In Section 4.5 and Section 4.6, two problems will be discussed, which have risky alternatives between which there is a decision surface. These problems particularly focus on taking initiative in dialogues, where an agent must decide whether to open a dialogue, and how much to invest in communicating its intention or contributing to the plan should it do so. Example 1 deals with initiative taken in grounding the speaker's intention, where the speaker can choose between strategies of different levels of risk of misunderstanding. The less risky strategies have a higher cost. The hearer can also take initiative in grounding the intention by planning a clarification subdialogue, which reduces risk. Example 2 deals with initiative in introducing a goal to a dialogue. In this problem actions have preconditions which can fail, which determines whether the speaker should introduce it, or take the risk free alternative of allowing the hearer to introduce the goal if his preconditions are satisfied. What is common to both of these problems is that the agent can choose between a less risky alternative, whose utility is more or less constant with respect to a belief, and one that is more risky, having a utility that varies with the belief. Because of this variation, a decision surface is formed.
It may be argued that there are few problems that exhibit a decision surface, and therefore not much need for the planner. However, one need only look to work on reinforcement learning (Section 2.9.1) to know that inference of a model of the user from dialogue data makes a difference to the strategy taken in a dialogue. Although reinforcement learning is not always used to adapt to one or a group of users, but rather to the characteristics of the dialogue itself (such as the execution cost of different strategies), some of the justifications for that work are inherited by the planner.
That decision surfaces do occur regularly in everyday dialogue is evidenced by the human tendency to find out about and commit to memory the state of the world and the mental state of the actors found in it. If few decisions depended on knowing whether preconditions were satisfied, people could go through life spending very little effort on learning about the world. For example, a mechanic would find a decision surface in choosing to ask his colleague to mend an exhaust and doing it himself, with beliefs about available tools and parts, his colleague's skills and availability, and the likely cause of the problem all potentially causing a decision surface for the alternatives.
The planner, whose belief model is probabilistic, should be compared with planners that use a logical belief model, as well as planners that use no belief model at all. It will be shown that at some intermediate point of probability for a belief, between 0 and 1, the strategy of the agent should change, and since a logical belief model does not record probabilities, it is impossible to use it to decide a strategy based on maximum expected utility. Moreover, the difference in utility between strategies on one side of the decision surface can strongly favour one strategy, whereas on the other side of the surface, strongly favour the other strategy. Therefore, the agent needs to maintain its state on a continuum of belief states rather than at the extreme points of this continuum.