Bayesian Programming and Learning for Multi-Player Video Games ...

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V T 0,1 BT O N Figure 7.7: Graphical model (plate notation) of the build tree Bayesian model, gray variables are known. Forms • P(BT ) is the prior distribution on the build trees. As we do not want to include any bias, we set it to the uniform distribution. • P(O1:N) is unspecified, we put the uniform distribution (we could use a prior over the most frequent observations). • P(λ|BT, O1:N) is a functional Dirac that restricts BT values to the ones than can co-exist with the observations: ⎧ ⎨P(λ = 1|bt, o1:N) = 1 if bt can exist with o1:N ⎩P(λ = 1|bt, o1:N) = 0 else A build tree value (bt) is compatible with the observations if it covers them fully. For instance, BT = {pylon, gate, core} is compatible with ocore = 1 but it is not compatible with oforge = 1. In other words, buildT ree is incompatible with o1:N iff {o1:N\{o1:N ∧ buildT ree}} �= ∅. • P(T |BT = bt) = N (µbt, σ2 bt ): P(T |BT ) are discrete normal distributions (“bell shapes”). There is one bell shape over T per bt. The parameters of these discrete Gaussian distributions are learned from the replays. Identification (learning) As we have full observations in the training phase, learning is just counting and averaging. The learning of the P(T |BT ) bell shapes parameters takes into account the uncertainty of the bt for which we have few observations: the normal distribution P(T |bt) begins with a high σ2 bt , and not a strong peak at µbt on the seen T value and sigma = 0. This accounts for the fact that the first(s) observation(s) may be outlier(s). This learning process is independent on the order of the stream of examples, seeing point A and then B or B and then A in the learning phase produces the same result. 130 0,1 λ
Questions The question that we will ask in all the benchmarks is: P(BT |T = t, O1:N = o1:N, λ = 1) ∝ P(t|BT )P(BT )P(λ|BT, o1:N) N� P(oi) (7.2) An example of the evolution of this question with new observations is depicted in Figure 7.8, in which we can see that build trees (possibly closely related) succeed each others (normal) until convergence. Bayesian program The full Bayesian program is: ⎧ V ariables ⎧⎪ Bayesian program ⎨ ⎧⎪ Description ⎨ Specification (π) ⎪⎩ T, BT, O1 . . . ON, λ Decomposition ⎪⎨ P(T, BT, O1 . . . ON, λ) = JD = P(λ|BT, O �1...N�)P(T |BT ) � N i=1 P(Oi)P(BT ) F orms P(λ|BT, O�1...N�) = functional Dirac (coherence) ⎪⎩ P(T |BT = bt) = discrete N (µbt, σ 2 bt ) Identification P(BT = bt|Opt = op) = 1+count(bt,op) |BT |+count(op) (µbt, σbt) = arg max µ,σ P(T |BT = bt; µ, σ2 ) Question ⎪⎩ P(BT |T = t, O1:N = o1:N, λ = 1) ∝ P(t|BT )P(BT )P(λ|BT, o1:N) �N i=1 P(oi) 7.5.2 Results All the results presented in this section represents the nine match-ups (races combinations) in 1 versus 1 (duel) of StarCraft. We worked with a dataset of 8806 replays (≈ 1000 per match-up) of skilled human players (see 7.1) and we performed cross-validation with 9/10th of the dataset used for learning and the remaining 1/10th of the dataset used for evaluation. Performance wise, the learning part (with ≈ 1000 replays) takes around 0.1 second on a 2.8 Ghz Core 2 Duo CPU (and it is serializable). Each inference (question) step takes around 0.01 second. The memory footprint is around 3Mb on a 64 bits machine. Metrics k is the numbers of buildings ahead that we can accurately predict the build tree of the opponent at a fixed d. d values are distances between the predicted build tree(s) and the reality (at fixed k). 131 i=1
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THÈSE Pour obtenir le grade de DOC
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Contents Contents 4 1 Introduction
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5.4.1 Bayesian unit . . . . . . . .
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Notations Symbols ← assignment of
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Complexity, real-time constraints a
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intuition of Bayesian modeling to r
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e played by humans, by opposition t
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As a first approach, programmers ca
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3 2 1 1 Figure 2.1: A Tic-tac-toe b
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Algorithm 2 Alpha-beta algorithm fu
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ewards on all the runs through node
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2.4.1 Monopoly In Monopoly, there i
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2.4.3 Poker Poker 4 is a zero-sum (
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2.5.2 State of the art FPS AI consi
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2.6.2 State of the art Methods used
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are no generic and efficient approa
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Strategy Tactics Action Strategic d
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2.8.4 Time constant(s) For novice t
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effects. In RTS games, there is a l
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Chapter 3 Bayesian modeling of mult
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programmer-specified states, the (m
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which derives the laws of probabili
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Indeed, when evaluating two models
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• energy/mana/stamina regenerator
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• The probability that the ith un
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3.3.4 Example This model has been a
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and P(Ai = false|T = i) = 0.6. To m
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Chapter 4 RTS AI: StarCraft: Broodw
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eplay is shown in appendix in Table
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Supply/Max supply Build Note (popul
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Figure 4.3: Military moves from a S
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Technology Strategy Army How? Econo
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• Robotic player (bot): chapter 8
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• Complexity: pspace-complete [Pa
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educing the complexity (no communic
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(grid-based) pathfinding was recent
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U A E Figure 5.4: In both figures,
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Fire Reload Figure 5.6: Fight FSM o
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Page 82 and 83: Identification Parameters and proba
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Page 86 and 87: 36 units setup vs OAI. For Bayesian
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Page 90 and 91: Probabilistic modality Finally, we
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Page 96 and 97: 6.3.2 Evaluating regions Partial ob
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Page 108 and 109: Figure 6.7: P(A) for varying values
Page 110 and 111: Towards a baseline heuristic The me
Page 112 and 113: Figure 6.9 displays the mean P(A, H
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Page 117 and 118: Chapter 7 Strategy Strategy without
Page 119 and 120: etween economy, technology and mili
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Page 123 and 124: 7.4.2 Probabilistic labeling Instea
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Page 129: 7.5 Build tree prediction The work
Page 133 and 134: Table 7.4 shows the full results, t
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Page 137 and 138: 7.6 Openings 7.6.1 Bayesian model W
Page 139 and 140: Questions The question that we will
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Page 145 and 146: 7.6.3 Possible uses We recall that
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Page 149 and 150: (tt) if it allows for building all
Page 151 and 152: 7.7.2 Results We did not evaluate d
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Page 157 and 158: Chapter 8 BroodwarBotQ Dealing with
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Page 163 and 164: 3 2 player 1 1 6 4 resources 8 play
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RTS Real-Time Strategy games are (m
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Sander C. J. Bakkes, Pieter H. M. S
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Julien Diard, Pierre Bessière, and
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Damian Isla. Handling complexity in
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Kinshuk Mishra, Santiago Ontañón,
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Mark Riedl, Boyang Li, Hua Ai, and
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Adrien Treuille, Seth Cooper, and Z
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• 0 (not at all, or irrelevant)
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Appendix B StarCraft AI B.1 Micro-m
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1|B, B ′ ) = 1.0 iff B = B ′ ,
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Figure B.2: Top: StarCraft’s Lost
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0,1 B' [0..5] T [0..2] E' 0,1 λ B
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C C A A C C A A 4 B B 4 3 4 B B 4 3
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