. Review on stochastic multi-armed bandit problem Consider a gambler playing against a N−armed slot machine and sequentially pulls up arms to minimize the expected regret. Each arm, i ∈ {1, . . . ,N } has a probability distribution Di supported on the closed interval [0,1]. Let μi be the expected value of the corresponding loss to arm i and define Ĩ = argmin1≤j≤N μj as the index of the optim...

function of μ) satisfies sample path convexity (a term that has been introduced by Shaked and Shanthikumar (1988)). Specifically, let 0 ≤ μ1 ≤ μ2 ≤ μ3 ≤ μ4 be four service rates such that μ1 + μ4 = μ2 + μ3, and fix λ, β(·) and η(·). Suppose that there exist Y1, ..., Y4, which are versions of the original head-count processes (Yi has service rate of μi) that satisfy the following two properties ...

We consider a multi-class queueing system with multiple homogeneous servers and customer abandonment. For each customer class i, the holding cost per unit time, the service rate and the abandonment rate are denoted by ci, μi and θi, respectively. We prove that under a many-server fluid scaling and overload conditions, a routing policy that assigns priority to classes according to their index ci...

The first scenario — identical items and unit-demand valuations — corresponds to special case in which μi(j) = 0 for all i and j ≥ 2. The second and third scenarios — which have non-identical goods but restrict to additive or unit-demand valuations, respectively — are incomparable to this one. Our goals are the usual ones — a simple ascending auction that is EPIC and in which sincere bidding le...

Bootstrap particle filter as a subcase of APF Here we will show that when q is a delta function, APF recovers the bootstrap particle filter. The Dirac delta function can be considered as the limit of a Gaussian as the variance goes to zero, δ(θ − μ) = limσ2→0N (θ;μ, σ). Therefore, we can view q as an exponential family distribution. Specifically we are dealing with a Gaussian distribution with ...

Let ν be a finite countably subadditive outer measure defined on all subsets of a set X, take a collection C of subsets of X containing X and ∅, we derive an outer measure ρ using ν on sets in C. By applying this general framework on two special cases in which ν = μ′′, one where μ ∈ Mσ(L) and the other where μ ∈ Mσ(L1), L1 ⊆ L2 being lattices on a set X, we obtain new characterizations of the o...

The density corrections, in terms of the isospin chemical potential μI , to the mass of the pions are investigated in the framework of the SU(2) low energy effective chiral invariant lagrangian. As a function of temperature and μI = 0, the mass remains quite stable, starting to grow for very high values of T , confirming previous results. However, the dependence for a non-vanishing chemical pot...