In this paper, we introduce tripled partially ordered sets and monotone functions on tripled partiallyordered sets. Some basic properties on these new dened sets are studied and some examples forclarifying are given.

Computers have already eclipsed the level of human play in competitive Scrabble, but there remains room for improvement. In particular, there is much to be gained by incorporating information about the opponent’s tiles into the decision-making process. In this work, we quantify the value of knowing what letters the opponent has. We use observations from previous plays to predict what tiles our ...

Interactive POMDPs (I-POMDPs) are a useful framework for describing POMDPs that interact with other POMDPs. I-POMDPs are solved recursively in levels: a level1 I-POMDP assumes the opponent acts randomly, and a levelk I-POMDP assumes the opponent is a level-(k-1) I-POMDP. In this paper, we introduce fully-nested I-POMDPs, which are uncertain about the physical state of the game, the level of the...

In ci componioiz paper [l] we have developed a frame,work fo,r rating 01‘ comparing navigation packages. For a giuen enuir.onment a navigation package consists of (I motion planner and a sensor to be used during nauigation. The cibility to rate or measure a navigation package is aniportant in order to address issues like sensor custom%zution for an environment and choice of a m.otion plarumr in...

in Euclidean spaces, with Fn(x, a ) and Gn(x) converging pointwise to functions F,(x,a) and G,(x), respectively, and give conditions for the limiting P O model Xt+l = F,(xt,at) + t t , Yt = G,(xt) + rlt to have an a-discount optimal policy. AMS Classification: 93320, 90C40.

The partially observable Markov decision process (POMDP) framework has been applied in dialogue systems as a formal framework to represent uncertainty explicitly while being robust to noise. In this context, estimating the dialogue POMDP model components is a significant challenge as they have a direct impact on the optimized dialogue POMDP policy. To achieve such an estimation, we propose meth...

We consider a special case of partially observable Markov decision processes that arises when state information is perfect but arrives with a delay. We rst formulate the decision process in its standard form and derive the Bellman equation that corresponds to it. We then introduce a second decision process that has a much simpler Bellman equation than the rst, and is therefore, in general, much...

This paper develops exact finite sample and asymptotic distributions for structural equation tests based on partially restricted reduced form estimates. Particular attention is given to models with large numbers of instruments, wherein the use of partially restricted reduced form estimates is shown to be especially advantageous in statistical testing even in cases of uniformly weak instruments ...