Dávid Pál

Yahoo Labs
229 West 43rd Street, 11th Floor
New York, NY 10036

home address:
1 River Place, Apt. 2918
New York, NY 10036

home phone: +1 (917) 965 2187
cell phone: +1 (646) 206 4832


I am a research scientist at Yahoo! Labs in New York City.

My research interests are machine learning, algorithms, game theory and combinatorics. Curriculum Vitae from 2015.

September 2011 - September 2014, I was a software engineer at Google in New York City.

July 2009 – June 2011, I was a post-doctoral fellow at AICML at Department of Computing Science at University of Alberta, Canada under supervision of Csaba Szepesvári.

In May 2009, I finished my PhD from School of Computer Science at University of Waterloo in Canada. My advisor was Shai Ben-David.

I did my undergrad at Faculty of Mathematics, Physics and Informatics at Comenius University in Bratislava, Slovakia. My undergrad thesis advisor was Martin Škoviera. At Comenius University, I also organized Internet Problem Solving Contest, and local math and programming contests and olympiads for high school students.

My wife Lucia and my brother Martin are also computer scientists.


  • Francesco Orabona, Dávid Pál
    Optimal Non-Asymptotic Lower Bound on the Minimax Regret of Learning with Expert Advice
    Summary: We show a non-asymptotic optimal lower bounds on the expected value of maximum of independent Gaussians and the expected value of maximum of independent symmetric random walks. Both bounds are asymptotically optimal, i.e. they imply known limit theorems for these quantities. Simple application of the lower bound for symmetric random walk is a lower bound of the regret for the problem of learning with expert advice which is a classical online learning problem.
    Bib info: preprint
    Download: [arXiv]
  • Satyen Kale, Chansoo Lee, Dávid Pál
    Hardness of Online Sleeping Combinatorial Optimization Problems
    Summary: We show computational hardness of sleeping variants of six combinatorial sequential decision making problems (Online Shortest Paths, Online Minimum Spanning Tree, Online k-Subsets, Online k-Truncated Permutations, Online Minimum Cut, and Online Bipartite Matching). We show that sleeping variants of these problems are as hard as PAC learning DNF expressions.
    Bib info: preprint
    Download: [arXiv]
  • Francesco Orabona, Dávid Pál
    Scale-Free Algorithms for Online Linear Optimization
    Summary: We design algorithms for online linear optimization that are invariant to scaling of the loss vectors. Scale invariance, as a design principle, almost instantly leads to better algorithms and cleaner regret analysis. We design and analyze two scale-free variants of Follow The Regularized Leader Algorithm. The two algorithms are simple, fully adaptive and work with any strongly convex regularizer.
    Bib info: ALT 2015
    Download: [PDF] [arXiv] Slides [1] [2] [3]
  • Gábor Bartók, Dávid Pál, Csaba Szepesvári, István Szita
    Online Learning Lecture Notes
    Summary: In spring 2011, Csaba taught an online learning course with occasional help from Gábor and István and me. As we were teaching, we were continuously writing lecture notes. The focus of the course was no-regret non-stochastic learning (learning with expert advice, switching experts, follow the regularized leader algorithm, online linear regression), and brief explanation of online-to-batch conversion and multi-armed bandits. Our goal was to develop the theory from first principles.
    Bib info: lecture notes
    Download: [PDF]
  • Yasin Abbasi-Yadkori, Dávid Pál, Csaba Szepesvári
    Online-to-Confidence-Set Conversions and Application to Sparse Stochastic Bandits
    Summary: We show how to convert a regret bound for an online algorithm for linear prediction under quadratic loss (e.g. online least squares, online gradient, p-norm algorithm) into a confidence set for the weight vector of the linear model under any sub-Gaussian noise. The lower the regret of the algorithm, the smaller the confidence set. As an application, we use these confidence sets to construct online algorithms for the linear stochastic bandit problem. Using an online linear prediction algorithm for sparse models, we are able to construct an algorithm for the sparse linear stochastic bandit problem i.e. problem where the underlying linear model is sparse.
    Bib info: AISTATS 2012
    Download: [PDF], [Slides], [Overview Talk]
  • Yasin Abbasi-Yadkori, Dávid Pál, Csaba Szepesvári
    Improved Algorithms for Linear Stochastic Bandits
    Summary: We provide an upper bound for the tail probability of the norm of a vector-valued martingale. This bound immediately gives rise to a confidence set (ellipsoid) for online regularized linear least-squares estimator. We apply these confidence sets to the stochastic multi-armed bandit problem and the stochastic linear bandit problem. We show that the regret of the modified UCB algorithm is constant for any fixed confidence parameter! Furthermore, we improve the previously known bounds for the stochastic linear bandit problem by a poly-logarithmic factor.
    Bib info: NIPS 2011
    Download: [PDF], [arXiv]
  • Gábor Bartók, Dávid Pál, Csaba Szepesvári
    Minimax Regret of Finite Partial-Monitoring Games in Stochastic Environments
    Summary: We continue with our ALT 2010 paper by classification of minimax regret of all partial games with finite number of actions and outcomes. However, we restrict ourselves to stochastic environments, i.e. the environment choose outcomes i.i.d. from a fixed but unknown probability distribution. We show that regret of any game falls into one of the four categories: zero, T1/2, T2/3 or T. We provide algorithms that achieve that regret within logarithmic factor. We believe that this result can be lifted to adversarial setting also; however that's left as a future work.
    Bib info: Proceedings COLT 2011
    Download: [PDF]
  • Gábor Bartók, Dávid Pál, Csaba Szepesvári
    Toward a Classification of Partial Monitoring Games
    Summary: Partial monitoring games are online learning problems where a decision maker repeatedly makes a decision, receives a feedback and suffers a loss. Multi-armed bandits and dynamic pricing are special cases. We give characterization of min-max regret of all finite partial monitoring games with two outcomes. We show that regret of any such game falls into one of the four categories: zero, T1/2, T2/3 or T. Our characterization is nice and simple combinatorial/geometrical condition on the loss matrix.
    Bib info: Proceedings of ALT 2010, Gábor received for this paper the best student paper award.
    Download: [PDF], [arXiv]
  • Dávid Pál, Barnabás Póczos, Csaba Szepesvári
    Estimation of Rényi Entropy and Mutual Information Based on Generalized Nearest-Neighbor Graphs
    Summary: We consider simple and computationally efficient nonparametric estimators of Rényi entropy and mutual information based on an i.i.d. sample drawn from an unknown, absolutely continuous distribution over Rd. The estimators are calculated as the sum of p-th powers of the Euclidean lengths of the edges of the `generalized nearest-neighbor' graph of the sample and the empirical copula of the sample respectively. Under mild conditions we prove the almost sure consistency of the estimators. In addition, we derive high probability error bounds assuming that the density underlying the sample is Lipschitz continuous.
    Bib info: Proceedings of NIPS 2010
    Download: conference version: [PDF], extended version with proofs: [PDF], [arXiv], poster: [PDF]
  • Shai Ben-David, Dávid Pál, Shai Shalev-Shwartz
    Agnostic Online Learning
    Summary: We generalize the Littlestone's online learning model to the agnostic setting where no hypothesis makes zero error. Littlestone defined a combinatorial parameter of the hypothesis class, which we call Littlestone's dimension and which determines the worst-case number of prediction mistakes made by an online learning algorithm in the realizable setting. Point of our paper is that Littlestone's dimension characterizes learnability in the agnostic case as well. Namely, we give upper and lower bounds on the regret in terms of the Littlestone's dimension.
    This is a similar story to what happened to the Valiant's PAC model. The key quantity there is Vapnik-Chervonekis dimension. Valiant's PAC model is the ``realizable case''. Our work can be paralleled to what Haussler and others did in 1992 when they generalized the PAC model to the agnostic setting and showed that Vapnik-Chervonekis dimension remains the key quantity characterizing learnability there as well.
    Bib info: COLT 2009
    Download: [PDF], [slides], [slides sources]
  • PhD thesis.
    Contributions to Unsupervised and Semi-Supervised Learning
    This thesis is essentially a compilation of the two older papers on clustering stability and an part of the paper on semi-supervised learning. The formal gaps, especially in the first paper on clustering stability, were filled in and presentation was improved.
    Download: [PDF], [sources]
  • Tyler Lu, Dávid Pál, Martin Pál
    Showing Relevant Ads via Lipschitz Context Multi-Armed Bandits
    Summary: We study context multi-armed bandit problems where the context comes from a metric space and the payoff satisfies a Lipschitz condition with respect to the metric. Abstractly, a context multi-armed bandit problem models a situation in which, in a sequence of independent trials, an online algorithm chooses an action based on a given context (side information) from a set of possible actions so as to maximize the total payoff of the chosen actions. The payoff depends on both the action chosen and the context. In contrast, context-free multi-armed bandit problems, studied previously, model situations where no side information is available and the payoff depends only on the action chosen.
    For concreteness we focus in this paper on an application to Internet search advertisement where the task is to display ads to a user of a Internet search engine based on his search query so as to maximize the click-trough rate of the ads displayed. We cast this problem as a context multi-armed bandit problem where queries and ads form metric spaces and the payoff function is Lipschitz with respect to both the metrics. We present an algorithm, give upper bound on its regret and show an (almost) matching lower bound on the regret of any algorithm.
    Bib info: Proceedings of AISTATS 2010
    Download: [PDF], [slides], [slides sources]
  • Shai Ben-David, Tyler Lu, Dávid Pál, Miroslava Sotáková
    Learning Low-Density Separators
    Summary: We define a novel, basic, unsupervised learning problem - learning the lowest density homogeneous hyperplane separator of an unknown probability distribution. This task is relevant to several problems in machine learning, such as semi-supervised learning and clustering stability. We investigate the question of existence of a universally consistent algorithm for this problem. We propose two natural learning paradigms and prove that, on input unlabeled random samples generated by any member of a rich family of distributions, they are guaranteed to converge to the optimal separator for that distribution. We complement this result by showing that no learning algorithm for our task can achieve uniform learning rates (that are independent of the data generating distribution).
    Bib info: Proceedings of AISTATS 2009
    Download: [PDF] [arXiv]
  • Shai Ben-David, Tyler Lu, Dávid Pál
    Does Unlabeled Data Provably Help? Worst-case Analysis of the Sample Complexity of Semi-Supervised Learning
    Summary: We mathematically study the potential benefits of the use of unlabeled data to decrease classification error. We propose a simple model of semi-supervised learning (SSL) in which the unlabeled data distribution is perfectly known to the learner. We compare this model with the standard PAC model (and its agnostic version) for supervised learning, in which the unlabeled distribution is uknown to the learner. Does there exists a supervised algorithm which for any unlabeled distribution needs in the worst case (over possible targets) at most by a constant factor more labeled samples than any SSL learner? It seems that the ERM algorithm is such a candidate. We prove, for some special cases, that this indeed the case.
    Bib info: Proceedings of COLT 2008
    Note: See also Tyler's Master's thesis. Download: [PDF] [sources]
  • Gagan Aggarwal, S. Muthukrishnan, Dávid Pál, Martin Pál
    General Auction Mechanism for Search Advertising
    Summary: We propose a new auction mechanism for search advertising that generalizes both Generalized Second Price auction (which is currently, in 2008, used by Google, Yahoo! and MSN) and the famous Vickrey-Clarke-Groves mechanism adapted to the search auctions. Our mechanism allows each bidder to specify a subset of slots in which (s)he is interested, and the value and the maximum price of each slot. For the auctioneer (the search engine) it allows to specify for every slot-bidder pair a reserve (minimum) price. Our auction computes the bidder-optimal stable matching. The running time is O(nk^3), where n is the number of bidders and k is the number of slots. We also prove that our auction mechanism is truth-revealing, that is, dominant strategy of each bidder is not to lie.
    Bib info: Proceedings of WWW 2009
    Download: [PDF]
  • Shai Ben-David, Dávid Pál, Hans Ulrich Simon
    Stability of K-means Clusterings
    Summary: This is follow-up of the previous paper. We consider the clustering algorithm A which minimizes the k-means cost precisely. (Such algorithm is not realistic, since the optimization problem is known to be NP-hard. Nevertheless, the classical Lloyd's heuristic a.k.a. "the k-mean algorithm" tries to do this.) We analyze how stable is the clustering outputted by A with respect to a random draw of the sample points. Given a probability distribution, draw two i.i.d. samples of the same size. If with high probability, the clustering of the first sample does not differ from the clustering of the second sample too much, we say that A is stable on the probability distribution. For discrete probability distributions we show that instability happens if and only if the probability distribution has two or more clusterings with optimal k-means cost.
    Bib info: Proceedings of COLT 2007
    Download: [PDF] (extended version),   [PDF] (short conference version)
  • Shai Ben-David, Dávid Pál, Ulrike von Luxburg
    A Sober look at Clustering Stability
    Summary: We investigate how stable is the clustering outputted by a clustering algorithm with respect to a random draw of the sample points. Given a probability distribution, draw two i.i.d. samples of the same size. If with high probability, the clustering of the first sample does not differ from the clustering of the second sample too much, we say that algorithm is stable on the probability distribution. We show that for that for algorithms that optimize some cost function stability depends on the uniqueness of the optimal solution of the optimization problem for the "infinite" sample represented by the probability distribution.
    Bib info: Proceedings of COLT 2006, Best Student Paper Award
    Download: [PDF],   [Slides in PDF],   [Slides source files]
  • Dávid Pál, Martin Škoviera
    Colouring Cubic Graphs by Small Steiner Triple Systems
    Summary: Steiner triple system is a collection of 3-element subsets (called triples) of a finite set of points, such that every two points appear together in exactly one triple. Given Steiner triple system S, one can ask whether it is possible to color the edges of a cubic graph with points of S, in such way that colors of the three edges at a vertex form a triple of S. We construct a small Steiner triple system (of order 21) which colors all simple cubic graphs.
    Note: This is the main result of my "Magister" Thesis at Comenius University under my advisor Martin Škoviera, 2004.
    Bib info: Graphs and Combinatorics, 2007
    Download: [PDF],   [Postscript],   [Source files]
Yasin Abbasi-Yadkori
Gagan Aggarwal
Gábor Bartók
Shai Ben-David
Satyen Kale
Chansoo Lee
Tyler Lu
Ulrike von Luxburg
S. Muthukrisnan
Francesco Orabona
Martin Pál
Barnabás Póczos
Hans Ulrich Simon
Miroslava Sotáková
Martin Škoviera
Shai Shalev-Shwartz
Csaba Szepesvári

Last updated: November 8, 2015