Observational Learning of Rules of GamesIntroduction Visual System Knowledge Transfer System Rule...
Transcript of Observational Learning of Rules of GamesIntroduction Visual System Knowledge Transfer System Rule...
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Observational Learning of Rules of Games
Debidatta DwibediY9227188
Advisors: Prof. Amitabha Mukerjee, Prof. K S Venkatesh
Dept. of Electrical EngineeringIIT Kanpur
June 2, 2014
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Games and AIProblem StatementRelated WorkProposed Approach
Games and AI
Easy to model
discretedeterministicfully observable
Computers have defeated the best players in many games
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Games and AIProblem StatementRelated WorkProposed Approach
A General Game Playing System
An AI program which plays more than one game successfully
Devise strategies to win for multiple games
Rules need to be provided in Game Description Language(GDL)
Game states as a series of factsGame mechanics as logical rules
Game learning system identifies states and discovers the rules
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Games and AIProblem StatementRelated WorkProposed Approach
Problem Statement
Given a video of people playing a game, learn its rules.
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Games and AIProblem StatementRelated WorkProposed Approach
Autonomous Game Learning
Barbu et al.[2] learnt rules of Hexapawn and Tic-Tac-ToeFitted a 3 × 3 grid and use HSV values calculated at the timeof calbration to decide game statesUse Inductive Logic Programming to learn rulesLots of background knowledge like frame axioms, linearity test
Figure: Setup of Game-playing robot(Barbu et al.)
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Games and AIProblem StatementRelated WorkProposed Approach
Autonomous Game Learning
Kaiser[6] learnt rules of two-player, grid-based games likeTic-Tac-Toe, Connect4
Canny edge detector and Hough transform to fit grid anddecide occupied by X or O or unoccupiedDescriptive complexity to learn rules
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Games and AIProblem StatementRelated WorkProposed Approach
Autonomous Game Learning
Bjornsson [3] learns rules of simplified board gamesMovement pattens of pieces by looking at change incoordinatesPrefix tree automata(PTA) from observation converted tominimum state deterministic finite automata(DFA).
Figure: Example of a Rule in DFA for a piece that only moves forward
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Games and AIProblem StatementRelated WorkProposed Approach
Objective
Objective
Use RGBD images to minimize game-specific backgroundknowledge to an ILP to learn rules of games
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Games and AIProblem StatementRelated WorkProposed Approach
Proposed Approach
Figure: Pipeline of Proposed Algorithm
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Point Clouds
Collection of points in 3DRGB from a normal cameraDepth from infrared laser
Figure: A sample point cloud from http://pointclouds.org
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Game Piece Segmentation
Figure: Extract all game pieces as separate clusters.
Difficult to segment from images
Separated in space in point clouds
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Euclidean Clustering of Game Pieces
Cluster points that are close to each other in 3D space
Model free detection of game pieces
We assume that game pieces have either perceptually differentcolours or are separated in space
Remove hand using HSV filter
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Segmentation Results
Figure: 4 game pieces in 1D Peg Solitaire
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Segmentation Results
Figure: 4 game pieces in Animated Towers of Hanoi
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Segmentation Results
Figure: 4 game pieces in Real Towers of Hanoi
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Problems in Multi-object Tracking
Can’t track by detection
Occlusion by hand and other objects
Centroid tracking might fail if more than one object is movingsimultaneously and their paths cross
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Multi-object Tracking = Assignment Problem
Multi-object tracking problem is equivalent to assignment oflabels from one frame to the next
Figure: The Assignment Problem. Taken fromhttp://www.frc.ri.cmu.edu/ lantao/
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Octree Overlap
Figure: Overlap between an object in one frame and the same object inthe next frame.
Use octree overlap between same object in consecutive framesas a metric in he assignment problem
Maximize sum of overlaps during assignment
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Multi-object Tracking Results
Figure: Tracking game pieces in Real Towers of Hanoi
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Semantic Graphs to Represent Scenes
Graph to represent scene(Aksoy et al.)[1](Yang et al.)[7]
Objects as nodes
Relationship between each other as edges
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Semantic Graphs to Represent Scenes
Figure: Semantic Event Chain from Aksoy et al.[1]
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Semantic Graphs of Game Scenes
Figure: B - Board, 1 - Yellow, 2 - Red, 3 - Green, 4 - Blue
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Unsupervised Discovery of Game States
Figure: B - Board, 1 - Yellow, 2 - Red, 3 - Green, 4 - Blue
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Discover Valid Locations for Game Pieces
SVD on positions of game pieces during game states
Significant number of eigen vectors gives number ofdimensions game is being played in
Transform from the camera to the board
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Discover Valid Locations for Game Pieces
Figure: Clusters in positions in 1D Peg Solitaire
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Discover Valid Locations for Game Pieces
Figure: Clusters in positions in Real Towers of Hanoi
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Discover Valid Locations
Do k-Means by varying k
Look for elbow in Sum Squared Error graph
Figure: SSE v/s k for 1D Peg Solitaire
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Discover Valid Locations
Do k-Means by varying k
Look for elbow in Sum Squared Error graph
Figure: SSE v/s k for Real Towers of Hanoi
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Respresenting Game States
Figure: Game State:[{a},{b},{},{d},{e}]
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Point CloudsSegmentationTrackingSemantic GraphsRepresenting Game States
Representing Game States
Figure: Game State:[{c},{b},{a,d}]
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Inductive Logic ProgrammingFrom Semantic Graphs to Logical ClausesAttribute based ClausesRelationship based ClausesMove based Clauses
Inductive Reasoning
Induce general rules by finding patterns from detailed facts
Rules might not be always true but explain the observations
Towers of Hanoi example:
Smaller piece is always being kept on bigger
Learning rules of games can also be modeled using inductionreasoning
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Inductive Logic ProgrammingFrom Semantic Graphs to Logical ClausesAttribute based ClausesRelationship based ClausesMove based Clauses
Inductive Logic Programming(ILP)
A logic program that comes up with hypotheses given:
background knowledgepositive examplenegative example
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Inductive Logic ProgrammingFrom Semantic Graphs to Logical ClausesAttribute based ClausesRelationship based ClausesMove based Clauses
Inductive Logic Programming(ILP)
Figure: Slide from http://www-ai.ijs.si/SasoDzeroski/
daughter(X,Y) :- female(X), parent(Y,X)
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Inductive Logic ProgrammingFrom Semantic Graphs to Logical ClausesAttribute based ClausesRelationship based ClausesMove based Clauses
From Semantic Graphs to Logical Clauses
Rule learning system takes input in form of logical clauses
Three kinds of clauses:
Attributes of game piecesRelationship between game piecesMovement of game pieces
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Inductive Logic ProgrammingFrom Semantic Graphs to Logical ClausesAttribute based ClausesRelationship based ClausesMove based Clauses
From Semantic Graphs to Logical Clauses
Rule learning system takes input in form of logical clauses
Three kinds of clauses:
Attributes of game pieces - from visual classifiersRelationship between game pieces - from visual classifiersMovement of game pieces - from game state changes
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Inductive Logic ProgrammingFrom Semantic Graphs to Logical ClausesAttribute based ClausesRelationship based ClausesMove based Clauses
Attribute based Clauses
colour(a,orange).
colour(d,green).
size(a,10).
size(d,2).
Working on shape classifiers for game pieces
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Inductive Logic ProgrammingFrom Semantic Graphs to Logical ClausesAttribute based ClausesRelationship based ClausesMove based Clauses
Relationship based Clauses
Relationship between objects in Semantic Graph converted tological clauses
contact(a,d). contact(d,a).
on(d,a).
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Inductive Logic ProgrammingFrom Semantic Graphs to Logical ClausesAttribute based ClausesRelationship based ClausesMove based Clauses
Move based Clauses
Move from one valid location to another
move(d,l1,l2).
Piece d moves from location l1 to l2
Effect of move on the location clusters
fromto(d,[a,d],[c,d]).
Piece d moves from the cluster whose previous state was{a,d} and the cluster where it moved is {c,d} after the move.
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Background KnowledgePositive examples1D Peg SolitaireTowers of HanoiMore Complex Games
Meta-clause/Rule Generator
Logical system should be able to compare numerical featureslike size or height
Meta-clause generator creates comparators for any numericalfeature
greatersize(A,B) :- piece(A),piece(B),
size(A,NA),size(B,NB),
NA>NB.
greaterheight(A,B) :- piece(A),piece(B),
height(A,NA),height(B,NB),
NA>NB.
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Background KnowledgePositive examples1D Peg SolitaireTowers of HanoiMore Complex Games
Background Knowledge
Attribute based clauses
Meta-clause generated rules
Rules built in system:
diff - difference between two locationsabsdiff - absolute difference between two locationstop - top element of a stackbottom - bottom element of a stack
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Background KnowledgePositive examples1D Peg SolitaireTowers of HanoiMore Complex Games
Positive examples
Relationship based clauses
Move based rules
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Background KnowledgePositive examples1D Peg SolitaireTowers of HanoiMore Complex Games
1D Peg Solitaire
Figure: Start State
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Background KnowledgePositive examples1D Peg SolitaireTowers of HanoiMore Complex Games
1D Peg Solitaire
Figure: End State
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Background KnowledgePositive examples1D Peg SolitaireTowers of HanoiMore Complex Games
Rules of 1D Peg Solitaire
Red pegs can take one step or two steps to the right into anempty hole.
Blue pegs can take one step or two steps to the left into anempty hole.
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Background KnowledgePositive examples1D Peg SolitaireTowers of HanoiMore Complex Games
Clauses Generated
piece(p1).
piece(p2).
piece(p3).
piece(p4).
color(p1,red).
color(p2,red).
colour(p3,blue).
color(p4,blue).
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Background KnowledgePositive examples1D Peg SolitaireTowers of HanoiMore Complex Games
Clauses Generated
move(p3,l4,l3).
fromto(p3,[p3],[p3]).
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Background KnowledgePositive examples1D Peg SolitaireTowers of HanoiMore Complex Games
Rules Learnt
move(A,B,C) means piece A moves from B to C
move(A,B,C) :- diff(B,C,-2), color(A,blue).
move(A,B,C) :- diff(B,C,-1), color(A,blue).
move(A,B,C) :- diff(B,C,1), color(A,red).
move(A,B,C) :- diff(B,C,2), color(A,red).
fromto(A,[A],[A]).
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IntroductionVisual System
Knowledge Transfer SystemRule Learning System
Conclusion and Future Work
Background KnowledgePositive examples1D Peg SolitaireTowers of HanoiMore Complex Games
Towers of Hanoi
Figure: Start State
Figure: End State
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Background KnowledgePositive examples1D Peg SolitaireTowers of HanoiMore Complex Games
Rules of Towers of Hanoi
Only one disk can be moved at a time.
Each move consists of taking the upper disk from one of thestacks and placing it on top of another stack
No disk may be placed on top of a smaller disk.
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Clauses Generated
move(d,l2,l3).
fromto(d,[d],[c,d]).50 / 60
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Background KnowledgePositive examples1D Peg SolitaireTowers of HanoiMore Complex Games
Rules Learnt
on(A,B) :- greatersize(B,A).
fromto(A,B,C) :- top(A,B), top(A,C).
fromto(A,B,C) means piece A moves from the stack B to thestack C
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Background KnowledgePositive examples1D Peg SolitaireTowers of HanoiMore Complex Games
More Complex Games
Modified Towers of Hanoi
on(A,B) :- colour(B,red),colour(A,green),
greatersize(B,A).
Chess with hundreds of manually written clauses
move(bishop,pos(A,B),pos(C,D)) :- xdiff(B,D,E),
ydiff(A,C,E).
move(knight,pos(A,B),pos(C,D)) :- xdiff(B,D,1),
ydiff(A,C,2).
move(knight,pos(A,B),pos(C,D)) :- xdiff(B,D,2),
ydiff(A,C,1).
ILP is powerful in inducing rules of games if the clausesencode the rule being followed
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Conclusion
Successfully learnt rules of two games with very different rules
Semantic Graphs from point clouds
Unsupervised discovery of game clusters and representation ofgame states
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ConclusionFuture Work
Future Work
Convert rules, start and end states to GDL to play games
3d spatial puzzles and assembly
Ground natural language descriptions in semantic graphs
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ConclusionFuture Work
References I
Eren Erdal Aksoy, Alexey Abramov, Johannes Dorr, Kejun Ning, BabetteDellen, and Florentin Worgotter.
Learning the semantics of object–action relations by observation.
The International Journal of Robotics Research, 30(10):1229–1249, 2011.
Andrei Barbu, Siddharth Narayanaswamy, and Jeffrey Mark Siskind.
Learning physically-instantiated game play through visual observation.
In Robotics and Automation (ICRA), 2010 IEEE International Conferenceon, pages 1879–1886. IEEE, 2010.
Yngvi Bjornsson.
Learning rules of simplified boardgames by observing.
In ECAI, pages 175–180, 2012.
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ConclusionFuture Work
References II
Neil Dantam, Irfan Essa, and Mike Stilman.
Linguistic transfer of human assembly tasks to robots.
In Intelligent Robots and Systems (IROS), 2012 IEEE/RSJ InternationalConference on, pages 237–242. IEEE, 2012.
Shyamanta M Hazarika and Alexy Bhowmick.
Learning rules of a card game from video.
Artificial Intelligence Review, 38(1):55–65, 2012.
Lukasz Kaiser.
Learning games from videos guided by descriptive complexity.
In Twenty-Sixth AAAI Conference on Artificial Intelligence, 2012.
Yezhou Yang, Cornelia Fermuller, and Yiannis Aloimonos.
Detection of manipulation action consequences (mac).
In CVPR 2013, 2013.
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Thank You
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How good are computers at playing games?
Chinook beat Grandmaster Don Lafferty in Checkers (1995)
Deep Blue defeated Kasparov in Chess (1997)
Quackle beat Scrabble world champion David Boys (2010)
MoGoTW defeated Go player Catalin Taranu (2010)
Watson defeat previous winners on Jeopardy! (2011)
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Octree
Figure: Octree from http://wikipedia.org
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Autonomous Game Learning
Hazarika and Bhowmick[5] learn rules of card games fromvideos
Visual features to classify cardsDecision trees to learn rules
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