This paper addresses the minimax regret sink location problem in dynamic tree networks. In our model, a dynamic tree network consists of an undirected tree with positive edge lengths and uniform edge capacity, and the vertex supply which is a positive value is unknown but only the interval of supply is known. A particular realization of supply to each vertex is called a scenario. Under any scen...

Many situations involve repeatedly making decisions in an uncertain environment: for instance, deciding what route to drive to work each day, or repeated play of a game against an opponent with an unknown strategy. In this chapter we describe learning algorithms with strong guarantees for settings of this type, along with connections to game-theoretic equilibria when all players in a system are...

This paper studies the problem of treatment choice between a status quo treatment with a known outcome distribution and an innovation whose outcomes are observed only in a representative finite sample. I evaluate statistical decision rules, which are functions that map sample outcomes into the planner’s treatment choice for the population, based on regret, which is the expected welfare loss due...

We propose a general approach for nding minmax regret solutions for a class of combinatorial optimization problems with an objective function of minimax type and uncertain objective function coe cients. The approach is based on reducing a problem with uncertainty to a number of problems without uncertainty. The method is illustrated on bottleneck combinatorial optimization problems, minimax mul...

For problems of data compression, gambling, and prediction of individual sequences 1 the following questions arise. Given a target family of probability mass functions ( 1 ), how do we choose a probability mass function ( 1 ) so that it approximately minimizes the maximum regret /belowdisplayskip10ptminus6pt max (log 1 ( 1 ) log 1 ( 1 )̂) and so that it achieves the best constant in the asymptot...

We study the stochastic Multi-Armed Bandit (MAB) problem under worst-case regret and heavy-tailed reward distribution. modify minimax policy MOSS for sub-Gaussian distribution by using saturated empirical mean to design a new algorithm called Robust MOSS. show that if moment of order $1+\epsilon $ exists, then refined strategy has matching lower bound while maintaining distribution-dependent lo...

We extend the domain of preferences to include menu-dependent preferences and characterize the maximal subset of this domain in which the revelation principle holds. Minimax-regret preference is shown to be outside this subset.

Motivated by practical applications, chiefly clinical trials, we study the regret achievable for stochastic bandits under the constraint that the employed policy must split trials into a small number of batches. We propose a simple policy that operates under this contraint and show that a very small number of batches gives close to minimax optimal regret bounds. As a byproduct, we derive optima...