Demonstration 5: Efficiency

The system was compared with a fixed strategy planner, using a method very similar to that used in example 1. Taking just the upper branch of the game tree, a comparison was made for the decision between offer and chat that is made by the agent. The subtree was pruned to produce two fixed-strategy trees. In figure 4.22 (a) the gain that the planner obtains over the fixed strategy of chat is plotted. In figure 4.22 (b) the gain that the planner obtains over the fixed strategy of offer is plotted. The squared point style indicates where a gain is obtained. Against the chat strategy, the planner obtains a small gain of up to 1.8, in a small region of the belief space. This is expected since in this region, it is almost certain that a window seat is intended, yet the user believes that there is none available. Against the offer strategy, a larger gain of as much as 12.0 is obtained. The maximum length of the dialogue is 15 units, corresponding with the longest path in the game tree, and so for belief models which cross the decision surface during their lifetime, there are some significant gains to be made.

A second configuration of the problem was explored, since in the first configuration, the amount of initiative over the belief space is perhaps unrealistically low (see figure 4.21). The plot shows that the agent only offers window seats when it believes it very likely that the user wants one. In the second configuration, the reward for an agent who wants a window seat but ends up not obtaining one has been dropped from 85 to 65 to encourage initiative. As a result, the initiative distribution shown in figure 4.23, was obtained, where the agent only fails to offer a window seat when it is very sure that the user does not intend to have one.

The efficiency of the planner for this configuration is a little better than that obtained for the first configuration (figure 4.24). Against the chat strategy, a maximum gain of 4.60 was obtained, and against the offer strategy, a maximum gain of 12.0 was obtained. This is a good fraction of the total dialogue length of 15.

Figure 4.22: Comparison of planner with each fixed strategy against P(intend(book-flight-window) and P(bel(have-seat))

Figure 4.23: Density of initiative against P(intend(book-flight-window) and P(bel(have-seat))
Figure 4.24: Comparison of planner with each fixed strategy against P(intend(book-flight-window) and P(bel(have-seat))