Policy optimisation of POMDP-based dialogue systems without state space compression

The partially observable Markov decision process (POMDP) has been proposed as a dialogue model that enables automatic improvement of the dialogue policy and robustness to speech understanding errors. It requires, however, a large number of dialogues to train the dialogue policy. Gaussian processes (GP) have recently been applied to POMDP dialogue management optimisation showing an ability to substantially increase the speed of learning. Here, we investigate this further using the Bayesian Update of Dialogue State dialogue manager. We show that it is possible to apply Gaussian processes directly to the belief state, removing the need for a parametric policy representation. In addition, the resulting policy learns significantly faster while maintaining operational performance. © 2012 IEEE.

Uniform stability of a particle approximation of the optimal filter derivative

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity, or derivative, of the optimal filter with respect to the static parameters of the state-space model; for instance, in order to obtain maximum likelihood model parameters of interest, or to compute the optimal controller in an optimal control problem. In Poyiadjis et al. [2011] an original particle algorithm to compute the filter derivative was proposed and it was shown using numerical examples that the particle estimate was numerically stable in the sense that it did not deteriorate over time. In this paper we substantiate this claim with a detailed theoretical study. Lp bounds and a central limit theorem for this particle approximation of the filter derivative are presented. It is further shown that under mixing conditions these Lp bounds and the asymptotic variance characterized by the central limit theorem are uniformly bounded with respect to the time index. We demon- strate the performance predicted by theory with several numerical examples. We also use the particle approximation of the filter derivative to perform online maximum likelihood parameter estimation for a stochastic volatility model.