We discuss the relationship between the statistical embedding curvature [1, 2] and the logarithmic regret [11] (regret for short) of the Bayesian prediction strategy (or coding strategy) for curved exponential families and Markov models. The regret of a strategy is defined as the difference of the logarithmic loss (code length) incurred by the strategy and that of the best strategy for each dat...

We study the problems of offline and online contextual optimization with feedback information, where instead observing loss, we observe, after-the-fact, optimal action an oracle full knowledge objective function would have taken. aim to minimize regret, which is defined as difference between our losses ones incurred by all-knowing oracle. In setting, decision-maker has information available fro...

This paper is devoted to sequential decision making with Rank Dependent expected Utility (RDU). criterion generalizes Expected and enables model a wider range of observed (rational) behaviors. In such setting, two conflicting objectives can be identified in the assessment strategy: maximizing performance viewed from initial state (optimality), minimizing incentive deviate during implementation ...

We consider the problem of online linear regression on individual sequences. The goal in this paper is for the forecaster to output sequential predictions which are, after T time rounds, almost as good as the ones output by the best linear predictor in a given l-ball in R. We consider both the cases where the dimension d is small and large relative to the time horizon T . We first present regre...

We prove non-asymptotic lower bounds on the expectation of the maximum of d independent Gaussian variables and the expectation of the maximum of d independent symmetric random walks. Both lower bounds recover the optimal leading constant in the limit. A simple application of the lower bound for random walks is an (asymptotically optimal) non-asymptotic lower bound on the minimax regret of onlin...

This paper establishes minimax rates for online regression with arbitrary classes of functions and general losses.1 We show that below a certain threshold for the complexity of the function class, the minimax rates depend on both the curvature of the loss function and the sequential complexities of the class. Above this threshold, the curvature of the loss does not affect the rates. Furthermore...

This paper introduces a new solution concept, a minimax regret equilibrium, which allows for the possibility that players are uncertain about the rationality and conjectures of their opponents. We provide several applications of our concept. In particular, we consider pricesetting environments and show that optimal pricing policy follows a non-degenerate distribution. The induced price dispersi...

Minimax regret is an exact method for deriving a recommendation based on a small sample. It can incorporate costs in its measurement of opportunity loss (regret) in terms of not making the best choice. In this paper we present the methodolgy and implement it in four examples from di¤erent …elds: medicine, development policy, experimental game theory and macro economics. We focus on the comparis...