Plan Objectives

Regular PDDL goals are used to express goal-type performance objectives. A goal statement (:goal φ) for a probabilistic planning problem encodes the objective that the probability of achieving φ should be maximized, unless an explicit optimization metric is specified for the planning problem. For planning problems instantiated from a domain declaring the :rewards requirement, the default plan objective is to maximize the expected reward. A goal statement in the specification of a reward oriented planning problem identifies a set of absorbing states. In addition to transition rewards specified in action effects, it is possible to associate a one-time reward for entering a goal state. This is done using the (:goal-reward f) construct, where f is a numeric expression.

In general, a statement (:metric maximize f) in a problem definition means that the expected value of f should be maximized. Reward-oriented problems, for example a problem instance of the coffee-delivery domain in Figure 2, would declare (:metric maximize (reward)) as the optimization criterion (this declaration is the default if the :rewards requirement has been specified). PPDDL defines goal-achieved as a special optimization metric, which can be used to explicitly specify that the plan objective is to maximize (or minimize) the probability of goal achievement. The value of the goal-achieved fluent is 1 if execution ends in a goal state. The expected value of goal-achieved is therefore equal to the probability of goal achievement. A declaration (:metric maximize (goal-achieved)) takes precedence over any reward specifications in a domain or problem definition, and it is the default if the :rewards requirement has not been specified (for example, the “Bomb and Toilet” problem in Figure 1).

Håkan L. S. Younes