During the recent Dialog State Tracking Challenge (DSTC), a fundamental question was raised: “Would better performance in dialog state tracking translate to better performance of the optimized policy by reinforcement learning?” Also, during the challenge system evaluation, another nontrivial question arose: “Which evaluation metric and schedule would best predict improvement in overall dialog p...

Recall that a metric space M is said to be complete if every Cauchy sequence in M converges to a limit in M . Not all metric spaces are complete, but it is a fact that all metric spaces can be “completed”, in a way that preserves the essential structure of the metric space. If the space in question is a normed linear space this process completes the space to a Banach space, and an inner product...

The goal of this paper is to study the path-following method for univariate polynomials. We propose complexity and condition properties when Newton applied as a correction operator. Then we geodesics metric along those curves. Last, compute approximations how number varies with quality approximation.

This paper presents a methodology for goal-oriented decision support. The method uses fuzzy cognitive map based on immune algorithm to find the initial state of system from among a large number of possible states. The initial state can answer the question that the course of events leads to a certain state in give scenario. Finally, an illustrative example is provided, and its results suggest th...

We propose an “answerer in questioner’s mind” (AQM) framework, a novel approach for goal-oriented dialogue. In AQM, a questioner asks and infers based on an approximated probabilistic model of the answerer in the questioner’s model. The questioner figures out the answerer’s intent by selecting a plausible question following the principle of information theory, which explicitly calculates the in...

Dendrons and their products admit a natural, continuous median operator. We prove that there exists a two-dimensional metric continuum with a continuous median operator, for which there is no median-preserving embedding in a product of finitely many dendrons. Our method involves ideas and results concerning graph colouring and abstract convexity. The main result answers a question in [16] negat...

Experimental verification has been the method of choice for verifying the stability of a multi-agent reinforcement learning (MARL) algorithm as the number of agents grows and theoretical analysis becomes prohibitively complex. For cooperative agents, where the ultimate goal is to optimize some global metric, the stability is usually verified by observing the evolution of the global performance ...