TASK DEFINITION: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
PROBLEM: We consider the design of online learning algorithms in a general learning setting, with the goal of obtaining computationally efficient no-regret algorithms, when given access to an oracle for the offline optimization version of the problem. We present an algorithm that we call Generalized Follow-thePerturbed-Leader (Generalized FTPL) and provide conditions under which it achieves vanishing regret and is efficiently implementable with an oracle. Our second main contribution is the introduction of a new online adversarial auction-design framework for revenue maximization and an application of our oracle-efficient learning results to the adaptive optimization of auctions. Our learning algorithm is a generalization of the classic FTPL algorithm of Kalai and Vempala [27], playing at every iteration the historically best-performing action after adding some perturbation to the performance of each of its actions. The crux of our design is adding perturbations in a manner that leads to oracle-efficiency. We reduce this to designing a translation matrix, which translates a low dimensional vector with independent noise components into a high dimensional vector of perturbations on the learner’s action space. Our approach generalizes prior work on oracle-efficient online learning [11, 22, 27, 35], ranging from online combinatorial optimization, learning in simultaneous auctions, and contextual learning. Our auction-design framework considers an auctioneer learning an optimal auction rule in an online manner, every day observing an adversarially chosen vector of valuations. The auctioneer’s goal is to achieve revenue that competes with the revenue of the optimal auction in hindsight among those in some target class. We give oracle-efficient learning results for: (1) VCG auctions with bidder-specific reserves in single-parameter settings with matroid constraints, (2) envy-free item pricing in multi-item auctions with unlimited supply, and (3) s-level auctions of Morgenstern and Roughgarden [28] for singleitem settings. The last result implies good regret against the optimal overall auction when valuations are coming from a fast mixing Markov chain, that is independent across bidders. We also extend our results to the case when the learner observes side information on the bidders before running the auction (contextual learning). We present additional extensions to contextual learning and learning with approximate oracles, implemented by FPTAS or Maximal-in-Range algorithms. We provide further applications in online welfare maximization in multi-unit auctions and in no-regret learning in simultaneous item auctions, answering an open question from prior work. ∗Microsoft Research, New York, mdudik@microsoft.com †Computer Science Department, Carnegie Mellon University, nhaghtal@cs.cmu.edu ‡Microsoft Research, New York, haipeng@microsoft.com §Microsoft Research, New York, schapire@microsoft.com ¶Microsoft Research, New England, vasy@microsoft.com ‖Microsoft Research, New York, jenn@microsoft.com ar X iv :1 61 1. 01 68 8v 1 [ cs .L G ] 5 N ov 2 01 6

SOLUTION: Oracle-Efficient Learning and Auction Design

PROBLEM: Various tasks in decision making and decision support systems require selecting a preferred subset of a given set of items. Here we focus on problems where the individual items are described using a set of characterizing attributes, and a generic preference specification is required, that is, a specification that can work with an arbitrary set of items. For example, preferences over the content of an online newspaper should have this form: At each viewing, the newspaper contains a subset of the set of articles currently available. Our preference specification over this subset should be provided offline, but we should be able to use it to select a subset of any currently available set of articles, e.g., based on their tags. We present a general approach for lifting formalisms for specifying preferences over objects with multiple attributes into ones that specify preferences over subsets of such objects. We also show how we can compute an optimal subset given such a specification in a relatively efficient manner. We provide an empirical evaluation of the approach as well as some worst-case complexity results.

SOLUTION: Generic Preferences over Subsets of Structured Objects

PROBLEM: Well-established automatic analyses of texts mainly consider frequencies of linguistic units, e.g. letters, words and bigrams, while methods based on cooccurrence networks consider the structure of texts regardless of the nodes label (i.e. the words semantics). In this paper, we reconcile these distinct viewpoints by introducing a generalized similarity measure to compare texts which accounts for both the network structure of texts and the role of individual words in the networks. We use the similarity measure for authorship attribution of three collections of books, each composed of 8 authors and 10 books per author. High accuracy rates were obtained with typical values from 90% to 98.75%, much higher than with the traditional the TF-IDF approach for the same collections. These accuracies are also higher than taking only the topology of networks into account. We conclude that the different properties of specific words on the macroscopic scale structure of a whole text are as relevant as their frequency of appearance; conversely, considering the identity of nodes brings further knowledge about a piece of text represented as a network.

SOLUTION:
On the role of words in the network structure of texts: application to authorship attribution