We present a competitive analysis of some non-parametric Bayesian algorithms in a worst-case online learning setting, where no probabilistic assumptions about the generation of the data are made. We consider models which use a Gaussian process prior (over the space of all functions) and provide bounds on the regret (under the log loss) for commonly used non-parametric Bayesian algorithms — incl...

The normalized maximum likelihood distribution achieves minimax coding (log-loss) regret given a fixed sample size, or horizon, n. It generally requires that n be known in advance. Furthermore, extracting the sequential predictions from the normalized maximum likelihood distribution is computationally infeasible for most statistical models. Several computationally feasible alternative strategie...

We study the problem of minimising regret in two-armed bandit problems with Gaussian rewards. Our objective is to use this simple setting to illustrate that strategies based on an exploration phase (up to a stopping time) followed by exploitation are necessarily suboptimal. The results hold regardless of whether or not the difference in means between the two arms is known. Besides the main mess...

In the classical multi-armed bandit problem, d arms are available to the decision maker who pulls them sequentially in order to maximize his cumulative reward. Guarantees can be obtained on a relative quantity called regret, which scales linearly with d (or with √ d in the minimax sense). We here consider the sparse case of this classical problem in the sense that only a small number of arms, n...

Constraint-based optimization requires the formulation of a precise objective function. However, in many circumstances, the objective is to maximize the utility of a specific user among the space of feasible configurations (e.g., of some system or product). Since elicitation of utility functions is known to be difficult, we consider the problem of incremental utility elicitation in constraintba...

In contexts in which players have no priors, we analyze a learning process based on ex-post regret as a guide to understand how to play games of incomplete information under private values. The conclusions depend on whether players interact within a fixed set (fixed matching) or they are randomly matched to play the game (random matching). The relevant long run predictions are minimal sets that...

The normalized maximum likelihood model achieves the minimax coding (log-loss) regret for data of fixed sample size n. However, it is a batch strategy, i.e., it requires that n be known in advance. Furthermore, it is computationally infeasible for most statistical models, and several computationally feasible alternative strategies have been devised. We characterize the achievability of asymptot...

Collusion in auctions, with different assumptions on distributions of bidders’ private valuation, has been studied extensively over the years. With the recent development of on-line markets, auctions are becoming an increasingly popular procurement method. The emergence of Internet marketplaces makes auction participation much easier and more convenient, since no physical presence of bidders is...

We axiomatically de...ne the behavior of a function that may capture the players’ beliefs in 2x2 one shot games. Among di¤erent existing concepts the unique one which ful...lls all the axioms is the mixed version of the minimax regret. This justi...es its use to approximate the beliefs of inexperienced players and it also provides the starting point for a simple procedure that heuristically sel...

Recently there has been a growing interest in non-linear aggregation models to represent the preferences of a decision maker in a multicriteria decision problem. Such models are expressive as they are able to represent synergies (positive and negative) between attributes or criteria, thus modeling different decision behaviors. They also make it possible to generate Pareto-optimal solutions that...