This section moves from evaluating a plan to computing an optimal plan
in the simulation-based framework. The most important idea is the
computation of *Q-factors*, . This is
an extension of the optimal cost-to-go, , that records optimal
costs for each possible combination of a state, , and action
. The interpretation of is the expected cost
received by starting from state , applying , and then following
the optimal plan from the resulting next state,
.
If happens to be the same action as would be selected by the
optimal plan, , then
. Thus, the
Q-value can be thought of as the cost of making an arbitrary choice in
the first stage and then exhibiting optimal decision making
afterward.

Steven M LaValle 2012-04-20