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Artistic Robots through Interactive Genetic Algorithm
with ELO rating system
Andy Goetz, Camille Huffman, Kevin Riedl, Mathias Sunardi and Marek
Perkowski
Department of Electrical Engineering, Portland State University
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Portland Portland Cyber Cyber
TheatreTheatre
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Making Making science out science out
of robot of robot theater?theater?
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How to make a science from How to make a science from robot theatre?robot theatre?
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We want to evaluate sound, shape, motion, color,etc.
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Behavior Generation and Verification
Interactive Genetic
Algorithm
Behavior Behavior expressioexpressio
nn
Behavior Behavior AutomatonAutomaton
Probabilistic Automaton
behavior Generator and verifier
robotrobot
Human Human evaluatorsevaluators
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Main Idea of this Main Idea of this paper paper
• A new approach to create fitness function for Interactive Genetic Algorithm in which (possibly) many humans evaluate robot motions via Internet page.
• Based on ELO rating system known from chess.
• The robots use:1. a genetic algorithm, 2. fuzzy logic, 3. probabilistic state machines, 4. a small set of functions for creating picture
components, 5. and a user interface which allows the Internet users to
rate individual sequences.
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Previous work on IEC systems
1. Human-based genetic algorithm.
2. Interactive evolution strategy,
3. Interactive genetic programming,
4. Interactive genetic algorithm.
Mostly for music composition and graphics
Usually weighted functions were used
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Ranking Systems in Sports
Rating systems for many sports award points in accordance with subjective evaluations of the 'greatness' of certain achievements.
For example, winning an important golf tournament an important golf tournament might be worth an arbitrarily chosen five times as many points as winning a lesser tournament.
A statisticalstatistical endeavor, by contrast, uses a model that relates the game results to underlying variables representing the ability of each player.
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Elo rating systemElo rating system
• The Elo rating system is a method for calculating the relative skill levels of players in two-player games such as chess.
• It is named after its creator Arpad Elo, a Hungarian-born American physics American physics professor.
• The Elo system was invented as an improved chess rating system, but today it is also used in many other games.
• It is also used as a rating system for multiplayer competition in a number of video games.
• It has been adapted to team sports including association football, American college football, basketball, and Major League Baseball.
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Previous Previous worksworks
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Pairwise Pairwise ComparisoCompariso
nn
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Pairwise Comparison
Method:Method:
Compare each two candidates (players) head-to-head.
Award each candidate one point for each head-to-head victory.
The candidate with the most points wins.
N(N-1)/2 comparisons.
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Pairwise Comparison - Example
Selection of best robot best robot facial expressionfacial expression:
4 candidates: {A,B,C,D} and 4 rankings of them
37 voters
5 trials (columns)
Table shows the rankings of the candidates (rows) and the number of voters (columns) that ranked the candidates that way
# of Voters
Rank 14 10 8 4 1
1st A C D B C
2nd B B C D D
3rd C D B C B
4th D A A A A
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Pairwise Comparison - Example
Compare candidates A & B:
14 voters ranked A higher than B
10+8+4+1=23 voters ranked B higher than A
So, B wins against A
# of Voters
Rank 14 10 8 4 1
1st A C D B C
2nd B B C D D
3rd C D B C B
4th D A A A A
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Pairwise Comparison - Example
Next, compare candidates A & C:
14 voters ranked A higher than C
10+8+4+1=23 voters ranked C higher than A
So, C wins against A
Continue for next pairs: A vs. D, B vs. C, B vs. D, C vs. D
Exclude:
permutations (e.g. C vs. A = A vs. C)
comparison with itself (e.g. A vs. A)
# of Voters
Rank 14 10 8 4 1
1st A C D B C
2nd B B C D D
3rd C D B C B
4th D A A A A
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Pairwise Comparison - Example
Record points:
wins=1, lose=0
# of Voters (total=37)
Rank 14 10 8 4 1
1st A C D B C
2nd B B C D D
3rd C D B C B
4th D A A A A
A B C D Wins over
Lost agains
tPoints
A 14 14 14
B 23 18 28
C 23 19 25
D 23 9 12
Cell values: number of voters Cell values: number of voters that ranked candidate (row) that ranked candidate (row)
over candidate (column)over candidate (column)
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Pairwise Comparison - Example
Record points:
wins=1, lose=0
# of Voters (total=37)
Rank 14 10 8 4 1
1st A C D B C
2nd B B C D D
3rd C D B C B
4th D A A A A
A B C D Wins over
Lost agains
tPoints
A 14 14 14 - B,C,D 0
B 23 18 28
C 23 19 25
D 23 9 12
Cell values: number of voters Cell values: number of voters that ranked candidate (row) that ranked candidate (row)
over candidate (column)over candidate (column)
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Pairwise Comparison - Example
Record points:
wins=1, lose=0
# of Voters (total=37)
Rank 14 10 8 4 1
1st A C D B C
2nd B B C D D
3rd C D B C B
4th D A A A A
A B C D Wins over
Lost agains
tPoints
A 14 14 14 - B,C,D 0
B 23 18 28 A,D C 2
C 23 19 25 A,B,D - 3
D 23 9 12 A B,C 1
Cell values: number of voters Cell values: number of voters that ranked candidate (row) that ranked candidate (row)
over candidate (column)over candidate (column)
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Pairwise Comparison - Example
Record points:
wins=1, lose=0
# of Voters (total=37)
Rank 14 10 8 4 1
1st A C D B C
2nd B B C D D
3rd C D B C B
4th D A A A A
A B C D Wins over
Lost agains
tPoints
A 14 14 14 - B,C,D 0
B 23 18 28 A,D C 2
C 23 19 25 A,B,D - 3
D 23 9 12 A B,C 1
Cell values: number of voters Cell values: number of voters that ranked candidate (row) that ranked candidate (row)
over candidate (column)over candidate (column)
C wins!C wins!
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Pairwise Comparison - Example
Record points:
wins=1, lose=0
# of Voters (total=37)
Rank 14 10 8 4 1
1st A C D B C
2nd B B C D D
3rd C D B C B
4th D A A A A
A B C D Wins over
Lost agains
tPoints
A - B C D - B,C,D 0
B - - C B A,D C 2
C - - - C A,B,D - 3
D - - - - A B,C 1
Another way to calculate the winner: use Another way to calculate the winner: use half the table triangle, mark the winner, half the table triangle, mark the winner,
and count the number of times the player and count the number of times the player appearsappears
C wins!C wins!
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Other possible scenario
A three-way tie:
Inconsistency:
A wins over B, B wins over C, C wins over A
A B C
A - A C
B - - B
C - - -
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ELO ELO Rating Rating SystemSystem
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Overview of ELO
A player’s skill is assumed to be a normal distribution:
True skill is around the mean
Elo System gives two things:
A players expected chance of winning
A method to update a player’s Elo Rating
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Basic Ideas of ELO• One cannot look at a sequencecannot look at a sequence of moves and say, "That
performance is 2039."
• Performance can only be inferred from wins, draws and losses.
• Therefore, if a player wins a game, he is assumed to have performed at a higher level than his opponent for that game.
• Conversely if he loses, he is assumed to have performed at a lower level.
• If the game is a draw, the two players are assumed to have performed at nearly the same level.
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A player’s ranking is updated based on its:
Expected value of winning (E)
Which depends on the ranking difference with the opponent
Outcome of the match (S for ‘score’)
1 = win
0 = lose
0.5 = draw
Scores and ranking of Scores and ranking of playersplayers
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Expected score (E)
Where:
EA, EB = expected score for player A and B, respectively
RA, RB = Rating of player A and B, respectively
Remember: 1=win, 0=lose, 0.5=draw
Expected scores in Elo Rating
http://en.chessbase.com/home/TabId/211/PostId/4007114
scorescore
ratingrating
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Characteristics of ELOA player with higher Elo ranking than his opponent has a higher expected value (i.e. chance of winning), and vice versa.
When both players have similar Elo rankings, the chance of having a draw having a draw is higher.
After the match, both players’ rankings are updated with the same amount, but:
the winner gains the rank (rating),
the loser loses the rank.
If a higher ranking player (‘stronger’) wins against a weaker player, the rank changes are smaller than when the weaker player wins against the higher ranking player.
Subjective value K
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Basic Assumptions of ELOElo's central assumption was that the chess performance of each player in each game is a normally distributed normally distributed random variable. random variable.
Although a player might perform significantly better or worse from one game to the next, ELO assumed that the mean value of the performances of any given player changes only slowly over time.
A further assumption is necessary, because chess performance in the above sense is still not measurable.
Our question: “Is ELO good for human evaluation of robot art (motion, behavior)?”
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How ELO WorksHow ELO WorksA player's expected score is his probability of probability of winning winning plus halfhalf his probability of drawing.
Thus an expected score of 0.75 could represent a 75% chance of winning, 25% chance of losing, and 0% chance of drawing.
On the other extreme it could represent a 50% chance of winning, 0% chance of losing, and 50% chance of drawing.
The probability of drawingprobability of drawing, as opposed to having a decisive result, is not specified in the Elo system.
Instead a draw is considered half a win and half a loss.
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How ELO Works
The relative difference in rating between two players determines an estimate for the expected score between them.
Both the average and the spread of ratings can be arbitrarily chosen.
Elo suggested scaling ratings so that a difference of 200 rating points in chess would mean that the stronger player has an expected score (which basically is an expected average score) of approximately 0.75,
The USCF initially aimed for an average club player to have a rating of 1500.
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Elo Rating - Elo Rating - ExampleExample
Suppose a Robot Boxing league:
The league has tens, hundreds, or more robots
Each robot has a ranking (higher number = higher rank)
A robot’s ranking is updated after each match
But it can also be done after multiple matches
A match is a one-vs-one battle
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Expected score (E)
Suppose:
Robot A rank: 1500
Robot B rank: 1320
Then:
EA = 1 / (1 + 10(1320 - 1500)/400) = 0.738
EB = 1 - 0.738 = 0.262
Elo Rating Example: scores for robots
Expected Expected to winto win
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Elo Rating Example: Adjusting ratings after
matchNext, the match is held.
After the match, the ratings of both robots will be adjusted by:
Where:
R’A = Robot A’s new rating
RA = Robot A’s old/current rating
K = some constant*, for practical reasons we choose K=24 in this example
S = Score/match result (1=win, 0=lose, 0.5=draw)
EA = Expected score
Similarly for robot B
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Elo Rating Example: Adjusting scores after one
matchSuppose the outcome of the match:
Robot A wins!
Robot B wins!
It’s a draw!
Robot A rank: 1500
Robot B rank: 1320
Remember before the match it was:
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Elo Rating Example: adjusting rankings after five
matchesSuppose rank update is done after 5 matches:
Robot A current rank: 1500
Opponent/matchOpponent rank
(RB)EA
Score/match outcome (1=win, 0=lose,
0.5=draw)
1 1320 0.738 1
2 1700 0.240 1
3 1480 0.529 0
4 1560 0.415 0.5
5 1800 0.151 0
Total 2.073 2.5
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About K in chessK is the rate of adjustments to one’s rating.
Example when Robot A wins (B loses):
Some Elo implementations adjust K based on some criteria. For example:
FIDE (World Chess Federation):
K = 30 for a player new to the rating list until s/he has completed events with a total of at least 30 games.
K = 15 as long as a player's rating remains under 2400.
K = 10 once a player's published rating has reached 2400, and s/he has also completed events with a total of at least 30 games. Thereafter it remains permanently at 10.
USCF (United States Chess Federation):USCF (United States Chess Federation):
Players below 2100 --> K-factor of 32 used
Players between 2100 and 2400 --> K-factor of 24 used
Players above 2400 --> K-factor of 16 used.
How about robot art?
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Picture Picture Drawing Drawing RobotsRobots
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Audience votes through a Webpage
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ELO for art (motion) scoring
Score of 194
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Score of 0
ELO for art (motion) scoring
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Physical Robot DERPY
Derpy with a sharpie marker
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Fuzzy/Probabilistic state Machine operates differently in dark and light
areas.
Image with dark and light areas.
Examples of fuzzy variables.
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Fuzzy and Fuzzy and Probabilistic Probabilistic
MachinesMachines
Simple probabilistic machine of Derpy
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“Robot art” on butcher paper located on a floor.
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Another piece of art from Derpy
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Now use Part 2 of slides
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Auxiliary Auxiliary SlidesSlides
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MicrosofMicrosoft t
TrueSkillTrueSkill
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Microsoft TrueSkillAddressing:
Subjective K value - instead, based on players’ skill
Ranking of multiple players (>2)
Can find “interesting” matches - balanced, where either player have comparable chance of winning the match.
Build “Leaderboards” (ranking of all players)
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Microsoft TrueSkillPlayer’s skill is modeled as normal distribution, with mean as the player’s “true skill” and standard deviation as uncertainties (about the player’s skill)
Player start with some “mean skill” and uncertainty values.
As player plays more games/matches, the mean skill gets adjusted, and the uncertainty (i.e. std. dev) decreases.
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Microsoft TrueSkill
Updating mean and standard deviation
ββ22 is unknown, which is unknown, which is the variance of the is the variance of the performance around performance around
the skill of each the skill of each player.player.
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Microsoft TrueSkill
v and w
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Microsoft TrueSkill
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Microsoft TrueSkill
Microsoft TrueSkill http://research.microsoft.com/en-us/projects/trueskill/Details.aspx#How_to_Update_Skills
unbalanced matches (can't win or can't lose) are not interesting
balanced matches are interesting (even chance of winning)
accommodates two or more players
a module to track skills of all players based on game outcomes between players (update)
TA module to arrange interesting matches for its members (Matchmaking)
module to recognize and potentially publish skills of members (leader boards)
Truskill is skill-based ranking system
so interesting matches can reliably arranged within a league
uses Bayesian inference for ranking
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Microsoft TrueSkill• The intuition is that the greater the difference between two player’s μ values
– assuming their σ value are similar – the greater the chance of the player with the higher μ value performing better in a game.
• This principle holds true in the TrueSkill ranking system. But, this does not mean that the players with the larger μ's are always expected to win, but rather that their chance of winning is higher than that of the players with the smaller μ's.
• The TrueSkill ranking system assumes that the performance in a single match is varying around the skill of the player, and that the game outcome (relative ranking of all players participating in a game) is determined by their performance.
• Thus, the skill of a player in the TrueSkill ranking system can be thought of as the average performance of the player over a large number of games.
• The variation of the performance around the skill is, in principle, a configurable parameter of the TrueSkill ranking system.
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Microsoft TrueSkill
mu and sigma are updated based on outcome of game (win/lose). score difference makes no impact.
1. assumes skill of each player may change slightly between current and previous game -> sigma is increased (a configurable parameter) "It is this parameter that both allows the TrueSkill system to track skill improvements of gamers over time and ensures that the skill uncertainty σ never decreases to zero ("maintaining momentum")."
2. determine the probability of game outcome for given skills of participating players, and weight by probability of corresponding skill beliefs. --> average over all possible performances (weighted by their probability - Bayes Law) and derive the game outcome from performances: player with highest performance is winner, second highest is first tuner up, and s on.
3. if player performance are very close, true skill considers the outcome to be draw. The larger the draw margin is defined in a league, the more likely a draw is to occur. The size of margin is configurable and adjusted by game mode.
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Measuring Measuring consistencconsistenc
yy
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Measuring consistency in
Pairwise ComparisonCan be done when comparison is done with “degree of importance”. E.g.:
1=equally important, 2=somewhat more important, 3=more important, 4=most important
Example:
Determining important criteria in buying a car
Price MPG Comfort Style
Price 3 2 2
MPG
Comfort 4
Style 4 2Values in cells are Values in cells are importance with importance with
respect to the row respect to the row itemitem
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Measuring consistency in
Pairwise ComparisonComplete the values in the matrix
Example:
Determining important criteria in buying a carPrice MPG Comfort Style
Price 1 3 2 2
MPG 1
Comfort 4 1
Style 4 2 1Criterion compared Criterion compared to itself is “equally to itself is “equally
important”important”
1=equally important, 2=somewhat more important, 3=more important, 4=most important
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Measuring consistency in
Pairwise ComparisonComplete the values in the matrix
Example:
Determining important criteria in buying a carPrice MPG Comfort Style
Price 1 3 2 2
MPG 1/3 1 1/4 1/4
Comfort 1/2 4 1 1/2
Style 1/2 4 2 1
1=equally important, 2=somewhat more important, 3=more important, 4=most important
Importance of less important criterion is reciprocal of the importance of the more important Importance of less important criterion is reciprocal of the importance of the more important criterioncriterion
e.g.: Price vs. Style => Style is two times more imporant than Price (2). So, Price is one half e.g.: Price vs. Style => Style is two times more imporant than Price (2). So, Price is one half as imporant than Style (1/2)as imporant than Style (1/2)
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Measuring consistency in
Pairwise ComparisonExample:
Determining important criteria in buying a car
Calculate weights of each criterion:
Price MPG Comfort Style
Price 1 3 2 2
MPG 1/3 1 1/4 1/4
Comfort 1/2 4 1 1/2
Style 1/2 4 2 1
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Evaluation Criteria for Ranking Methods
The Method of Pairwise Comparisons satisfies the Majority Criterion. (A majority candidate will win every pairwise comparison.)
The Method of Pairwise Comparisons satisfies the Condorcet Criterion. (A Condorcet candidate will win every pairwise comparison -- that's what a Condorcet candidate is!)
The Method of Pairwise Comparisons satisfies the Public-Enemy Criterion. (If there is a public enemy, s/he will lose every pairwise comparison.)
The Method of Pairwise Comparisons satisfies the Monotonicity Criterion. (Ranking Candidate X higher can only help X in pairwise comparisons.)
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ELOELO
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Agenda on ELO
Overview
How it works
Details
Mathematical details
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How it Works
Elo formulas
Expected value
Score
How to update the rank