DATA's view point

Basic characteristics

The decision tool DATA, is basically oriented to represent problems characterized by uncertainty situations. I mean, the system is more exploited when these kind of problems arise.

There are three representation methods in the system :

1-Decision trees,

2-Influence diagrams and

3-Markov's chains.

All of the tree methods are very intuitively handled by the system. DATA, based on this information, can provide the user with different kind of analysis, followed also by graphical and textual reports.

When DATA evaluates the graph, this is called roll-back. The roll-back works only on decision trees and Markov representations. DATA gives the oportunity to convert to a decision tree when the user has preferred to use an influence diagram by reasons of simplification of the decision model.

Roll-back works on four different criterias : expected value, path probability, payoff and maximin. This evaluation can be done on a multi-attribute base

Something good in DATA is that the user can define variables (local and global) and, in turn, global and local formulas. Global and local refer to whenever the item is applied from the root or from a specific node of the tree.

In taking uncertainty into account, DATA allows definition of intervals for variables in order to perform sensitivity analysis.

DATA doesn't permit specification of undesirable values, but because of the powerful mechanism for definition of formulas, this situation can be easily represented using, for example, the if function in combination with relational operators, i.e production rules. This, in a leaf, would allow to redefine the evaluation of a payoff formula.

Solving the problem

Note : see the outline code generated by DATA in the appendix.

I will propose a situation based on the figure 2..

The cells covered in the decision will be : (1,1), (1,2),(0,1),(1,3),(0,2),(0,3).

The payoffs HCondition and LCondition are formulas based on the formula 1

HCondition = Condition - 5*(Tc+1) and LCondition = HCondition - Dest.

DATA allows to define variables and formulas based on already existente variables. One can define the value of the variable affecting the whole tree (global), or a subtree starting from a specific node (local).

Condition is a global variable whose value is 15. Condition is the condition of the agent at the cell (1,1)

Dest is a local variable and represent the D term in the formula 1.

Is enough for a formula to contain a global variable, in order to affect the whole tree.


Figure 3 represents the decision tree generated by DATA.


Two different evaluation criterias

The following results were obtained from two different criterias.

Roll-back is the method used by DATA to evaluate a decision tree. Roll-back works based on four types of quantities : Expected value, Payoffs, Probabilities and Maximin.

I have selected Expected value and Maximin.

The following graph shows the Expected value that roll-back reports. Here the expected value is 8. It means that the average payoff, if the agent try this path many times is 8.


Figure 4


The above graph shows the average condition, if many agents would try this path under the same situation. The next one (Maximin) shows a decision, considering that the agent behaves pesimistic. If we consider that Payoff=0 means death, then the expected value path is not a "good" proposal. DATA decides that, after having jumped from the cell (1,2) to the cell (1,3) , the best you can do (being pesimistic) is to stay there, otherwise you could die (LCondition = 0) or get into a very low comdition (LCondition=1).

Figure 5


DATA can handle also Markov's chains. If, for example, I doubt about if this is a fair game or not, I can represent the problem as a Markov's process. In this case the cells are possible states. DATA allows to assign state rewards (rewards for being in a state) and transition rewards (rewards received in the "effort" of passing to another state). By specifying termination conditions, DATA allows to run a roll-back, giving as a result the final probabilities for being in each state and total rewards at the end of the process. If after an experiment using "minefield", you get as a result that the final probability to be at the gate cell is cero or almost cero, and just in the middle of the field (with final probability 0.8) you receive a reward equivalent to being dead, then the game has been arranged "JUST FOR YOU".

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