Solving the Quasigroup problem using Simulated Annealing

36 Pages·2003·1.71 MB·English

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IBM
’s
Robocode an AI Playground Rob
ocod
e
!IBM’s RoboCode
!Virtual platform to test AI concepts
!Little tanks battle each other
!Each tank has a gun and radar
by Diana Bullion !Each tank is allotted the same
resources (energy, ammunition)
Robots Battle
!Built 5 Robots with different strategies
–Diana’s First …simple tutorial-like robot
–BumperBot …brute force tank
–ThirdTimeCharmer …focused attack
–TheGreatX…stays out of the way
–MasterEvader… predicts aiming point
!Implement multiple robots with varying
levels of intelligence
!Wanted to prove intelligence and
strategy wins over brute force
3
BumperBot MasterEvader
!Basic robot scans for other robots !Advanced Robot
!Bumps into them and repeatedly shoots !Evasive Movements … random
!Brute force -low intelligence figure-eightishpattern
–Does not predict where robot will be !Predicts best path to fire bullet … taking
–Does not stay focused on closest robot into account future speed and location
when different robot is scanned of both target and source robots, time to
!Results were surprising -original turn gun, time for bullet to travel
objective was for the more intelligent !Fire power relative to target distance
robots to win against BumperBot
Results
The Rest
!ThirdTimeCharmer
–Advanced Robot
–Maintains a focused attack
–Standard movement pattern
! Survival –50 pts for everyone that died before it
!TheGreatX ! Last Survivor –10 pts for every robot in battle
–Travels great distances ! Bullet Damage –1 pt for each pt of inflicted damage
–Rarely shoots ! Bullet Damage Bonus –20% kill bonus of all the
damage it did
–Lets others run out of energy
! Ram Damage –2 pts for every pt of ram damage
!Diana’s First ! Ram Damage Bonus –30% kill bonus of all ram
damage it did
–My first robot … modified tutorial
Robocode Rules
!Evironmentloop
–Robot code executed, time incremented, Learning Go with TD(λ)
bullets move, robots move, robots scan
!Bullets
–Bullet damage = 4*firepower (plus
Todd Detwiler
2*(firepower-1) if firepower > 1)
CSE 592
–Bullet speed = 20 –3*firepower
Winter 2003
–Energy returned on hit = 3 * firepower
!Robot Collision = .6 damage each
!Advanced Robots take Wall Collision
penalty
4
What is GO? The Rules
(cid:127) Players alternate placing stones on open
(cid:127) One of the oldest and most popular board intersections of the board (a 19x19 grid)
(cid:127) Adjacent stones form groups
games in the world (around 4000 yrs old)
(cid:127) Empty intersections adjacent to groups form its
(cid:127) A game of territory acquisition
liberties
(cid:127) Deterministic, perfect-information, zero- (cid:127) A group is captured when all of its liberties are
sum, 2 player strategy game removed
(cid:127) 2 passes signify the end of the game
(cid:127) A “grand challenge” in AI (Rivest1993)
(cid:127) Ko
Captures Why is Go so Hard?
(cid:127) Pspace-complete
If white plays at –Average branching factor of game tree around
the location 200
indicated by the
red circle, they –Size of game tree on the order of 10170
will capture the (compared to around 1050for Chess)
black stone by –Too large for look-ahead evaluation
removing its last
liberty. (cid:127) No good evaluation function for game
states
TD(λ) Approach The Pieces that I Started With
(cid:127) Learn an evaluation function (cid:127) OpenGo5.1 beta
–Use neural network as a function estimator –A set of pre-written Go objects as well as an
(cid:127) Temporal credit assignment environment for playing in
(cid:127)Very buggy, not as useful as I initially suspected
(cid:127) Nonlinear TD/Backproppseudo C-code
–Allen BondeJr. and Richard Sutton
–I have extended this to be an actual C++ object
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Player Design One Problem
(cid:127) Like TD-Gammon, games (state
sequences) are generated by pitting my Go
player against itself
(cid:127) Unlike TD-Gammon, I am using off-line
learning
(cid:127) Initially give player rules only, no strategy
(cid:127) Later augmented with one rudimentary
extension to reduce plies/game
The Extension Current Status
(cid:127) Don’t fill in simple, size 1 eyes (cid:127) Player
– Identifies all legal moves
(cid:127) Super Ko
– Plays against itself
– Detects win
– Black tracks game states for learning
(cid:127) TD(λ) network is implemented, but not fully
tested
– Currently testing load/save functionality
(cid:127) Learning has not yet been achieved
Questions?
Letter Recognition by Using
Multi-Layer Neural Network
Meng Tat Fong
03/13/2003
6
Problem Domain Data Set
Create a classifier to identity the 26 David Slate donated to UCI machine
! !
capital letters in the English Alphabet learning repository
Extensible 20,000 samples
! !
Create electronic document from letter images from black-and-white
! !
scanned documents, newspapers, etc. displays
20 different fonts
!
randomly distorted (all unique samples)
!
Data Set Backgrounds
16 integer attributes Not using any existing Machine
! !
Normalize to 0.0 (cid:150)1.0 Learning libraries
!
! 26 output classes (A-Z) ! Java
750-800 samples each
!
2,4,4,3,2,7,8,2,9,11,7,7,1,8,5,6,Z
!
4,7,5,5,5,5,9,6,4,8,7,9,2,9,7,10,P
!
Algorithms Algorithms
! Separate the sample data set into two sets ! Wji = Wji + ∆Wji
(~16,000 and ~4,000) ! ∆Wji= (cid:181)EjXji
! Network is trained and then verified ! Based on the idea that each unit is partially
! Stochastic gradient descent version of the responsible for the error of its parent.
BackPropagation algorithm
! Unit weight is updated after each sample Level N J
! Sigmoid Units to learn non-linear functions
Level N -1 I
7
Network Topology Improvements
Momentum --nth weight update
!
A partially depending on the previous
B update
C ! ∆Wji(N) = (cid:181)EjXji+ α∆Wji(N-1)
! Help to escape local minima
! Move along flat region during the search
Z ! Increase my network accuracy by 2.2%
! Momentum 0.58 (75.1% to 77.3%)
Input Layer Hidden Layer Output Layer
16 units 45 units 26 units
Improvements Improvements
! Learn from mistakes ! Ensemble
! Train the network with all the training ! Use multiple networks to perform
samples once
classification
! Fneeetwd otrhke, bsaumt oen slya mupsele isn tcoo rtrreacintl yt hcela ssify ! Each network will predict an outcome and
the majority will win
samples
! Give the network chances to correct its ! Improved the accuracy to >80%
mistakes
! Accuracy improved from 72.0% to 77.3%
Results Results
! Slate(cid:146)s Adaptive Classifiers (1990)--~80% ! Start small
! Weka(cid:146)sJ48 Decision Tree --87.75% ! Build a small network to solve a simple
! Weka(cid:146)sNaive network --64.23% problem. (no hidden unit, one output
! Weka(cid:146)sneural network (cid:150)no result after 10 class, trivial problem domain)
hours
Add more output classes
!
! My network (cid:150)up to 85%, alpha 0.60,
Add more hidden layers
momentum 0.58, hidden layer 1, 45 hidden !
units, >300,000 training examples
8
Results
! Hard to create a generic neural network Thank You!
Need to adjust the network topology,
!
learning rates, momentum, etc
Once you have a working network, it
!
will perform very well
Basic Idea
(cid:127) Bayesian networks serve as compact
Random Sampling in Mixtures representations of data
(cid:127) The data is represented in terms of
of Bayes Nets
conditional distributions
(cid:127) Draw random samples from these
conditional distributions to generate data
Manish Goyal
which can then be used for a variety of
purposes
Base system Explanation of Base System
(cid:127) Random sampling has been applied to a (cid:127) The model for each
character consists of a
problem relating to recognition of single mixture of Bayes
characters nweetisg(hBtNin1g, …fa.cBtoNrns) with w1 w2 w3
(cid:127) The base system consists of a model for w1,….wn
each character (cid:127) Models have been trained
for each of the 99 BN1 BN2 BN3
supported characters
(cid:127) The training set consists
of approximately 200
samples of each
character
9
Explanation of Bayesian Nets
Method of sampling
within each model
(cid:127) For each handwritten character we extract (cid:127) First randomly select which Bayesian
64 features Network you will select. The bayesian
(cid:127) These features are a mixture of networks are selected with
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of these features is not important (cid:127) For this we need to traverse the graph in
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64 features, there are 64 nodes in each (cid:127) Each node is specified in terms of its
Bayesian Network conditional mean and covariance given by
(cid:127) Ecpaoacnrhed ninttioso dnoeaf lti shd eirse tnrpiorbedusetei)onnt.e ide .i nP t(e nrmodse o/af ltlh the e (cid:127)(cid:127) CAMso evyaaonrui=a tMnrac=veµe=crC+s∑=e ptσ(hXcep -gµrpa)ph, generate the 1 3 4
observation for the particular node by
sampling from a Gaussian distribution with 2
Mean=M and Covariance=C
(cid:127) Once the observations of all the parents are 5
known, the conditional mean can be
……. …. (cid:127) Dcooob msthepirsuv tafeotidro anfol lcr t ahthnea bnt eon domedased aen fdo rh tehnact en oadne 6 7
(cid:127) Iterate through this generating as many
samples as are required.
Verification Results
(cid:127) Use the generated data to train a feed (cid:127) Original training set Error on test set
contains approx 200
forward neural network (fully connected,1
samples per code point
hidden layer)
(cid:127) Generated 200 and 500 NN trained used 20.32 %
(cid:127) Compare the error rate using the samples for each code original data
point using the random
generated data to a net trained using
sampling method NN trained 24.30 %
original data using generated
(cid:127) Test set used consists of
data(200
(cid:127) See if these two error rates are 17000 samples samp/code pt)
comparable NN trained 23.97 %
using generated
data(500
samp/code pt)
Results contd. Pipe dream
(cid:127) Twhhee pnr ewveio wuse rree ssualmtsp wlinegre f raolml a Error on test set (cid:127) Rather than using the S
distribution with mean=M and generated data
(cid:127) Wcoev caarina ninccer=eCase or decrease NN trained 24.30 % separately, could we BN NN
tgchoeevn aerarrianatdneocdme d ngaeivtsaes nb o ybf uyt hshien* Cg aw here using h=1 uthsee oitr itgoi nsaulp tpraleinminegn t G G+S
h is a heuristic
(cid:127) Dtrifafeinreedn tf onre dtsif fheareven tb veaelune s of NusNin tgra hin=e0d.1 41.96 % dmaatnan ?e rIf wuislle wd ein b teh is Error on test set
the heuristic factor NN trained using 20.32 %
(cid:127) As can be seen h=1 gives the able to improve the original data
beexpset cretesdu ltth (eaosr wetoicualdll yb).e NusNin tgra hin=e2d 24.45 % base accuracy of the NgeNn etrraaitneedd s uasminpgle 2s0 0 20.8 %
(cid:127) Spaominpt=le2s0 g0enerated per code neural network ? pdearta code pt +original
NN trained using 200 22.26 %
generated samples
per code pt +original
data
10