1. ART – Artificial Reasoning Toolkit Evolving a complex system Marco Lamieri lamieri@econ.unito.it

2. Agenda: Overview on genetic algorithm; Create a mind for agents: learning classifier system Some improvement to the methods, the ART project; Our theoretical applications with ART; Move to real world with an industry application: the Penelope project References

3. The idea of genetic algorithm Starting from “Survival of the fittest” [Darwin, 1859] Genetic Algorithms (GA) are evolutionary programs that manipulate a population of individuals represented by fixed- format strings of information. The background theory is the “adaptation in artificial system” discussed by Holland [1975]. GA are used to solve real-world optimization problems within a very large solution space and “ill-defined” problems.

4. How does a GA work An initial population of individuals (solutions) is generated; –individuals represent potential solutions to the given problem and are described as binary strings; –each character in the individual’s data string is called a gene and each possible value that the gene can take on is called an allele. parents and individuals that are going to survive to the next generation are selected using a fitness proportional mechanism; The selected individuals are evolved by means of reproduction using two operators: –crossover, –mutation. Process go on untill the population almost converge to a specific individual.

5. Example (square root of 2) The solution space is bounded between 0 and 1. We use a binary representation on 10 digits. There are 1024 numbers [2^10], starting from 0 and ending at 1023 [2*10 -1].

6. Generate random population A population of solutions is generated randomly. For the square root problem, a fixed number of 10 character binary strings are generated randomly.

7. Define the fitness function Darwinian evolution of a population implies that the strongest individuals will probably survive. The fitness of an individual is a numerical assessment of that individual’s ability to solve the problem - it is the ability of the individual to satisfy the requirements of the environment. In terms of the square root problem, the perfect individual is the numerical value approximated by 1.414213562373. In economic problems,the profit can be used to generate a fitness function

9. Selection process (roulette wheel) To select individuals is used the roulette wheel technique. The roulette wheel implementation implicitly forces fitness- proportionate reproduction. Selection is divided in 2 steps: 1.Individuals that are going to survive to the next generation are selected; 2.Individuals that are going to reproduce are selected.

10. Crossover Crossover swaps some of the genetic material of two individuals, creating two new individuals (children), who are possibly better than their parents.

11. Mutation In order to recover from this loss of genetic material, the individuals are allowed to change their genes randomly.

12. Convergence John Holland’s Schema Theorem [Holland, 1992] is widely accepted as mathematical proof that the genetic algorithm, due to its fitness-proportionate reproduction, converges to better solutions. Via the convergence method is possible to solve non “well- defined” problems where the best solution is not known a priori.

13. Remarks There is no ultimate goal or problem that must be solved by natural evolution. Evolution itself does not guarantee the creation of fitter individuals. The GA use a fuzzy logic that not always lead to the best solution but to a good one. The algorithm is problem independent.

14. ART – Some improvement to the method ART, starting from John Holland's work, introduces some extensions and innovations: extended alphabet: each gene can be represented by up to 32000 values. In a standard representation the genes have a binary alphabet and can become meaningless. With the extended alphabet each allele can be a meaningful part of the solution and the translation process is easier. multi genome: the multi genome schema give a high degree of freedom to the user in formalizing problems in which coexist different binded aspects. rescale fitness operator: the natural selection process has been modified in order to improve efficiency and manage negative fitness values. univocal genome: using this option each value of the alphabet is unique within the genome.

15. Classifier systems Classifier system is an induction self-learning system based on a set of simple logical rules called classifiers. Each rule has the following structure: ”if condition then action”. During learning process rules priorities (strengths) are changed. In case of success current and previous activated rules are encouraged. Evolutionary methods are used for new rules searching. CS consist of four principal components: –List of classifiers (population of classifiers). –List of messages that plays the role of a ”message board” for communications and short term memory. –Input interface (detector) that represents the environment state. –Output interface (effector) that ensures interaction with the environ- ment or its change.

16. The computations of a CS are the follows: 1.add messages obtained with the help of the input interface to the input message list; 2.compare all the messages on the message list with the condition parts of all classifiers and remember all the classifiers for which coincidence has been observed; 3.select by a auction some classifier actions; 4.pass the messages obtained through the output interface; 5.replace the contents of the message list with new messages from the environment; 6.if a classifier chain is implemented add to message list also the classifier’s action; 7.auction’s bid is paied using the bucket brigade algorithm.

17. ART CS – Some improvement to the method Reward’s Memory: –the metaphor is that in most difficult situation a sub optimal response can be acceptable (if a trading strategy was successful in the past it could earn again money in the future) while the opposite is true for a easy situation (if it is raining bring umbrella) and a sub optimal action is not acceptable –the reward given to a specific action is internally computed in respect to the average past reward. –If a strategy is harder to grasp than a reward higher than the average of the previous rewards has to be considered successful and at the opposite a non perfect outcome of a very easy strategy has to be considered a bed one. –the memory is limited by a parameter in order to emulate the cognitive limit of agents

18. Our applications Genetic algorithm Find the weight of a artificial neural network in order to solve the XOR problem Find the Cournot equilibrium in a simplified simulated economic Penelope… Classifier system Suggest diagnosis for chest pain where symptoms are ‘conditions’ and diagnosis are ‘actions’. Evolve a good strategy to play Minority Game introducing communication among agents Evolve a good strategy for the iterated prisoner dilemma where the mind of the agents is a classifier system. Evolve a good strategy for the Minority Game

19. References ART project http://eco83.econ.unito.it/golemhttp://eco83.econ.unito.it/golem Penelope project http://www.penelopeproject.orghttp://www.penelopeproject.org This presentation is available at: http://eco83.econ.unito.it/dottorato/marco_lamieri/20050114- isiWinterSchool-art.ppt http://eco83.econ.unito.it/dottorato/marco_lamieri/20050114- isiWinterSchool-art.ppt For any further information … lamieri@econ.unito.it morini@econ.unito.it