Objective Function Analysis Files

Objective Function Analysis models intelligence as a multi-dimensional probability mass function (MD-PMF) of the perceptions and responses (which are themselves perceived) of an entity and it’s inherent objective function (OF). We say that the entity has intelligence because it maintains the joint probability

P[OF, rj , pi] (1)

where OF is the objective function, pi is 1...n perceptions of the entity, rj is 1...m responses of the entity (note that responses are perceived just as if they were perceptions).

The OF expresses the probability of a successful response to the given set of perceptions. The learning algorithm is the action of

1) For the jth response, project and evaluate the effectiveness of the response by calculating the objective function (OF) for the jth response subject to the given set of perceptions.

2) Update the conditional probability of the OF corresponding to the jth response,

P[OF | rj , pi]                             (2)

3) Repeat steps 1 and 2 for all possible responses, then proceed to step 4.

4) Find the maximum conditional expected OF,

max { <OF>j = ∑k OFk * P[OF | rj , pi] }, (3)

then the actual response of the entity is the response corresponding to max{<OF>j}.

5) Having responded as in step 4, the entity is placed into a new set of values for the perceptions. The entity continues responding per steps 1 through 4 above.

As the learning algorithm progresses, the OF is either reinforced or diminished in the conditional probability subspace formed by the perceptions and responses, i.e. P[OF | rj , pi]. Stated another way, in response to its perceptions, an entity evaluates every possible value of the OF in the subspace defined by the n perceptions and m responses and chooses the response which maximizes the OF. Eventually the randomly seeded MD-PMF changes to reflect the logical and mathematical properties embodied in the OF.

A discussion paper of the theory and simulation results is provided in the file, OFApaper.odt(docx).

The learning capability of OFA is demonstrated by the various software simulations provided in the repository. All source code is provided to include a Makefile for building the executable. The source code was developed under Linux, but has no dependency on the operating system. Software dependencies do include C++11, Qt version 5, QwtPlot3d, and OpenGL.