  In this paper, we present a probabilistic framework for goal-driven spoken
dialog systems. A new dynamic stochastic state (DS-state) is then defined to
characterize the goal set of a dialog state at different stages of the dialog
process. Furthermore, an entropy minimization dialog management(EMDM) strategy
is also proposed to combine with the DS-states to facilitate a robust and
efficient solution in reaching a user's goals. A Song-On-Demand task, with a
total of 38117 songs and 12 attributes corresponding to each song, is used to
test the performance of the proposed approach. In an ideal simulation, assuming
no errors, the EMDM strategy is the most efficient goal-seeking method among
all tested approaches, returning the correct song within 3.3 dialog turns on
average. Furthermore, in a practical scenario, with top five candidates to
handle the unavoidable automatic speech recognition (ASR) and natural language
understanding (NLU) errors, the results show that only 61.7\% of the dialog
goals can be successfully obtained in 6.23 dialog turns on average when random
questions are asked by the system, whereas if the proposed DS-states are
updated with the top 5 candidates from the SLU output using the proposed EMDM
strategy executed at every DS-state, then a 86.7\% dialog success rate can be
accomplished effectively within 5.17 dialog turns on average. We also
demonstrate that entropy-based DM strategies are more efficient than
non-entropy based DM. Moreover, using the goal set distributions in EMDM, the
results are better than those without them, such as in sate-of-the-art database
summary DM.
