Jon Schneider

Competitive analysis of the top- K ranking problem

Motivated by applications in recommender systems, web search, social choice and crowdsourcing, we consider the problem of identifying the set of top K items from noisy pairwise comparisons. In our setting, we are non-actively given r pairwise comparisons between each pair of n items, where each comparison has noise constrained by a very general noise model called the strong stochastic transitivity (SST) model. We analyze the competitive ratio of algorithms for the top-K problem. In particular, we present a linear time algorithm for the top-K problem which has a competitive ratio of O( √ n); i.e. to solve any instance of top-K, our algorithm needs at most O( √ n) times as many samples needed as the best possible algorithm for that instance (in contrast, all previous known algorithms for the top-K problem have competitive ratios of Ω(n) or worse). We further show that this is tight: any algorithm for the top-K problem has competitive ratio at least Ω( √ n). Stern School of Business, New York University, email: xchen3@stern.nyu.edu Department of Computer Science, Princeton University, email: sgopi@cs.princeton.edu Department of Computer Science, Princeton University, email: jiemingm@cs.princeton.edu Department of Computer Science, Princeton University, email: js44@cs.princeton.edu 1

Information Complexity Is Computable

The information complexity of a function

Condorcet-Consistent and Approximately Strategyproof Tournament Rules.

f

Information complexity is computable.

is the minimum amount of information Alice and Bob need to exchange to compute the function

Contextual Search via Intrinsic Volumes

f

Selling to a No-Regret Buyer

. In this paper we provide an algorithm for approximating the information complexity of an arbitrary function

Optimal Instance Adaptive Algorithm for the Top-

f

K

to within any additive error

Ranking Problem

\alpha > 0

Multi-armed Bandit Problems with Strategic Arms.

, thus resolving an open question as to whether information complexity is computable. In the process, we give the first explicit upper bound on the rate of convergence of the information complexity of