arXiv subjects

Vasilis Syrgkanis

Publications and source records attributed to Vasilis Syrgkanis.

At least 109 records · Page 6Linked to original sources

arXiv2017

Combinatorial Assortment Optimization

Assortment optimization refers to the problem of designing a slate of products to offer potential customers, such as stocking the shelves in a convenience store. The price of each product is fixed in advance, and a probabilistic choice function describes which product a customer will choose from any given subset. We introduce the combinatorial assortment problem, where each customer may select a bundle of products. We consider a model of consumer choice where the relative value of different bundles is described by a valuation function, while individual customers may differ in their absolute willingness to pay, and study the complexity of the resulting optimization problem. We show that any sub-polynomial approximation to the problem requires exponentially many demand queries when the valuation function is XOS, and that no FPTAS exists even for succinctly-representable submodular valuations. On the positive side, we show how to obtain constant approximations under a "well-priced" condition, where each product's price is sufficiently high. We also provide an exact algorithm for $k$-additive valuations, and show how to extend our results to a learning setting where the seller must infer the customers' preferences from their purchasing behavior.

cs.GT↗

arXiv2017

Truthful Multi-Parameter Auctions with Online Supply: an Impossible Combination

We study a basic auction design problem with online supply. There are two unit-demand bidders and two types of items. The first item type will arrive first for sure, and the second item type may or may not arrive. The auctioneer has to decide the allocation of an item immediately after each item arrives, but is allowed to compute payments after knowing how many items arrived. For this problem we show that there is no deterministic truthful and individually rational mechanism that, even with unbounded computational resources, gets any finite approximation factor to the optimal social welfare.

cs.GT↗

arXiv2017

Efficiency Guarantees from Data

Analysis of efficiency of outcomes in game theoretic settings has been a main item of study at the intersection of economics and computer science. The notion of the price of anarchy takes a worst-case stance to efficiency analysis, considering instance independent guarantees of efficiency. We propose a data-dependent analog of the price of anarchy that refines this worst-case assuming access to samples of strategic behavior. We focus on auction settings, where the latter is non-trivial due to the private information held by participants. Our approach to bounding the efficiency from data is robust to statistical errors and mis-specification. Unlike traditional econometrics, which seek to learn the private information of players from observed behavior and then analyze properties of the outcome, we directly quantify the inefficiency without going through the private information. We apply our approach to datasets from a sponsored search auction system and find empirical results that are a significant improvement over bounds from worst-case analysis.

cs.GT↗

arXiv2017

Robust Optimization for Non-Convex Objectives

We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. We develop a reduction from robust improper optimization to Bayesian optimization: given an oracle that returns $α$-approximate solutions for distributions over objectives, we compute a distribution over solutions that is $α$-approximate in the worst case. We show that de-randomizing this solution is NP-hard in general, but can be done for a broad class of statistical learning tasks. We apply our results to robust neural network training and submodular optimization. We evaluate our approach experimentally on corrupted character classification, and robust influence maximization in networks.

cs.LG↗

arXiv2017

A Proof of Orthogonal Double Machine Learning with $Z$-Estimators

We consider two stage estimation with a non-parametric first stage and a generalized method of moments second stage, in a simpler setting than (Chernozhukov et al. 2016). We give an alternative proof of the theorem given in (Chernozhukov et al. 2016) that orthogonal second stage moments, sample splitting and $n^{1/4}$-consistency of the first stage, imply $\sqrt{n}$-consistency and asymptotic normality of second stage estimates. Our proof is for a variant of their estimator, which is based on the empirical version of the moment condition (Z-estimator), rather than a minimization of a norm of the empirical vector of moments (M-estimator). This note is meant primarily for expository purposes, rather than as a new technical contribution.

stat.ML↗

arXiv2017

A Sample Complexity Measure with Applications to Learning Optimal Auctions

We introduce a new sample complexity measure, which we refer to as split-sample growth rate. For any hypothesis $H$ and for any sample $S$ of size $m$, the split-sample growth rate $\hatτ_H(m)$ counts how many different hypotheses can empirical risk minimization output on any sub-sample of $S$ of size $m/2$. We show that the expected generalization error is upper bounded by $O\left(\sqrt{\frac{\log(\hatτ_H(2m))}{m}}\right)$. Our result is enabled by a strengthening of the Rademacher complexity analysis of the expected generalization error. We show that this sample complexity measure, greatly simplifies the analysis of the sample complexity of optimal auction design, for many auction classes studied in the literature. Their sample complexity can be derived solely by noticing that in these auction classes, ERM on any sample or sub-sample will pick parameters that are equal to one of the points in the sample.

cs.GT↗

arXiv2017

Simple vs Optimal Mechanisms in Auctions with Convex Payments

We investigate approximately optimal mechanisms in settings where bidders' utility functions are non-linear; specifically, convex, with respect to payments (such settings arise, for instance, in procurement auctions for energy). We provide constant factor approximation guarantees for mechanisms that are independent of bidders' private information (i.e., prior-free), and for mechanisms that rely to an increasing extent on that information (i.e., detail free). We also describe experiments, which show that for randomly drawn monotone hazard rate distributions, our mechanisms achieve at least 80\% of the optimal revenue, on average. Both our theoretical and experimental results show that in the convex payment setting, it is desirable to allocate across multiple bidders, rather than only to bidders with the highest (virtual) value, as in the traditional quasi-linear utility setting.

cs.GT↗

arXiv2016

The Price of Anarchy in Auctions

This survey outlines a general and modular theory for proving approximation guarantees for equilibria of auctions in complex settings. This theory complements traditional economic techniques, which generally focus on exact and optimal solutions and are accordingly limited to relatively stylized settings. We highlight three user-friendly analytical tools: smoothness-type inequalities, which immediately yield approximation guarantees for many auction formats of interest in the special case of complete information and deterministic strategies; extension theorems, which extend such guarantees to randomized strategies, no-regret learning outcomes, and incomplete-information settings; and composition theorems, which extend such guarantees from simpler to more complex auctions. Combining these tools yields tight worst-case approximation guarantees for the equilibria of many widely-used auction formats.

cs.GT↗

arXiv2016

Improved Regret Bounds for Oracle-Based Adversarial Contextual Bandits

We give an oracle-based algorithm for the adversarial contextual bandit problem, where either contexts are drawn i.i.d. or the sequence of contexts is known a priori, but where the losses are picked adversarially. Our algorithm is computationally efficient, assuming access to an offline optimization oracle, and enjoys a regret of order $O((KT)^{\frac{2}{3}}(\log N)^{\frac{1}{3}})$, where $K$ is the number of actions, $T$ is the number of iterations and $N$ is the number of baseline policies. Our result is the first to break the $O(T^{\frac{3}{4}})$ barrier that is achieved by recently introduced algorithms. Breaking this barrier was left as a major open problem. Our analysis is based on the recent relaxation based approach of (Rakhlin and Sridharan, 2016).

cs.LG↗

arXiv2016

Learning in Auctions: Regret is Hard, Envy is Easy

A line of recent work provides welfare guarantees of simple combinatorial auction formats, such as selling m items via simultaneous second price auctions (SiSPAs) (Christodoulou et al. 2008, Bhawalkar and Roughgarden 2011, Feldman et al. 2013). These guarantees hold even when the auctions are repeatedly executed and players use no-regret learning algorithms. Unfortunately, off-the-shelf no-regret algorithms for these auctions are computationally inefficient as the number of actions is exponential. We show that this obstacle is insurmountable: there are no polynomial-time no-regret algorithms for SiSPAs, unless RP$\supseteq$ NP, even when the bidders are unit-demand. Our lower bound raises the question of how good outcomes polynomially-bounded bidders may discover in such auctions. To answer this question, we propose a novel concept of learning in auctions, termed "no-envy learning." This notion is founded upon Walrasian equilibrium, and we show that it is both efficiently implementable and results in approximately optimal welfare, even when the bidders have fractionally subadditive (XOS) valuations (assuming demand oracles) or coverage valuations (without demand oracles). No-envy learning outcomes are a relaxation of no-regret outcomes, which maintain their approximate welfare optimality while endowing them with computational tractability. Our results extend to other auction formats that have been studied in the literature via the smoothness paradigm. Our results for XOS valuations are enabled by a novel Follow-The-Perturbed-Leader algorithm for settings where the number of experts is infinite, and the payoff function of the learner is non-linear. This algorithm has applications outside of auction settings, such as in security games. Our result for coverage valuations is based on a novel use of convex rounding schemes and a reduction to online convex optimization.

cs.GT↗

arXiv2016

Efficient Algorithms for Adversarial Contextual Learning

We provide the first oracle efficient sublinear regret algorithms for adversarial versions of the contextual bandit problem. In this problem, the learner repeatedly makes an action on the basis of a context and receives reward for the chosen action, with the goal of achieving reward competitive with a large class of policies. We analyze two settings: i) in the transductive setting the learner knows the set of contexts a priori, ii) in the small separator setting, there exists a small set of contexts such that any two policies behave differently in one of the contexts in the set. Our algorithms fall into the follow the perturbed leader family \cite{Kalai2005} and achieve regret $O(T^{3/4}\sqrt{K\log(N)})$ in the transductive setting and $O(T^{2/3} d^{3/4} K\sqrt{\log(N)})$ in the separator setting, where $K$ is the number of actions, $N$ is the number of baseline policies, and $d$ is the size of the separator. We actually solve the more general adversarial contextual semi-bandit linear optimization problem, whilst in the full information setting we address the even more general contextual combinatorial optimization. We provide several extensions and implications of our algorithms, such as switching regret and efficient learning with predictable sequences.

cs.LG↗

arXiv2016

Optimal Auctions with Convex Perceived Payments

Myerson derived a simple and elegant solution to the single-parameter revenue-maximization problem in his seminal work on optimal auction design assuming the usual model of quasi-linear utilities. In this paper, we consider a slight generalization of this usual model---from linear to convex "perceived" payments. This more general problem does not appear to admit a solution as simple and elegant as Myerson's. While some of Myerson's results extend to our setting, like his payment formula (suitably adjusted), others do not. For example, we observe that the solutions to the Bayesian and the robust (i.e., non-Bayesian) optimal auction design problems in the convex perceived payment setting do not coincide like they do in the case of linear payments. We therefore study the two problems in turn. We derive an upper and a heuristic lower bound on expected revenue in our setting. These bounds are easily computed pointwise, and yield monotonic allocation rules, so can be supported by Myerson payments (suitably adjusted). In this way, our bounds yield heuristics that approximate the optimal robust auction, assuming convex perceived payments. We close with experiments, the final set of which massages the output of one of the closed-form heuristics for the robust problem into an extremely fast, near-optimal heuristic solution to the Bayesian optimal auction design problem.

cs.GT↗

arXiv2015

Fast Convergence of Regularized Learning in Games

We show that natural classes of regularized learning algorithms with a form of recency bias achieve faster convergence rates to approximate efficiency and to coarse correlated equilibria in multiplayer normal form games. When each player in a game uses an algorithm from our class, their individual regret decays at $O(T^{-3/4})$, while the sum of utilities converges to an approximate optimum at $O(T^{-1})$--an improvement upon the worst case $O(T^{-1/2})$ rates. We show a black-box reduction for any algorithm in the class to achieve $\tilde{O}(T^{-1/2})$ rates against an adversary, while maintaining the faster rates against algorithms in the class. Our results extend those of [Rakhlin and Shridharan 2013] and [Daskalakis et al. 2014], who only analyzed two-player zero-sum games for specific algorithms.

cs.GT↗

arXiv2015

No-Regret Learning in Bayesian Games

Recent price-of-anarchy analyses of games of complete information suggest that coarse correlated equilibria, which characterize outcomes resulting from no-regret learning dynamics, have near-optimal welfare. This work provides two main technical results that lift this conclusion to games of incomplete information, a.k.a., Bayesian games. First, near-optimal welfare in Bayesian games follows directly from the smoothness-based proof of near-optimal welfare in the same game when the private information is public. Second, no-regret learning dynamics converge to Bayesian coarse correlated equilibrium in these incomplete information games. These results are enabled by interpretation of a Bayesian game as a stochastic game of complete information.

cs.GT↗

arXiv2015

Pricing Queries Approximately Optimally

Data as a commodity has always been purchased and sold. Recently, web services that are data marketplaces have emerged that match data buyers with data sellers. So far there are no guidelines how to price queries against a database. We consider the recently proposed query-based pricing framework of Koutris et al and ask the question of computing optimal input prices in this framework by formulating a buyer utility model. We establish the interesting and deep equivalence between arbitrage-freeness in the query-pricing framework and envy-freeness in pricing theory for appropriately chosen buyer valuations. Given the approximation hardness results from envy-free pricing we then develop logarithmic approximation pricing algorithms exploiting the max flow interpretation of the arbitrage-free pricing for the restricted query language proposed by Koutris et al. We propose a novel polynomial-time logarithmic approximation pricing scheme and show that our new scheme performs better than the existing envy-free pricing algorithms instance-by-instance. We also present a faster pricing algorithm that is always greater than the existing solutions, but worse than our previous scheme. We experimentally show how our pricing algorithms perform with respect to the existing envy-free pricing algorithms and to the optimal exponentially computable solution, and our experiments show that our approximation algorithms consistently arrive at about 99% of the optimal.

cs.GT↗

arXiv2015

Econometrics for Learning Agents

The main goal of this paper is to develop a theory of inference of player valuations from observed data in the generalized second price auction without relying on the Nash equilibrium assumption. Existing work in Economics on inferring agent values from data relies on the assumption that all participant strategies are best responses of the observed play of other players, i.e. they constitute a Nash equilibrium. In this paper, we show how to perform inference relying on a weaker assumption instead: assuming that players are using some form of no-regret learning. Learning outcomes emerged in recent years as an attractive alternative to Nash equilibrium in analyzing game outcomes, modeling players who haven't reached a stable equilibrium, but rather use algorithmic learning, aiming to learn the best way to play from previous observations. In this paper we show how to infer values of players who use algorithmic learning strategies. Such inference is an important first step before we move to testing any learning theoretic behavioral model on auction data. We apply our techniques to a dataset from Microsoft's sponsored search ad auction system.

cs.GT↗

arXiv2015

The Price of Anarchy in Large Games

Game-theoretic models relevant for computer science applications usually feature a large number of players. The goal of this paper is to develop an analytical framework for bounding the price of anarchy in such models. We demonstrate the wide applicability of our framework through instantiations for several well-studied models, including simultaneous single-item auctions, greedy combinatorial auctions, and routing games. In all cases, we identify conditions under which the POA of large games is much better than that of worst-case instances. Our results also give new senses in which simple auctions can perform almost as well as optimal ones in realistic settings.

cs.GT↗

arXiv2015

Greedy Algorithms make Efficient Mechanisms

We study mechanisms that use greedy allocation rules and pay-your-bid pricing to allocate resources subject to a matroid constraint. We show that all such mechanisms obtain a constant fraction of the optimal welfare at any equilibrium of bidder behavior, via a smoothness argument. This unifies numerous recent results on the price of anarchy of simple auctions. Our results extend to polymatroid and matching constraints, and we discuss extensions to more general matroid intersections.

cs.GT↗