Proof. Let T ′ be the number of times we have updated BASE. Note that since the samples fed to BASE were drawn iid according to the arm distributions and given on the arms it requested, the regret on these samples is RT ′ . Clearly T ′ ≤ T since for every sample we give BASE, we must have correspondingly taken a step in the true environment1. So the expected regret of only those steps in which ...

Clark and Scarf (1960) consider a two-stage inventory system in a finite horizon. They show that echelon base-stock policies are optimal. The optimal base-stock levels can be obtained by solving two sets of recursive, functional equations. Nevertheless, finding the upstream base-stock level is more complex because the functional equation depends on the downstream base-stock level. This paper pr...

fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. therefore, a reliable and efficient technique as a solution is regarded.this paper develops approximate solutions for boundary value problems ofdifferential equations with non-integer order by using the shannon waveletbases. wavelet bases have d...

the notion of generalized locally bounded $i$-topological vectorspaces is introduced. some of their important properties arestudied. the relationship between this kind of spaces and thelocally bounded $i$-topological vector spaces introduced by wu andfang [boundedness and locally bounded fuzzy topological vectorspaces, fuzzy math. 5 (4) (1985) 87$-$94] is discussed. moreover, wealso use the fam...

We consider a series of configurations defined by fibers of a given base configuration. We prove that Markov degree of the configurations is bounded from above by the Markov complexity of the base configuration. As important examples of base configurations we consider incidence matrices of graphs and study the maximum Markov degree of configurations defined by fibers of the incidence matrices. ...

Reduplication, the remaining problem in computational morphology is a morphological process that involves copying the base form wholly or partially. Reduplication can also be classified as either bounded or unbounded reduplication. Some solutions have been proposed for bounded reduplication. Some of the proposed solutions use ordered replace rules while others use simultaneous two-level rules. ...