Technical note: Finite-time regret analysis of Kiefer-Wolfowitz stochastic approximation algorithm and nonparametric multi-product dynamic pricing with unknown demand

We consider the problem of nonparametric multi-product dynamic pricing with unknown demand and show that the problem may be formulated as an online model-free stochastic program, which can be solved by the classical Kiefer-Wolfowitz stochastic approximation (KWSA) algorithm. We prove that the expected cumulative regret of the KWSA algorithm is bounded above by where κ₁, κ₂ are positive constants and T is the number of periods for any T = 1, 2, … . Therefore, the regret of the KWSA algorithm grows in the order of , which achieves the lower bounds known for parametric dynamic pricing problems and shows that the nonparametric problems are not necessarily more difficult to solve than the parametric ones. Numerical experiments further demonstrate the effectiveness and efficiency of our proposed KW pricing policy by comparing with some pricing policies in the literature.     

Coalitions & the Legitimisation of UK Security Policy

Abstract

David Moore analyses the role of the Treasury in detemining and controlling defence policy and expenditure, and the place of the MoD within this function.     

Managerial inventory formulations with stockout objectives and fiscal constraints

Most inventory formulations seek to minimize the sum of ordering costs, holding costs, and stockout costs: however, management often directs inventory policy by specifying a maximum investment level and/or a purchasing budget constraint. Within these limitations, they expect lower level managers to optimize some level of customer satisfaction, such as minimum stockouts or minimum shortages. The author has developed several cases of these “managerial” inventory formulations and has presented some computational results.     

Large deviations of the winsorized mean of an exponential distribution

An asymptotic representation for large deviation probabilities of the Winsorized mean of a sequence of independent, identically distributed exponential random variables is derived. The Winsorized mean, a linear combination of exponential order statistics, is first transformed into a weighted sum of exponential random variables, and then a large deviation theorem for weighted sums can be applied. The representation obtained is then compared with results already known for the mean and the median, the two extreme cases of the Winsorized mean.     

On the optimality of the bayes prediction policy in two-echelon multistation inventory models

The present paper provides a proof that the Bayes prediction ordering policy developed in [3] is an optimal policy, in the sense that it minimizes the total expected discounted cost of ordering for any finite planning horizon.     

An algorithm for the solution of a location problem with metric constraints

In many location problems, the solution is constrained to lie within a closed set. In this paper, optimal solutions to a special type of constrained location problem are characterized. In particular, the location problem with the solution constrained to be within a maximum distance of each demand point is considered, and an algorithm for its solution is developed and discussed.