We present adaptive algorithms with strong datadependent regret guarantees for the problem of bandit convex optimization. In the process, we develop a general framework from which the main previous results in this setting can be recovered. The key method is the introduction of adaptive regularization. By appropriately adapting the exploration scheme, we show that one can derive regret guarantee...

We construct a new map from a convex function to a distribution on its domain, with the property that this distribution is a multi-scale exploration of the function. We use this map to solve a decadeold open problem in adversarial bandit convex optimization by showing that the minimax regret for this problem is Õ(poly(n) √ T ), where n is the dimension and T the number of rounds. This bound is ...

We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the modified ADMM method has an optimal regret bound of O(s log d/T ), where s is the sparsity level, d is the data dimension and T is the number of steps. This mat...

We consider preliminary test estimator based on the maximum likelihood estimator of the parameter of the pareto distribution. The optimal significance levels for the preliminary test are obtained using the minimax regret criterion. The corresponding critical values of the preliminary test are calculated. Mathematics Subject Classification: 62F10

We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the modified ADMM method has an optimal regret bound of O(s log d/T ), where s is the sparsity level, d is the data dimension and T is the number of steps. This mat...

We consider the problem of planning in a stochastic and discounted environment with a limited numerical budget. More precisely, we investigate strategies exploring the set of possible sequences of actions, so that, once all available numerical resources (e.g. CPU time, number of calls to a generative model) have been used, one returns a recommendation on the best possible immediate action to fo...

We consider adaptive sequential prediction of arbitrary binary sequences when the performance is evaluated using a general loss function. The goal is to predict on each individual sequence nearly as well as the best prediction strategy in a given comparison class of (possibly adaptive) prediction strategies, called experts. By using a general loss function, we generalize previous work on univer...

We describe the semantic foundations for elicitation of generalized additively independent (GAI) utilities using the minimax regret criterion, and propose several new query types and strategies for this purpose. Computational feasibility is obtained by exploiting the local GAI structure in the model. Our results provide a practical approach for implementing preference-based constrained configur...

We consider online learning in partial-monitoring games against an oblivious adversary. We show that when the number of actions available to the learner is two and the game is nontrivial then it is reducible to a bandit-like game and thus the minimax regret is Θ( √ T ).

This paper uses the minimax regret criterion to analyze choice between two treatments when one has observed a finite sample that is plagued by missing data. The analysis is entirely in terms of exact finite sample regret, as opposed to asymptotic approximations or finite sample bounds. It thus extends Manski (2007), who largely abstracts from finite sample problems, as well as Stoye (2006a), wh...