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  • Coevolving the "Ideal" Trainer
    of rules density over several generations It can be observed that diversity is maintained for about 500 generations during which different alternatives are explored simultaneously by the population of rules Then a solution is discovered that moves the search in the area where density is close to 0 5 Afterward several niches might still be explored however the coding used to construct the figures doesn t allow the representation of those different niches since all the rules have a similar density Usually this technique results in better performance on average However it takes also more time to converge This is a trade off between speed and quality of solutions Figure 3 Evolution of the distribution of the density of rules over time Learning in an Adapting Environment Coevolution The idea of using coevolution in search was introduced by Hillis 1992 In his work a population of parasites coevolves with a population of sorters The goal of parasites is to exploit weaknesses of sorters by discovering input vectors that sorters cannot solve correctly while sorters evolve strategies to become perfect sorting networks In coevolution individuals are evaluated with respect to other individuals instead of a fixed environment or landscape As a result agents adapt in response to other agents behavior For the work presented in this document I will define coevolutionary learning as a learning procedure involving the coevolution of two populations a population of learners and a population of problems Moreover the fitness of an individual in a population is defined only with respect to members of the other population Two cases can be considered in such a framework depending on whether the two populations benefit from each other or whether they have different interests i e if they are in conflict Those two modes of interaction are called cooperative and competitive respectively In the following paragraphs those modes of interaction are described experimentally in order to stress the different issues related to coevolutionary learning Cooperation between populations In this mode of interaction improvement on one side results in positive feedback on the other side As a result there is a reinforcement of the relationship between the two populations From a search point of view this can be seen as an exploitative strategy Agents are not encouraged to explore new areas of the search space but only to perform local search in order to further improve the strength of the relationship Following a natural extension of the evolutionary case to the cooperative model the fitness of rules and ICs can be defined as follows for the rho c 1 2 task For our experiments the same setup as the one described previously is used The population size is n R 200 for rules and n IC 200 for ICs The population of rules and ICs are initialized according to a uniform distribution over 0 0 1 0 for the density At each generation the top 95 of each population reproduces to the next generation and the remaining 5 is the result of crossover between parents from the top 95 selected using a fitness proportionate rule Figure 4 presents the evolution of the density of rules and ICs for one run using this cooperative model Without any surprise the population of rules and ICs quickly converge to a domain of the search space where ICs are easy for rules and rules consistently solve ICs There is little exploration of the search space Figure 4 Evolution of the distribution of the density of rules left and the density of ICs right over time Competition between populations In this mode of interaction the two populations are in conflict Improvement on one side results in negative feedback for the other population Two outcomes are possible Unstable behavior alternatively agents in one population outperform members of the other population until those discover a strategy to defeat the first one and vice versa This results in an unstable behavior where species appear then disappears and reappears again in a later generation a Stable state is reached this happens if one population consistently outperforms the other For instance a very strong strategy is discovered by agents in one population For the rho c 1 2 task the fitness defined in the cooperative case can be modified as follows to implement the competitive model Here the goal of the population of rules is to discover rules that defeat ICs in the other population by allowing the CA to relax to the correct state while the goal of ICs is to defeat the population of rules by discovering initial configurations that are difficult to classify Figure 5 describes an example of a run using this definition of the fitness In a first stage the two populations exhibit a cyclic behavior Rules with low density have an advantage because there are more ICs with low density In response to this ICs with high density have an evolutionary advantage and have more representatives in the population In turn rules with high density get an evolutionary advantage ldots This unstable behavior exhibited by the two populations is an instance of the Red Queen effect Cliff Miller 1995 fitness landscapes are changing dynamically as a result of agents from each population adapting in response to the evolution of members of the other population The performance of individuals is evaluated in a changing environment making continuous progress difficult A typical consequence is that agents have to learn again what they already knew in the past In the context of evolutionary search this means that domains of the state space that have already been explored in the past are searched again Then a stable state is reached in this case the population of rules adapts faster than the population of ICs resulting in a population focusing only on rules with high density and eliminating all instances of low density rules a finite population is considered Then low density ICs exploit those rules and overcome the entire population Figure 5 Evolution of the distribution of the

    Original URL path: http://www.demo.cs.brandeis.edu/coev_CA/ (2012-12-24)
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  • page explanation of the different experiments Read the explanation study the graph and then click on it to run the simulation dynamically The experiments use two coevolving populations where the members of each population play against members of the other population We use a very simple representation of an individual an integer or integer array in the populations and a very simple game comparing which integer is bigger to illustrate several ways in which coevolutionary dynamics may fail to evolve good strategies Different dynamics in the coevolving populations can be observed by changing properties of the game and characteristics such as how many opponents are sampled in each population The game is played between the members of two populations and based on some goal such as being larger or having the dimension that most differs between opponents decide the game In the experiments we are interested in comparing how the coevolving players think they are doing according to the score they get against opponents and how they are really doing in regard to objective improvement in our case this is the size of the number we use the terms subjective fitness and objective fitness to refer to these different measures

    Original URL path: http://www.demo.cs.brandeis.edu/pr/number_games/ (2012-12-24)
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  • Generative Representations for Design Automation
    using Lindenmayer systems L systems as the generative representation for an evolutionary algorithms Using this system we demonstrate a system that evolves hierarchically modular tables and locomoting robots called genobots Method The evolutionary system used to evolve designs consists of the design constructor and simulator the parsar for the generative representation and the evolutionary algorithm Each design is constructed from a sequence of construction commands similar to an assembly procedure which specify how to construct the design This string of construction commands is produced by parsing the generative encoding for which we use Lindenmayer systems L systems The evolutionary algorithm evolves a population of L systems using the fitness returned by a user defined fitness function A graphical example of an evolved L system is shown below along with the sequence of command strings it produces An example L system The sequence of assembly procedures it generates In these images production rules are represented by cubes with lines connecting them to their condition successor pairs The black sphere represents a condition and the following symbols are the contents of the production body Triangles are used to represent the repeat operator and spheres represent construction commands The final string is then used to construct the design Results This system has been used in the following substrates Static Structures 2D Genobots 3D Genobots Download The software used for this research is called GENRE which stands for GENerative REpresentations The source code for GENRE is available under the GNU GPL genre 1 1b tar gz 248k Note that this source code is for Linux and I have compiled and run it on RedHat 8 0 Publications on Generative Representations Hornby Gregory S Lipson Hod and Pollack Jordan B Generative Representations for the Automated Design of Modular Physical Robots IEEE Transactions on Robotics and

    Original URL path: http://www.demo.cs.brandeis.edu/pr/evo_design/evo_design.html (2012-12-24)
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  • Exact Representations from Feed-Forward Neural Networks
    than three it is not possible to directly visualize the decision region One way to gather information from our high dimensional polytopic decision regions is to describe them in terms of rules That is we bound each polytope inside a hyper rectangle and examine the rectangle s coordinates The rectangles can later be refined to enclose parts of polytopes thereby giving higher resolution rules In this case our decision region is covered by the following hyper rectangle min 4 45 5 79 3 90 7 93 max 6 47 6 01 7 39 6 07 Another way to examine the high dimensional polytope is to examine projections on to lower dimensional spaces In this figure we see two projections of the 4 D sphere decision region Needless to say the 4 D sphere looks less and less like an actual sphere It is fair to speculate that this is due to the difficulties of learning in higher dimensional spaces The higher dimensionality naturally promotes more complex decision regions with potential for greater artifact phenomena Ball Throwing Network A 40 hidden unit network was trained to predict whether a thrown ball will hit a target As input it received the throwing angle initial velocity and the target distance It achieved an 87 success rate on its training data In the following figure the network s decision region is contrasted with the analytical solution to the problem The network managed to encapsulate the gist of the analytical model but it may miss a few jump shots S P 500 Direction Predictor Network A neural network with 40 hidden units was trained to predict the average direction of movement up or down for the following month s S P 500 Index It was trained on macro economic data from 1953 to 1994 The network s inputs are the percentage change in the S P 500 from the past month the differential between the 10 year and 3 month Treasury Bill interest rates and the corporate bond differential for AAA and BAA rates After training the network achieved a greater than 80 success rate on the data In the figure we can see the network s decision regions Immediately we can surmise that the network would probably not generalize very well to out of sample data We can see that rather than extracting some underlying regularity some nice localized geometrical description of the data points the network tended to highly partition the space with small and irregular decision regions to try and enclose all the sporadic data points In the region of input space where the training data resides the network has 28 different decision regions Of these all but five have a bounding rectangle with a volume of less than one One decision region s rectangle encompasses the whole space If we slice this polytope using three hyperplanes each bisecting the input space across a different dimension then if the polytope was completely convex we would expect at most to get eight sub

    Original URL path: http://www.demo.cs.brandeis.edu/pr/DIBA/index.html (2012-12-24)
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  • The GNARL Project
    Brought to you by the DEMO Lab Download Source Reference An Evolutionary Algorithm that Constructs Recurrent Networks IEEE Transactions on Neural Networks 5 54 65 Copyright Notice

    Original URL path: http://www.demo.cs.brandeis.edu/pr/gnarl/ (2012-12-24)
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  • Educational Technologies Mission
    human mind We are developing a new kind of networked anytime learning system using adaptive computation which enables appropriate one to one human interactions sheilded by and facilitated on the Internet Just list agents in a market can trade without a central governor and biological systems can evolve without a designer groups of learners can often progress without a teacher Using students as each others s mentors across the internet

    Original URL path: http://www.demo.cs.brandeis.edu/pr/edtech/ (2012-12-24)
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  • Educational Technologies Mission

    (No additional info available in detailed archive for this subpage)
    Original URL path: /pr/edutechinfo/mission.html (2012-12-24)


  • TRON
    this TRON Our computer is slowly learning to play tron With every game you play it adds a new bit of information Over the following weeks or months we expect it to become a good player or at least better than it is right now First time The rules are very simple Start playing Java required Learn more about this experiment last updated Ranking Best human players Top 100 All

    Original URL path: http://www.demo.cs.brandeis.edu/tron/ (2012-12-24)
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