We search for behavioral rules that attain minimax regret under geometric discounting in the context of repeated decision making in a stationary environment where payo¤s belong to a given bounded interval. Rules that attain minimax regret exist and are optimal for Bayesian decision making under the prior where learning can be argued to be most di¢cult. Minimax regret can be attained by randomiz...

We investigate the problem of continuous-time causal estimation under a minimax criterion. Let X = {Xt, 0 ≤ t ≤ T} be governed by the probability law Pθ from a class of possible laws indexed by θ ∈ Λ, and Y T be the noise corrupted observations of X available to the estimator. We characterize the estimator minimizing the worst case regret, where regret is the difference between the causal estim...

In a partial monitoring game, the learner repeatedly chooses an action, the environment responds with an outcome, and then the learner suffers a loss and receives a feedback signal, both of which are fixed functions of the action and the outcome. The goal of the learner is to minimize his regret, which is the difference between his total cumulative loss and the total loss of the best fixed acti...

This paper provides an axiomatic model of decision making under uncertainty in which the decision maker is driven by anticipated ex-post regrets. Our model allows both regret aversion and likelihood judgement over states to coexist. Also, we characterize two special cases, minimax regret with multiple priors that generalizes Savage’s minimax regret, and a smooth model of regret aversion.

Classical stochastic programming has already been used with large scale LP models for long-term analysis of energy-environment systems. We propose a Minimax Regret formulation suitable for large scale linear programming models. It has been experimentally verified that the minimax regret strategy depends only on the extremal scenarios and not on the intermediate ones, thus making the approach co...

Stackelberg security games (SSGs) have been deployed in a number of real-world domains. One key challenge in these applications is the assessment of attacker payoffs, which may not be perfectly known. Previous work has studied SSGs with uncertain payoffs modeled by interval uncertainty and provided maximin-based robust solutions. In contrast, in this work we propose the use of the less conserva...

We introduce a notion of ‘relative redundancy’ for universal data compression and propose a universal code which asymptotically achieves the minimax value of the relative redundancy. The relative redundancy is a hybrid of redundancy and coding regret (pointwise redundancy), where a class of information sources and a class of codes are assumed. The minimax code for relative redundancy is an exte...