We study networks of communicating learning agents that cooperate to solve a common nonstochastic bandit problem. Agents use an underlying communication network to get messages about actions selected by other agents, and drop messages that took more than d hops to arrive, where d is a delay parameter. We introduce EXP3-COOP, a cooperative version of the EXP3 algorithm and prove that with K acti...

R management models traditionally assume that future demand is unknown but can be described by a stochastic process or a probability distribution. Demand is, however, often difficult to characterize, especially in new or nonstationary markets. In this paper, we develop robust formulations for the capacity allocation problem in revenue management using the maximin and the minimax regret criteria...

Portfolio optimization is one of the most important issues for effective and economic investment. There is plenty of research in the literature addressing this issue. Most of these pieces of research attempt to make the Markowitz’s primary portfolio selection model more realistic or seek to solve the model for obtaining fairly optimum portfolios. An efficient frontier in the ...

We address the online linear optimization problem with bandit feedback. Our contribution is twofold. First, we provide an algorithm (based on exponential weights) with a regret of order √ dn logN for any finite action set with N actions, under the assumption that the instantaneous loss is bounded by 1. This shaves off an extraneous √ d factor compared to previous works, and gives a regret bound...

This paper continues the investigation of minimax regret treatment choice initiated by Manski (2004). Consider a decision maker who must assign treatment to future subjects after observing outcomes experienced in a finite sample. A certain scoring rule is known to achieve minimax regret in numerous variants of this decision problem. I investigate the sensitivity of these findings to perturbatio...

We consider the problem of estimating a random vector x, with covariance uncertainties, that is observed through a known linear transformation H and corrupted by additive noise. We first develop the linear estimator that minimizes the worst-case meansquared error (MSE) across all possible covariance matrices. Although the minimax approach has enjoyed widespread use in the design of robust metho...

This paper considers a decision-maker who prefers to make a point decision when the object of interest is interval-identi…ed with regular bounds. When the bounds are just identi…ed along with known interval length, the local asymptotic minimax decision with respect to a symmetric convex loss function takes an obvious form: an e¢ cient lower bound estimator plus the half of the known interval le...

This paper considers minimax regret 1-sink location problems in dynamic path networks. A dynamic path network consists of an undirected path with positive edge lengths and constant edge capacity and the vertex supply which is nonnegative value, called weight, is unknown but only the interval of weight is known. A particular assignment of weight to each vertex is called a scenario. Under any sce...

The difficulty of an online learning problem is typically measured by its minimax regret. If the minimax regret grows sublinearly with the number of online rounds (denoted by T), we say that the problem is learnable. Until recently, we recognized only two classes of online learning problems: problems whose minimax regret grows at a slow rate of O(\sqrt(T)), and unlearnable problems with linear ...

We consider a setting where a system learns to rank a fixed set of m items. The goal is produce good item rankings for users with diverse interests who interact online with the system for T rounds. We consider a novel top-1 feedback model: at the end of each round, the relevance score for only the top ranked object is revealed. However, the performance of the system is judged on the entire rank...