We study the problem of data compression, gambling and prediction of a sequence x = x1x2...xn from a certain alphabet X , in terms of regret and redundancy with respect to a general exponential family. In particular, we evaluate the regret of the Bayes mixture density and show that it asymptotically achieves their minimax values when variants of Jeffreys prior are used. Keywords— universal codi...

Markov Decision Processes (MDPs) are an effective model to represent decision processes in the presence of transitional uncertainty and reward tradeoffs. However, due to the difficulty in exactly specifying the transition and reward functions in MDPs, researchers have proposed uncertain MDP models and robustness objectives in solving those models. Most approaches for computing robust policies h...

We investigate contextual online learning with nonparametric (Lipschitz) comparison classes under different assumptions on losses and feedback information. For full information feedback and Lipschitz losses, we design the first explicit algorithm achieving the minimax regret rate (up to log factors). In a partial feedback model motivated by second-price auctions, we obtain algorithms for Lipsch...

We consider the setting of prediction with expert advice with an additional assumption that each expert generates its losses i.i.d. according to some distribution. We first identify a class of “admissible” strategies, which we call permutation invariant, and show that every strategy outside this class will perform not better than some permutation invariant strategy. We then show that when the l...

Bargaining under uncertainty is modeled by the assumption that there are several possible states of nature, each of which is identified with a bargaining problem. We characterize bargaining solutions which generate ex ante efficient combinations of outcomes under the assumption that the bargainers have minimax regret preferences. For the case of two bargainers a class of monotone utopia-path so...

In this paper, we seek robust policies for uncertain Markov Decision Processes (MDPs). Most robust optimization approaches for these problems have focussed on the computation of maximin policies which maximize the value corresponding to the worst realization of the uncertainty. Recent work has proposed minimax regret as a suitable alternative to the maximin objective for robust optimization. Ho...

Markov decision processes (MDPs) are widely used in modeling decision making problems in stochastic environments. However, precise specification of the reward functions in MDPs is often very difficult. Recent approaches have focused on computing an optimal policy based on the minimax regret criterion for obtaining a robust policy under uncertainty in the reward function. One of the core tasks i...

Classic direct mechanisms suffer from the drawback of requiring full type (or utility function) revelation from participating agents. In complex settings with multi-attribute utility, assessing utility functions can be very difficult, a problem addressed by recent work on preference elicitation. In this work we propose a framework for incremental, partial revelation mechanisms and study the use...