Learnability of Non-I.I.D

Abstract Learnability has always been one of the most central problems in learning theory. Most previous studies on this issue were based on the assumption that the samples are drawn independently and identically according to an underlying (unknown) distribution. The i.i.d. assumption, however, does not hold in many real applications. In this paper, we study the learnability of problems where the samples are drawn from empirical process of stationary β-mixing sequence, which has been a widely-used assumption implying a dependence weaken over time in training samples. By utilizing the independent blocks technique, we provide a sufficient and necessary condition for learnability, that is, average stability is equivalent to learnability with AERM (Asymptotic Empirical Risk Minimization) in the non-i.i.d. learning setting. In addition, we also discuss the generalization error when the test variable is dependent on the training sample

Learning Cooperative Games

This paper explores a PAC (probably approximately correct) learning model in cooperative games. Specifically, we are given $m$ random samples of coalitions and their values, taken from some unknown cooperative game; can we predict the values of unseen coalitions? We study the PAC learnability of several well-known classes of cooperative games, such as network flow games, threshold task games, and induced subgraph games. We also establish a novel connection between PAC learnability and core stability: for games that are efficiently learnable, it is possible to find payoff divisions that are likely to be stable using a polynomial number of samples.Comment: accepted to IJCAI 201

Beliefs in Repeated Games

Consider a two-player discounted infinitely repeated game. A player's belief is a probability distribution over the opponent's repeated game strategies. This paper shows that, for a large class of repeated games, there are no beliefs that satisfy three conditions, learnability, consistency, and a diversity condition, CS. This impossibility theorem generalizes results in Nachbar (1997).

Learning Economic Parameters from Revealed Preferences

A recent line of work, starting with Beigman and Vohra (2006) and Zadimoghaddam and Roth (2012), has addressed the problem of {\em learning} a utility function from revealed preference data. The goal here is to make use of past data describing the purchases of a utility maximizing agent when faced with certain prices and budget constraints in order to produce a hypothesis function that can accurately forecast the {\em future} behavior of the agent. In this work we advance this line of work by providing sample complexity guarantees and efficient algorithms for a number of important classes. By drawing a connection to recent advances in multi-class learning, we provide a computationally efficient algorithm with tight sample complexity guarantees ($\Theta(d/\epsilon)$ for the case of $d$ goods) for learning linear utility functions under a linear price model. This solves an open question in Zadimoghaddam and Roth (2012). Our technique yields numerous generalizations including the ability to learn other well-studied classes of utility functions, to deal with a misspecified model, and with non-linear prices