1. Literature Survey
Structure for Credit-Apportionment Problem in Rule Based Systems
Overview
In this Project we are concerned with Credit-Apportionment Problem in Rule
Based Systems. For the implementation of Credit-Apportionment we will use
Bucket Brigade Algorithm in designing an expert system called GAMBLE
(Genetic Algorithm Based Machine Learning Expert). The various research
papers that we have gone through are part of IEEE digital library research papers
along with some other papers available on internet accessible to all. The first
Document that we referred was regarding the explanation of Credit-
Apportionment in rule based systems. The paper is available in IEEE digital
libraries “IEEE Transactions on Systems, Man and Cybernetics. Vol 19. No 3
May/June 1989” This paper talks about a framework of Credit-Apportionment and
then defines what actually Credit-Apportionment is. The Credit-Apportionment
process provides a formal basis for the problem analysis and algorithm design. It
includes
(1) System Environment sub - model which provides integrated view about the
payoff to, as well as the external and internal aspects of rule based system,
(2) Principles of Usefulness, which define the usefulness of rule actions and
(3) Definitions of the Credit-Apportionment problem which guides the algorithm
synthesis.
System Environment sub – model
The environment is modeled as a state space consisting of a set of states and a
state transition function. The state transition function specifies the next state as a
function or a random variable of the current state and the output of the rule based
system. The internal model or mental model of a rule based system is the model
for the system’s knowledge about its external world. The mental model is
represented as a state space. The states in the space are sets of messages in
the working memory. The environment is linked to the mental model with the help
of payoff. Payoff is the one way bridge sending feedback information from the
environment to mental model. Hence a rule based system is able to be aware of
the semantic aspects of the activities through payoff. As a semantic activity,
usefulness of actions conducted by rules is determined by the environment. One
way in which the environment determines the usefulness is expressed, by this
model as a set of principles of usefulness. Based on the system environment sub
model and principles of usefulness, the Credit-Apportionment problem can be
formulated as estimation of the inherent usefulness values in a particular context
the (local level problem) and as approximation to the inherent usefulness
functions ( the global level problem) from the payoffs. Therefore the task of

2. problem solving by a rule based system is to generate a sequence of outputs
driving the environment from initial state to terminal state. The quality of the
solution is indicated by the payoff, the higher the payoff, the more satisfactorily
the problem has been solved.
Principle of Usefulness
According to the system environment sub model, a rule based system conducts a
sequence of actions which drive the environment from initial state to final state
during a task of problem solving. In this sense, an action taken by a rule based
system can be useful or useless in solving the problem according to whether it
involves in driving the environment through the solution path.
Proposition 1:- All the external operators which are useful in a process of
problem solving are equally useful in the process. Their qualified usefulness in
this particular context equals to the payoff incurred at the terminal state of the
solution path.
The formulation of Credit-Apportionment Problem
This problem in a rule based system can be divided into local level and global
level.
The local level problem is defined as follows
Given: A trajectory of rule firing as well as the payoff, in a task of problem
solving.
Unknown: The inherent usefulness values of the actions conducted by
the rules in this trajectory.
Find: Estimate of the inherent usefulness values from the payoff by
apportioning the payoff to every rule in the trajectory (Usually estimators
are rule strengths).
The global level problem is defined as follows
Given: A set of rules.
Unknown: The inherent usefulness functions of the actions conducted by
the rules.
Find: The approximation to the inherent usefulness functions from a set of
payoffs by conducting a sequence of local level Credit-Apportionment
processes.

3. A new Credit-Apportionment Algorithm
As an implementation example of the model, a new Credit-Apportionment
algorithm: The context array Bucket Brigade Algorithm is used. This algorithm
is designed to overcome the information loss suffered by those algorithms using
scalar valued strengths and hence to improve the estimation and approximation
on rule inherent usefulness. This algorithm uses a set of domain-independent or
domain-dependent context variables to partition the contexts into context chunks.
Then algorithm employs array valued strengths to estimate the inherent
usefulness of rule actions under different context chunks. The justification of this
algorithm is based on the definitions of the inherent usefulness and Credit-
Apportionment problem. Obviously, it is improper to use a scalar valued strength
to represent the curve of inherent usefulness of a rule action. Therefore by using
a set of context variables to partition the contexts into chunks, and by processing
Credit-Apportionment on the context chunk level, array valued strength is
inevitably able to provide a better approximation of the inherent usefulness
function than a scalar valued strength can.
GAMBLE
The next reference paper is the research paper on “Genetic Algorithm Based
Machine Learning Expert system Indian Institute of Technology, Roorkee
India”. This talks about an expert system that is used for students who are
seeking admission into an engineering institute for obtaining a degree in
bachelors of engineering. After clearing the entrance examination the student is
advised by this system as to which branch would be most suited for him. An
algorithm is used for branch selection.
All the available seats in every branch are calculated and list of available
branches is formed. Then a branch aptitude total for the listed branches is
calculated for the listed branches. The various parameters like logic, imagination,
aesthetic sense, concentration level, etc are listed along with their weights.
These are variable parameters that would be automatically updated with
experience by the system. Then there is an idea about the Genetics based
Machine learning where discussion about classifier systems is given along with
its major 3 components.
(1)Rule and message system
(2)Apportionment of Credit system
(3)Genetic algorithm
The other part also talks about the Credit-Apportionment algorithm using the
Bucket Brigade algorithm, this part of the paper is much more deeply related to
our project proposal. Apportionment of Credit via competition and rule discovery

4. using genetic algorithms form a reasonable basis for constructing a machine
learning system atop the computationally convenient and complete framework of
classifiers.
The BBA service economy contains two components: an auction and a
clearinghouse. When classifiers are matched they do not directly post their
messages. Instead, having its tradition matched qualifies a classifier to
participate in an activation auction in which a record is maintained of its net worth
known as strength. The matching classifier makes a bid proportional to its
strength therefore following this method the rules that are more fit are given more
preference over other rules. The process of auctions allows appropriate
classifiers to be selected and post rules. The selected classifier has to clear its
payment through the clearinghouse, paying its bid to other classifiers for
matching message rendered. A classifier that has been matched and activated
sends its bid to those classifiers responsible for sending the messages that
matched the bidding classifier’s condition. The bid payment is divided in some
manner among the matching classifiers.