G5BAIM Artificial Intelligence Methods Dr. Rong Qu Evolutionary Algorithms

Learning in Computer Programs How Computer Program Learn? Another aspect of AI This lecture is only an introduction This techniques can be used as an optimisation strategy but we are going to look at a learning example

Evolutionary Algorithms Population based algorithm Genetic algorithm Ant algorithm Evolutionary strategies

Evolutionary Algorithms Chapter 8 of Michalewicz, Z. (1996). Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, ISBN Good description of EA History of ES GA vs. ES

Evolutionary Algorithms Almost anything by David Fogel Fogel, D. B. (1994) IEEE Transactions on Neural Networks, Vol 5:1, pp3-14 Fogel, D.B. (1998) Evolutionary Computation The Fossil Record, IEEE Press, ISBN , pp 3-14 Michalewicz, Z. and Fogel, D. (2000). How to Solve It : Modern Heuristics. Springer-Verlag, ISBN

Learning in Computer Programs There are other ways that we could design computer programs so that they “learn” For example, knowledge based on some suitable logic symbolism Use inference rules Learning by remembering and forgetting Using memory

Learning in Computer Programs Look at how Evolutionary Strategies (ES’s) can be used as evolving learning strategies Easily convert to optimisation tools

Learning in Computer Programs ES’s vs EP not confuse evolutionary strategies (ES’s) with evolutionary programming (EP) EP is about writing programs that write programs

Evolutionary Algorithms vs. GA’s GA’s Population of chromosomes Reproduction operators (more details in GAs section) Mutation Crossover Selection strategy Generations

Evolutionary Algorithms vs. GA’s ES’s are an algorithm that only uses mutation and does not use crossover This is not a formal definition and there is no reason why we cannot incorporate crossover (as Michalewicz, 1996 shows)

Evolutionary Algorithms vs. GA’s ES’s are normally applied to real numbers (continuous variables) rather than discrete values. Again, this is not a strict definition and work has been done on using ES’s for discrete problems (Bäck, 1991) and (Herdy, 1991)

Evolutionary Algorithms vs. GA’s ES’s are a population based approach Originally only a single solution was maintained and this was improved upon.

Evolutionary Algorithms vs. GA’s In summary ES’s are Like genetic algorithms but only use mutation and not crossover They operate on real numbers They are a population based approach But we can break any, or all, of these rules if we wish!

Evolutionary Algorithms - How They Work An individual in an ES is represented as a pair of real vectors, v = (x,σ) x, represents a point in the search space and consists of a number of real valued variables The second vector, σ, represents a vector of standard deviations how spread out the values in a data set are

Evolutionary Algorithms - How They Work Mutation is performed by replacing x by x t+1 = x t + N(0, σ) N(0, σ) is a random Gaussian number with a mean of zero and standard deviations of σ changing value by adding random noise drawn from normal distribution

Evolutionary Algorithms - How They Work This mimics the evolutionary process that small changes occur more often than larger ones An algorithm (in C++) that produces Gaussian random numbers is supplied in the handout

Evolutionary Algorithms - How They Work Set t = 0 Create initial point x t =  x 1 t,…,x n t  REPEAT Draw n i from a normal distribution for all i = 1,…,n y i t = x i t + n i New generation Set t = t+1 UNTIL (stopping condition)

Evolutionary Algorithms - How They Work In the earliest ES’s (where only a single solution was maintained), the new individual replaced its parent if it had a higher fitness Two-numbered evolution scheme Compete upon two individuals Survival become new parent

Evolutionary Algorithms - How They Work In addition, these early ES’s, maintained the same value for σ throughout the duration of the algorithm It has been proven that if this vector remains constant throughout the run then the algorithm will converge to the optimal solution

Evolutionary Algorithms - How They Work Problem Although the global optimum can be proved to be found with a probability of one, it also states that the theorem holds for sufficiently long search time The theorem tells us nothing about how long that search time might be

Evolutionary Algorithms - How They Work To try and speed up convergence Rechenberg has proposed the “1/5 success rule.” It can be stated as follows The ratio, , of successful mutations to all mutations should be 1/5. Increase the variance of the mutation operator if  is greater than 1/5; otherwise, decrease it

Evolutionary Algorithms - How They Work Motivation behind 1/5 rule If we are finding lots of successful moves then we should try larger steps in order to try and improve the efficiency of the search If we not finding many successful moves then we should proceed in smaller steps

Evolutionary Algorithms - How They Work The 1/5 rule is applied as follows if  (k) < 1/5 then σ = σc d if  (k) > 1/5 then σ = σc i if  (k) = 1/5 then σ = σ

Evolutionary Algorithms - How They Work if  (k) < 1/5 then σ = σc d if  (k) > 1/5 then σ = σc i if  (k) = 1/5 then σ = σ k dictates how many generations should elapse before the rule is applied c d and c i determine the rate of increase or decrease for σ c i must be greater than one and c d must be less than one Schwefel (1981) used c d = 0.82 and c i = 1.22 (=1/0.82)

Evolutionary Algorithms - How They Work Problem with the applying the 1/5 rule It may lead to premature convergence for some problems premature convergence Increase the population size, which now turns ES’s into a population based approach search mechanism

Evolutionary Algorithms - How They Work Increase population size The population size is now (obviously) > 1. All members of the population have an equal probability of mating - compare with GA’s We could now introduce the possibility of crossover

Evolutionary Algorithms - How They Work Increase population size As we have more than one individual we have the opportunity to alter σ independently for each member We have more options with regards to how we control the population (discussed next)

Evolutionary Algorithms - How They Work In evolutionary computation there are two variations as to how we create the new generation

Evolutionary Algorithms - How They Work (  + ), uses  parents and creates offspring After mutation, there will be  + members in the population All these solutions compete for survival, with the  best selected as parents for the next generation

Evolutionary Algorithms - How They Work ( , ), works by the  parents producing offspring (where >  ) Only the compete for survival. Thus, the parents are completely replaced at each new generation Or, to put it another way, a single solution only has a life span of a single generation

Evolutionary Algorithms - How They Work The original work on evolution strategies (Schwefel, 1965) used a (1 + 1) strategy This took a single parent and produced a single offspring Both these solutions competed to survive to the next generation

Evolutionary Algorithms - Case Study Develop agent that knows how to play poker learns to adapt its play when faced with different playing styles

Evolutionary Algorithms - Case Study Barone (1999) Calculate the probability x of winning at any position By enumerating all possible hands that can be held by the opponents

Evolutionary Algorithms - Case Study Barone (1999) Learning how to play Poker fold(x) = exp(-eval(b) * (x – a)) call(x) = eval(c) * exp(-eval(b) 2 * (x-a) 2 ) raise(x) = exp(eval(b) * (x + a – 1.0)) a, b, c: constants that shape the functions, which need to be learnt

Evolutionary Algorithms - Case Study Barone (1999) (1+1) strategy Mean of zero Pre-defined standard deviation Using the above model Evolve a poker player Adapt to player styles of four different players

Evolutionary Algorithms - Case Study Simplified Blackjack Blackjack is a two player game comprising of a dealer and a player. The dealer deals two cards (from a normal pack of 52 cards) to the player and one card to himself. All cards are dealt face up. All cards take their face value, except Jack, Queen and King which count as 10 and Aces which can count as one or eleven

Evolutionary Algorithms - Case Study Simplified Blackjack The aim for the player is to draw as many cards as he/she wishes (zero if they wish) in order to get as close as possible to 21 without exceeding 21 Other concepts (doubling down)

Evolutionary Algorithms - Case Study Simplified Blackjack Known good strategies Thorp (1966) – basic strategy What to do for every possible pair of cards Based on what the dealer’s “up card” is As more cards, what to do when approaching 21

Evolutionary Algorithms - Case Study Simplified Blackjack How might we write an agent that learns how to play blackjack? Specify rules exactly Make it be able to learn new set of rules Without re-writing program

Evolutionary Algorithms - Case Study Simplified Blackjack Identify each possible situation How many potential hands we may have Taking into account doubling down Assign each of these hands the same probability what to do Agent learn the probabilities by playing many (millions) of times of hands

Evolutionary Algorithms - Your Go Questions  Do you think this would work?  Should we use a single candidate for each probability or should we have a population greater than one?  What sort of evolutionary scheme should we use; (  + ) or ( , ); and what values should we give  and ?  Can you come up with a better representation; other than trying to learn probabilities?

Evolutionary Algorithms - Finally Evolutionary algorithms can be used as search methods as well as a learning mechanism It just needs saying!

Summary Learning in computer program Evolutionary strategies Knowledge based systems ES’s vs. GA’s Mutation and Crossover Real and discrete variables Probability of selecting parents

Summary How ES’s work? v = (x,σ) x t+1 = x t + N(0, σ) 1/5 success rule Population: (  + ), ( , ) Case study Poker blackjack

G5BAIM Artificial Intelligence Methods Dr. Rong Qu End of Evolutionary Algorithms