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

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Bayesian program The Bayesian program of the model is as follows: ⎧ V ariables Bayesian program ⎧⎪ ⎨⎪ ⎩ Description ⎧⎪ ⎨⎪ ⎩ Specification (π) ⎪⎨ A1:n, E1:n, T1:n, T A1:n, B1:n, B ′ 1:n, λB,1:n, T ′ 1:n, λT,1:n, E ′ 1:n, λE,1:n, ID ′ 1:n, λID,1:n, GD ′ 1:n, λGD,1:n, AD ′ 1:n, λAD,1:n, H1:n, GD1:n, AD1:n, ID1:n, HP, T T Decomposition P(A1:n, E1:n, T1:n, T A1:n, B1:n, B ′ 1:n, λB,1:n, T ′ 1:n, λT,1:n, E ′ 1:n, λE,1:n, ID ′ 1:n, λID,1:n, GD ′ 1:n, λGD,1:n, AD ′ 1:n, λAD,1:n, H1:n, GD1:n, AD1:n, ID1:n, HP, T T ) = � n i=1 [P(Ai)P(Ei, Ti, T Ai, Bi|Ai) P(λB,i|B1:n, B′ 1:n)P(B ′ 1:n)P(λT,i|T1:n, T ′ 1:n)P(T ′ 1:n) P(λE,i|E1:n, E ′ 1:n)P(E ′ 1:n)P(λID,i|ID1:n, ID ′ 1:n)P(ID ′ 1:n)P(λGD,i|GD1:n, GD ′ 1:n)P(GD ′ 1:n) P(λAD,i|AD1:n, AD ′ 1:n)P(AD ′ 1:n) P(ADi, GDi, IDi|Hi)P(Hi|HP )] P(HP |T T )P(T T ) F orms P(Ar) prior on attack in region i P(E, T, T A, B|A) covariance/probability table P(λX|X, X ′ ) = 1.0 iff X = X ′ , else P(λX|X, X ′ ) = 0.0 (Dirac) P(AD, GD, ID|H) covariance/probability table P(H|HP ) = Categorical(4, HP ) P(HP = hp|T T ) = 1.0 iff T T → hp, else P(HP |T T ) = 0.0 ⎪⎩ P(T T ) comes from a strategic model Identification (using δ) P(Ar = true) = n battles n battles+n not battles = µ battles/game µ regions/map (probability to attack a region) it could be learned online (preference of the opponent) : P(Ar = true) = 1+nbattles(r) 2+ � i∈regions n (online for each game) battles(i) 1+nbattles(e,t,ta,b) |E|×|T |×|T A|×|B|+ � E,T,T A,B nbattles(E,T,T A,B) 1+nbattles(ad,gd,id,h) |AD|×|GD|×|ID|+ � AD,GD,ID nbattles(AD,GD,ID,h) 1+nbattles(h,hp) |H|+ � H nbattles(H,hp) P(E = e, T = t, T A = ta, B = b|A = T rue) = P(AD = ad, GD = gd, ID = id|H = h) = P(H = h|HP = hp) = Questions decision − making ∀i ∈ regionsP(Ai|tai, λB,i = 1, λT,i = 1, λE,i = 1) ∀i ∈ regionsP(Hi|tt, λID,i = 1, λGD,i = 1, λAD,i = 1) 200
Figure B.2: Top: StarCraft’s Lost Temple map (one of the most famous maps with Python). We can see features like cliffs, ramps, walls, waters and resources (minerals and gas). Bottom: output of BWTA* with the regions slicing. We can see regions with one or several chokes, but also isolated regions as gray is non walkable terrain (crossable by flying units only). 201
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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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• Obj i∈�1...n� ∈ {T rue,
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Identification Parameters and proba
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⎧⎪ Bayesian program ⎨ ⎧⎪
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36 units setup vs OAI. For Bayesian
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we learned, by optimizing the effic
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Probabilistic modality Finally, we
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• Type: prediction is problem of
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can possibly be in the future. In t
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6.3.2 Evaluating regions Partial ob
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Pylon Gate Core Range Gate Core Pyl
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events (detected by a heuristic, se
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• AD1:n ∈ {no, low, med, high}:
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The model is highly modular, and so
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attacked: P(ei�=r, ti�=r, tai
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Figure 6.7: P(A) for varying values
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Towards a baseline heuristic The me
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Figure 6.9 displays the mean P(A, H
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Finally, our approach is not exclus
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Chapter 7 Strategy Strategy without
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etween economy, technology and mili
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power to the player (it allows for
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7.4.2 Probabilistic labeling Instea
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• Variables: - X i∈�1...n�
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Figure 7.3: Protoss vs Terran distr
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7.5 Build tree prediction The work
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Questions The question that we will
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Table 7.4 shows the full results, t
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that this average “missed” (unp
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7.6 Openings 7.6.1 Bayesian model W
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Questions The question that we will
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Figure 7.12: Evolution of P(Opening
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Table 7.5: Prediction probabilities
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7.6.3 Possible uses We recall that
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• U t+1 ∈ ([0, 1] . . . [0, 1])
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Page 186 and 187: Damian Isla. Handling complexity in
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Page 190 and 191: Mark Riedl, Boyang Li, Hua Ai, and
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Page 197 and 198: Appendix B StarCraft AI B.1 Micro-m
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