5-competitive algorithm, which achieves the known upper bound for such "non-adaptive" algorithms. We then modify this approach to be "semi-adaptive:" if the chosen target has already succeeded, choose the arrival's "second choice" instead (while still updating the probabilities non-adaptively). With one additional tweak to control the analysis, we show that this algorithm achieves a competitive ratio of 0.534 for the unequal, vanishing probabilities setting. A "fully-adaptive" version of this algorithm turns out to be identical to an algorithm proposed, but not analyzed, in Mehta and Panigrahi (2012); we do not manage to analyze it either since it introduces too many dependencies between the stochastic processes. Our semi-adaptive algorithm thus can be seen as allowing analysis of competitive ratio while still capturing the power of adaptivity.

There are now several large scale deployments of differential privacy used to collect statistical information about users. However, these deployments periodically recollect the data and recompute the statistics using algorithms designed for a single use. As a result, these systems do not provide meaningful privacy guarantees over long time scales. Moreover, existing techniques to mitigate this effect do not apply in the "local model" of differential privacy that these systems use. In this paper, we introduce a new technique for local differential privacy that makes it possible to maintain up-to-date statistics over time, with privacy guarantees that degrade only in the number of changes in the underlying distribution rather than the number of collection periods. We use our technique for tracking a changing statistic in the setting where users are partitioned into an unknown collection of groups, and at every time period each user draws a single bit from a common (but changing) group-specific distribution. We also provide an application to frequency and heavy-hitter estimation. IntroductionAfter over a decade of research, differential privacy [12] is moving from theory to practice, with notable deployments by Google [15,6], Apple [2], Microsoft [10], and the U.S. Census Bureau [1]. These deployments have revealed gaps between existing theory and the needs of practitioners. For example, the bulk of the differential privacy literature has focused on the central model, in which user data is collected by a trusted aggregator who performs and publishes the results of a differentially private computation [11]. However, Google, Apple, and Microsoft have instead chosen to operate in the local model [15,6,2,10], where users individually randomize their data on their own devices and send it to a potentially untrusted aggregator for analysis [18]. In addition, the academic literature has largely focused on algorithms for performing one-time computations, like estimating many statistical quantities [7, 22,16] or training a classifier [18,9,4]. Industrial applications, however have focused on tracking statistics about a user population, like the set of most frequently used emojis or words [2]. These statistics evolve over time and so must be re-computed periodically.Together, the two problems of periodically recomputing a population statistic and operating in the local model pose a challenge. Naïvely repeating a differentially private computation causes the privacy loss to degrade as the square root of the number of recomputations, quickly leading to enormous values of ǫ. This naïve strategy is what is used in practice [15,6,2]. As a result, Tang et al. [23] discovered that the privacy parameters guaranteed by Apple's implementation of differentially private data 32nd Conference on Neural Information Processing Systems (NIPS 2018), Montréal, Canada.