Evolutionary Computation Artificial Neural Networks Out put Signals Input Signals First Second Input hidden hidden Output layer layer layer layer Fixed Architecture Require training set 2 Genetic algorithm Fixed size chromosome Neuro-Genetic Hybrid x1 0.9 1 4 -0.8 From neuron: 1 2 3 4 5 6 7 8 0.1 -0.6 To neuron: 1 0 0 0 0 0 0 0 0 0.4 2 0 0 0 0 0 0 0 0 5 -0.3 0.1 3 0 0 0 0 0 0 0 0 y x2 0.6 4 0.9 -0.3 -0.7 0 0 0 0 0 2 8 5 -0.8 0.6 0.3 0 0 0 0 0 -0.2 -0.2 0.5 6 0.1 -0.2 0.2 0 0 0 0 0 6 7 0.4 0.5 0.8 0 0 0 0 0 -0.7 0.3 0.9 8 0 0 0 -0.6 0.1 -0.2 0.9 0 0.2 x3 3 0.8 7 Chromosome: 0.9 -0.3 -0.7 -0.8 0.6 0.3 0.1 -0.2 0.2 0.4 0.5 0.8 -0.6 0.1 -0.2 0.9 GA replaces Back-propagation to train the NN Fixed NN architecture, fixed size chromosome Evolutionary Complexification • Two major goals in intelligent systems are the discovery and improvement of solutions to complex problems. • Complexification, i.e. the incremental elaboration of solutions through adding new structure, achieves both these goals. • To discover and improve complex solutions, evolution, and search in general, should be allowed to complexify as well as optimize. Evolutionary Computation • Class of algorithms that can be applied to open-ended learning problems in AI • Traditionally such algorithms evolve fixed length genomes assuming the space of the genome is sufficient to encode the solution • In many cases a solution may be known to exist in that space Indefinite numbers of parameters • Many common structures are defined by an indefinite number of parameters • E.g., the number of neurons in an ANN • So it is often not clear what number of genes is appropriate to solve a problem • Researchers must use heuristics to determine a priori the appropriate number of genes Fixed Length Encoding • Pre-determination of the appropriate number of genes is difficult • Larger the genome the larger the search space • Sometimes the solutions should evolve in an open-ended way (games) with no final solution • Fixing the maximum size of the genome also fixes the maximum complexity of the evolved solutions Examples • Ping-pong playing robot - solution is to make the genome very large • Open-ended problems when no final solution can be accepted, improving after a certain point not possible with a fixed length genome Continual Evolution • Such continual evolution is difficult with a fixed genome for two reasons: • When a good strategy is found in a fixed-length genome, the entire representational space of the genome is used to encode it. Thus, the only way to improve it is to alter the strategy, thereby sacrificing some of the functionality learned over previous generations. • Fixing the size of the genome in such domains arbitrarily fixes the maximum complexity of evolved creatures, defeating the purpose of the experiment. Complexification • Extending the length and size of the genome • Adds new genes that lead to increased phenotypic complexity • Called complexification • Specifically with evolving neural nets it means adding nodes and connections to an already functional ANN • Allow more complex strategies to elaborate on simpler strategies. Evolving neuro-architecture • Over many generations, new hidden nodes and connections are added, complexifying the space of potential solutions. • In this way, more complex strategies elaborate on simpler strategies, focusing search on solutions that are likely to maintain existing capabilities. Alteration vs. Elaboration Alteration vs. Elaboration • The dark robot must evolve to avoid the lighter robot, which attempts to cause a collision. • In the alteration scenario (top), the dark robot first evolves a strategy to go around the left side of the opponent. However, the strategy fails in a future generation when the opponent begins moving to the left. • The dark robot alters its strategy by evolving the tendency to move right instead of left. However, when the light robot later moves right, the new, altered, strategy fails because the dark robot did not retain its old ability to move left. • In the elaboration scenario (bottom), the original strategy of moving left also fails. However, instead of altering the strategy, it is elaborated by adding a new ability to move right as well. Thus, when the opponent later moves right, the dark robot still has the ability to avoid it by using its original strategy. • Elaboration is necessary for a coevolutionary arms race to emerge and it can be achieved through complexification. Key ideas • Keeping track of which genes match with differently sized genes throughout evolution • Speciation, so that solutions of differing complexity can exist independently • Beginning with a uniform population of small networks Scalability • Open-ended problems with no explicit fitness function • Fitness depends on comparisons with other agents performing the same task (uses coevolution) • Robot duel domain. No known best strategy for a robot. Complexification in Nature • In nature optimization does not occur with fixed size genes • New genes are occasionally added to the genome • Speciation protects newly formed more complex genes Gene duplication • Gene duplication is a kind of mutation in which multiple copies of parental genes are copied into offspring genome • The offspring has redundant genes expressing the same proteins • Gene duplication is a possible explanation how natural evolution expanded the size of genomes throughout evolution Evidence for Gene Duplication • Gene duplication has been responsible for key innovations in overall body morphology over the course of natural evolution • A major gene duplication event occurred around the time that vertebrates separatedfrom invertebrates. • Invertebrates have a single HOX cluster (of genes) while vertebrates have four, suggesting that cluster duplication significantly contributed to elaborations in vertebrate bodyplans • Researchers agree that gene duplication in some form contributed significantly to body-plan elaboration. Gene Duplication and Genetic Programming • Gene duplication is a possible explanation how natural evolution indeed expanded the size of genomes throughout evolution, and provides inspiration for adding new genes to artificial genomes as well. • Gene duplication motivated Koza (1995) to allow entire functions in genetic programs to be duplicated through a single mutation, and later differentiated through further mutations. • When evolving neural networks, this process means adding new neurons and connections to the networks. Challenges • Such systems evolve different sized and shaped network topologies which are difficult to crossover without losing information • Artificial crossover may disrupt evolved topologies • Optimizing variable length genomes may take longer and more complex networks be eliminated before they have had a chance to be optimized Implementing Variable Length Genes • Crossover causes problems through misalignment • Optimization takes longer causing early elimination of possible innovations Alignment • Depending on when new structure was added, the same gene may exist at different positions, or conversely, different genes may exist at the same position. • Thus, artificial crossover may disrupt evolved topologies through misalignment. • Alignment processes have been observed in nature – synapsis Speciation • Second, innovations in nature are protected through speciation. Organisms with significantly divergent genomes never mate because they are in different species. • If any organism could mate with any other, organisms with initially larger, less-fit genomes would be forced to compete for mates with their simpler, more fit counterparts. • As a result, the larger, more innovative genomes would fail to produce offspring and disappear from the population. NEAT ALGORITHM • NeuroEvolution of Augmenting Topologies (NEAT) improved genetic algorithms by making including complexification and speciation in the algorithm • Alignment during crossover through synapsis • Speciation protects complexification Competitive Coevolution • Fitness signifies only the relative strength of solutions • Ideally solutions evolve in an “arms race” towards better performance • Interesting strategies only evolve if the arms race continues for a large number of generations Progress in Evolution • Evolution finds simplest strategy that can win • Strategies switch back and forth opportunistically between variations, losing some abilities and attaining others • Techniques: “Hall of Fame”, Fitness Sharing, Pareto Coevolution – finding the best learners and best teachers in a population • These techniques allow sustaining the arms race longer but do not encourage continual evolution – creating new solutions that maintain existing capabilities. Complexification • Complexification elaborates strategies by adding new dimensions, enabling indefinite progress NeuroEvolution of Augmenting Topologies • Using historical markings to line up genes for crossover • Protecting topological evolution through speciation • Minimization of topologies throughout evolution Genetic Encoding • A genome includes a list of connecting genes, an in-node, an out-node, weight, expression enable bit and an innovation number Genetic Encoding Mutation • Mutation in NEAT can change both connection weights and network structures. • Connection weights mutate (usual NE algorithm) • Structural mutation operates in two ways - add connection and add node – connection split, new in-weight of 1 out-weight same as old weight so functionality does not change initially Structural Mutation in NEAT The connection between the first node and the old node is given the weight 1 and the connection between the new node and the second is given the same weight of the connection being split. Historical Markings • If the two above mutations occur consecutively the innovation numbers associated with the new genes allow the system to keep track of the histories of every gene in the system Crossover using innovation numbers Historical markings are lined up and randomly chosen for the offspring Genes that do not match are inherited from the more fit parent or randomly. Disabled genes are inherited at 25% Speciating • It turns out that a population of varying complexities cannot maintain topological innovations on its own. • Because smaller structures optimize faster than larger structures, and adding nodes and connections usually initially decreases the fitness of the network, recently augmented structures have little hope of surviving more than one generation even though the innovations they represent might be crucial towards solving the task in the long run. • The solution is to protect innovation by speciating the population. Speciation • NEAT speciates the population so that individuals compete primarily within their own niches instead of with the population at large. This way, topological innovations are protectedand have time to optimize their structure before they have to compete with other niches in the population. • Speciation prevents bloating of genomes: Species with smaller genomes survive as long as their fitness is competitive, ensuring that small networks are not replaced by larger ones unnecessarily. • Protecting innovation through speciation follows the philosophy that new ideas must be given time to reach their potential before they are eliminated. Speciation Distance between networks E is the number of excess genes D is the number of disjoint genes W is the average weight difference of matching genes N is the number of genes in the larger genome If the distance of from a test gene to a randomly chosen member of a species is less than the current compatibility threshold the test gene is placed in the species Speciation Fitness Sharing Organisms in the same species must share the fitness of their niche. The adjusted fitness f’ for organism i is calculated according to its distance from every other organism j in the population where sh is set to 0 when the distance is above the threshold and 1 otherwise. The factor reduces to the number of organisms in the same species as organism i Every species is assigned a potentially different number of offspring in proportion to the sum of adjusted fitnesses f’i of its member organisms. Species reproduce by first eliminating the lowest performing members from the population. The entire population is then replaced by the offspring of the remaining organisms in each species. A Run models increasing complexity • Run begins with a uniform population with no hidden nodes that differ in the random assignments of weights • The gradual production of increasingly complex structures constitutes the model of complexification Coevolution Domain • Domain where it is possible to develop a wide range increasingly sophisticated strategies • Sophistication can be readily measured. • A coevolution domain is particularly appropriate because a sustained arms race should lead to increasing sophistication. Duel Robot Domain Food is represented by sandwiches and robots by the circles representing sensors and arrows representing directions. The objective is to forage to obtain a higher level of energy than the opponent and then collide with it The duel domain supports sophisticated strategies that are recognizable http://nn.cs.utexas.edu/pages/research/neatdemo.html The Robot ANN Each has five robot finder sensors and five to sense food. Each has two wheels controlled by separate motors and can read the opponents energy level and has a wall sensor. Energy is consumed in proportion to the amount applied to the motors. About the duel domain • The observed state taken by the sensors does not include the internal state of the opponent • The next observed state depends on the decision of the opponent • It is necessary for the robots to learn to predict what the opponent is likely to do. Opponent Sampling • Evolve two separate populations. • In each generation, each population is evaluated against an intelligently chosen sample of networks from the other population. • The population currently being evaluated is called the host population, and the population from which opponents are chosen is called the parasite population Competition • Each host was evaluated against the four highest species’ champions. They are good opponents because they are the best of the best species, and they are guaranteed to be diverse because their distance must exceed the species threshold • Another eight opponents were chosen randomly from a Hall of Fame composed of all generation The Hall of Fame ensures that existing abilities need to be maintained to obtain a high fitness. • Together speciation, fitness sharing, opponent sampling and Hall of Fame comprise an effective competitive coevolution methodology. Population and Competition • Each population had 256 networks • Host networks received 1 point for each win and 0 for losing • Each host was evaluated in 24 games (12 opponents x 2 games each) • Of the 12, 4 were species champions and 8 were Hall of Famers. Difficulty of tournaments • For example, if strategy A defeats 499 out of 500 opponents, and B defeats 498, counting will designate A as superior to B even if B defeats A in a direct comparison. • In order to decisively track strategic innovation, we need to identify dominant strategies - those that defeat all previous dominant strategies. • This way, we can make sure that evolution proceeds by developing a progression of strictly more powerful strategies, instead of e.g. switching between alternative ones. Dominance Tournament • A run returns record of every generation champion from both populations • A network a is superior to a network b if a wins more games than b out of 288 total games with different food placements • A generational champion is the winner of a 288 game comparison between the host and parasite champions of a single generation • The first dominant strategy d1 is the first generation champion • The dominant strategy dj, j> 1 is a generation champion such that for all i < j dj is superior to di • Process is called a dominance tournament Features of a dominance tournament • Fewer games than other tournaments • Allows identification of a sequence of increasingly sophisticated strategies (dominant individuals) Results – 33 Evolutions • Each of the 33 evolution runs took between 5 and 10 days on a 1GHz Pentium III processor, depending on the progress of evolution and sizes of the networks involved. Measuring Complexity • Define complexity as the number of nodes and connections in a network: The more nodes and connections there are in the network, the more complex behavior it can potentially implement. • The results were analyzed to answer three questions: • (1) As evolution progresses does it also continually complexify? • (2) Does such complexification lead to more sophisticated strategies? • (3) Does complexification allow better strategies to be discovered than does evolving fixed-topology networks? Emergence of Complexity The hashed lines represent the average over 13 runs of the structure of the highest dominant network in each generation. A hash mark appears each time a new dominant network emerged. The two other lines represent the average over five runs of the most and least complex networks without fitness selection (random assignment of fitness). This shows that without fitness a wide range of complexity is evolved. Emergence of Strategies Dn – network with dominance level n Sk – best network in species S at generation k hl – l’th hidden node to arise from a structural mutation Begin with S100: Mature no hidden node strategy, followed even when the opponent had more energy leaving it vulnerable to attack S200: Evolved a resting strategy. Not a complexification S267: h22 appeared. Switched between resting and all out attack S315: improved ability to attack at appropriate times. Best Complexifying Network 11 hidden nodes and 202 connections Fixed-Topology vs Complexification Conclusions Complexifying Evolution only searches higher-dimensional structures that are elaborations of known good lower-dimensional structures. The values of the existing genes have already been optimized over preceding generations. This may mean that the search in the higher- dimensional space is starting in a position of some advantage compared to a purely random position in that space. This may explain why this method is able to find solutions that fixed topology coevolution cannot.
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