It is important to note that the models presented here are not the only accepted ways to make good decisions. In game theory, the key idea is to minimize ``regret.'' This is the feeling you get after making a bad decision and wishing that you could change it after the game is finished. Suppose that after you choose some , you are told which was applied by nature. The regret is the amount of cost that you could have saved by picking a different action, given the nature action that was applied.
For each combination of and , the regret, , is defined as
Suppose that minimizing regret is the primary concern, as opposed to the actual cost received. Under the nondeterministic model, the action that minimizes the worst-case regret is
Steven M LaValle 2012-04-20