g5baim artificial intelligence methods dr. rong qu evolutionary algorithms
TRANSCRIPT
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 3-540-60676-9 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 0-7803-3481-7, pp 3-14
Michalewicz, Z. and Fogel, D. (2000). How to Solve It : Modern Heuristics. Springer-Verlag, ISBN 3-540-66061-5
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
xt+1 = xt + 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 = 0Create initial point xt = x1
t,…,xnt
REPEATDraw ni from a normal distribution for all i = 1,
…,nyi
t = xit + ni
New generationSet 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 = σcd
if (k) > 1/5 then σ = σci
if (k) = 1/5 then σ = σ
Evolutionary Algorithms - How They Work
if (k) < 1/5 then σ = σcd
if (k) > 1/5 then σ = σci
if (k) = 1/5 then σ = σ k dictates how many generations should elapse before
the rule is applied cd and ci determine the rate of increase or decrease
for σ ci must be greater than one and cd must be less than
one Schwefel (1981) used cd = 0.82 and ci = 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 problemspremature 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 BlackjackBlackjack 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 BlackjackThe 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) xt+1 = xt + N(0, σ) 1/5 success rule Population: ( + ), (, )
Case study Poker blackjack