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

2005-12-06