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Martin Pál

Martin Pál

Martin Pál graduated from Comenius University in Slovakia ("mgr." '00) and Cornell University (PhD '04). He held a postdoc at Rutgers and Bell Labs in '04/'05, and has been working as an engineer at Google since then.

Martin's interests include approximation algorithms, combinatorial optimization, auctions and game theory.

Authored Publications
Google Publications
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    Preview abstract We study the fundamental problem of selling a single indivisible good to one ofnbuyers with independentvaluations. We seek to design improved approximations to the optimal revenue achievable through two simpleand widely used mechanisms: second price auction with eager personalized reserve prices, and sequentialposted price mechanisms. Until recently, the best known approximation for both these mechanisms was 1−1e.We give improved approximations of 1−1e+0.022∼0.6543 for the sequential posted price mechanism and1−1e+0.029∼0.662 for the second price auction with eager reserve prices. We also make some progresstowards the problem of computing the optimal personalized eager reserve prices for a second price auction. View details
    Preview abstract We study the question of setting and testing reserve prices in single item auctions when the bidders are not identical. At a high level, there are two generalizations of the standard second price auction: in the lazy version we first determine the winner, and then apply reserve prices; in the eager version we first discard the bidders not meeting their reserves, and then determine the winner among the rest. We show that the two versions have dramatically different properties: lazy reserves are easy to optimize, and A/B test in production, whereas eager reserves always lead to higher welfare, but their optimization is NP-complete, and naive A/B testing will lead to incorrect conclusions. Despite their different characteristics, we show that the overall revenue for the two scenarios is always within a factor of 2 of each other, even in the presence of correlated bids. Moreover, we prove that the eager auction dominates the lazy auction on revenue whenever the bidders are independent or symmetric. We complement our theoretical results with simulations on real world data that show that even suboptimally set eager reserve prices are preferred from a revenue standpoint. View details
    Showing Relevant Ads via Lipschitz Context Multi-Armed Bandits
    Tyler Lu
    Dávid Pál
    Thirteenth International Conference on Artificial Intelligence and Statistics, Journal of Machine Learning Research (2010)
    Preview abstract We study contextual 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 contextual multi-armed bandit problem models a situation where, in a sequence of independent trials, an online algorithm chooses, based on a given context (side information), an action 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, a focus of much previous research, model situations where no side information is available and the payoff depends only on the action chosen. Our problem is motivated by sponsored web search, where the task is to display ads to a user of an Internet search engine based on her search query so as to maximize the click-through rate (CTR) of the ads displayed. We cast this problem as a contextual multi-armed bandit problem where queries and ads form metric spaces and the payoff function is Lipschitz with respect to both the metrics. For any $\epsilon > 0$ we present an algorithm with regret $O(T^{\frac{a+b+1}{a+b+2} + \epsilon})$ where $a,b$ are the covering dimensions of the query space and the ad space respectively. We prove a lower bound $\Omega(T^{\frac{\tilde{a}+\tilde{b}+1}{\tilde{a}+\tilde{b}+2} \epsilon})$ for the regret of any algorithm where $\tilde{a}, \tilde{b}$ are packing dimensions of the query spaces and the ad space respectively. For finite spaces or convex bounded subsets of Euclidean spaces, this gives an almost matching upper and lower bound. View details
    Preview abstract In sponsored search, a number of advertising slots is available on a search results page, and have to be allocated among a set of advertisers competing to display an ad on the page. This gives rise to a bipartite matching market that is typically cleared by the way of an automated auction. Several auction mechanisms have been proposed, with variants of the Generalized Second Price (GSP) being widely used in practice. There is a rich body of work on bipartite matching markets that builds upon the stable marriage model of Gale and Shapley and the assignment model of Shapley and Shubik. This line of research offers deep insights into the structure of stable outcomes in such markets and their incentive properties. In this paper, we model advertising auctions in terms of an assignment model with linear utilities, extended with bidder and item specific maximum and minimum prices. Auction mechanisms like the commonly used GSP or the well-known Vickrey-Clarke-Groves (VCG) can be interpreted as simply computing a bidder-optimal stable matching in this model, for a suitably defined set of bidder preferences, but our model includes much richer bidders and preferences. We prove that in our model the existence of a stable matching is guaranteed, and under a non-degeneracy assumption a bidder-optimal stable matching exists as well. We give an algorithm to find such matching in polynomial time, and use it to design truthful mechanism that generalizes GSP, is truthful for profit-maximizing bidders, correctly implements features like bidder-specific minimum prices and position-specific bids, and works for rich mixtures of bidders and preferences. Our main technical contributions are the existence of bidder-optimal matchings and strategyproofness of the resulting mechanism, and are proved by induction on the progress of the matching algorithm. View details
    An Online Mechanism for Ad Slot Reservations with Cancellations
    Florin Constantin
    S. Muthukrishnan
    Fourth Workshop on Ad Auctions; Symposium on Discrete Algorithms (SODA) (2009)
    Preview abstract We examine several online matching problems, with applications to Internet advertising reservation systems. Consider an edge-weighted bipartite graph G, with partite sets L, R. We develop an 8-competitive algorithm for the following secretary problem: Initially given R, and the size of L, the algorithm receives the vertices of L sequentially, in a random order. When a vertex l \in L is seen, all edges incident to l are revealed, together with their weights. The algorithm must immediately either match l to an available vertex of R, or decide that l will remain unmatched. Dimitrov and Plaxton show a 16-competitive algorithm for the transversal matroid secretary problem, which is the special case with weights on vertices, not edges. (Equivalently, one may assume that for each l \in L, the weights on all edges incident to l are identical.) We use a similar algorithm, but simplify and improve the analysis to obtain a better competitive ratio for the more general problem. Perhaps of more interest is the fact that our analysis is easily extended to obtain competitive algorithms for similar problems, such as to find disjoint sets of edges in hypergraphs where edges arrive online. We also introduce secretary problems with adversarially chosen groups. Finally, we give a 2e-competitive algorithm for the secretary problem on graphic matroids, where, with edges appearing online, the goal is to find a maximum-weight acyclic subgraph of a given graph. View details
    Sponsored Search Auctions for Markovian Users
    S. Muthukrishnan
    Fourth Workshop on Ad Auctions; Workshop on Internet and Network Economics (WINE). (2008)
    Preview abstract Sponsored search involves running an auction among advertisers who bid in order to have their ad shown next to search results for specific keywords. The most popular auction for sponsored search is the “Generalized Second Price” (GSP) auction where advertisers are assigned to slots in the decreasing order of their score, which is defined as the product of their bid and click-through rate. One of the main advantages of this simple ranking is that bidding strategy is intuitive: to move up to a more prominent slot on the results page, bid more. This makes it simple for advertisers to strategize. However this ranking only maximizes efficiency under the assumption that the probability of a user clicking on an ad is independent of the other ads shown on the page. We study a Markovian user model that does not make this assumption. Under this model, the most efficient assignment is no longer a simple ranking function as in GSP. We show that the optimal assignment can be found efficiently (even in near-linear time). As a result of the more sophisticated structure of the optimal assignment, bidding dynamics become more complex: indeed it is no longer clear that bidding more moves one higher on the page. Our main technical result is that despite the added complexity of the bidding dynamics, the optimal assignment has the property that ad position is still monotone in bid. Thus even in this richer user model, our mechanism retains the core bidding dynamics of the GSP auction that make it useful for advertisers. View details
    Improved Algorithms for Orienteering and Related Problems
    Chandra Chekuri
    Proc. 19th Annual Symposium on Discrete Algorithms (SODA), SIAM (2008)
    A Truthful Mechanism for Offline Ad Slot Scheduling
    S. Muthukrishnan
    Evdokia Nikolova
    Symposium on Algorithmic Game Theory (2008)
    Theory research at Google
    Nir Ailon
    Florin Constantin
    Eyal Even-Dar
    Gereon Frahling
    Monika R. Henzinger
    S. Muthukrishnan
    Noam Nisan
    Anastasios Sidiropoulos
    SIGACT News, vol. 39 (2008), pp. 10-28
    Sharing the cost more efficiently: Improved approximation for multicommodity rent-or-buy
    L. Becchetti
    J. Könemann
    S. Leonardi
    ACM Transactions on Algorithms, vol. 3, no 2 (2007), pp. 23
    Stochastic Models for Budget Optimization in Search-Based Advertising
    S. Muthukrishnan
    Internet and Network Economics (WINE), Springer, San Diego (2007), pp. 131-142
    Maximizing a Submodular Set Function subject to a Matroid Constraint
    Chandra Chekuri
    Gruia Calinescu
    Jan Vondrák
    Proceedings of the Twelfth Conference on Integer Programming and Combinatorial Optimization (IPCO) 2007
    Budget Optimization in Search-Based Advertising Auctions
    S. Muthukrishnan
    Cliff Stein
    Proc. ACM Conference on Electronic Commerce, ACM, San Diego (2007)
    Preview abstract Internet search companies sell advertisement slots based on users' search queries via an auction. While there has been previous work onthe auction process and its game-theoretic aspects, most of it focuses on the Internet company. In this work, we focus on the advertisers, who must solve a complex optimization problem to decide how to place bids on keywords to maximize their return (the number of user clicks on their ads) for a given budget. We model the entire process and study this budget optimization problem. While most variants are NP-hard, we show, perhaps surprisingly, that simply randomizing between two uniform strategies that bid equally on all the keywordsworks well. More precisely, this strategy gets at least a 1-1/ε fraction of the maximum clicks possible. As our preliminary experiments show, such uniform strategies are likely to be practical. We also present inapproximability results, and optimal algorithms for variants of the budget optimization problem. View details
    Approximation via Cost Sharing: Simpler and Better Approximation Algorithms for Network Design
    Anupam Gupta
    Amit Kumar
    Tim Roughgarden
    Journal of the ACM, vol. 54, no 3 (2007), pp. 11
    Proportional Fairness in Multi-Rate Wireless LANs
    Li (Erran) Li
    Yang Richard Yang
    INFOCOM 2008, IEEE