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

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B.2 Tactics 0,1 Obj [0..3] Dmg [0..2] A 0,1 Dir Figure B.1: Plate diagram of a Bayesian unit with N possible directions. frame player name player id order/action X pos. Y pos. unit . . . . . . . 6650 L.Nazgul[pG] 0 Train Probe 6720 SaFT.eSu 1 Train Probe 6830 L.Nazgul[pG] 0 Train Probe 7000 SaFT.eSu 1 Train Probe 7150 L.Nazgul[pG] 0 Build 39 108 Forge 7245 L.Nazgul[pG] 0 Build 36 108 Citadel of Adun 7340 L.Nazgul[pG] 0 Train Probe 7405 SaFT.eSu 1 Train Probe 7415 L.Nazgul[pG] 0 Train Probe 7480 SaFT.eSu 1 Train Shuttle 7510 SaFT.eSu 1 Build 26 24 Robotics Support Bay . . . . Table B.1: Example of what is in a replay (in human readable format), lines with non-empty positions are constructions of buildings. Several other action types are not represented (current selection, move/attack orders...) B.2.1 Decision-making: soft evidences and coherence variables Here we will present the full tactical model for decision making, with soft evidences of variables we know only partially (variables we have only the distribution). Variables In the tactical model (section 6.5), for some variables, we take uncertainty into account with “soft evidences”: for instance for a region in which no player has a base, we have a soft evidence that it belongs more probably to the player established closer. In this case, for a given region, we introduce the soft evidence variable(s) B ′ and the coherence variable λB and impose P(λB = [0..2] . E [0..2] Occ . N .
1|B, B ′ ) = 1.0 iff B = B ′ , else P(λB = 1|B, B ′ ) = 0.0; while P(λB|B, B ′ )P(B ′ ) is a new factor in the joint distribution. This allows to sum over P(B ′ ) distribution (soft evidence). We do that for all the variables which will not be directly observed in decision-making. Decomposition The joint distribution of our model contains soft evidence variables for all input family variables (E, T, B, GD, AD, ID) as we cannot know for sure the economical values of the opponent’s regions under the fog of war* (E), nor can we know exactly the tactical value (T ) for them, nor the possession of the regions (B), nor the exact defensive scores (GD, AD, ID). Under this form, it deals with all possible uncertainty (from incomplete information) that may come up in a game. For the n considered regions, we have: Forms = P(A1:n, E1:n, T1:n, T A1:n, B1:n, B ′ 1:n, λB,1:n, T ′ 1:n, λT,1:n, (B.1) E ′ 1:n, λE,1:n, ID ′ 1:n, λID,1:n, GD ′ 1:n, λGD,1:n, AD ′ 1:n, λAD,1:n, (B.2) H1:n, GD1:n, AD1:n, ID1:n, HP, T T ) (B.3) n� [P(Ai)P(Ei, Ti, T Ai, Bi|Ai) (B.4) i=1 P(λB,i|B1:n, B ′ 1:n)P(B ′ 1:n)P(λT,i|T1:n, T ′ 1:n)P(T ′ 1:n) (B.5) P(λE,i|E1:n, E ′ 1:n)P(E ′ 1:n)P(λID,i|ID1:n, ID ′ 1:n)P(ID ′ 1:n) (B.6) P(λGD,i|GD1:n, GD ′ 1:n)P(GD ′ 1:n)P(λAD,i|AD1:n, AD ′ 1:n)P(AD ′ 1:n) (B.7) P(ADi, GDi, IDi|Hi)P(Hi|HP )] P(HP |T T )P(T T ) (B.8) The full plate diagram of this model is shown in Figure B.6. To the previous forms (section 6.5.1), we add for all variables which were doubles (X with X ′ ): ⎧ ⎨ Identification P(λX|X, X ′ ) = 1.0 iff X = X ′ ⎩P(λX|X, X ′ ) = 0.0 else The identification and learning does not change, c.f. section 6.5.1. Questions ∝ ∝ ∀i ∈ regions P(Ai|tai, λB,i = 1, λT,i = 1, λE,i = 1) � � � B i,B ′ i T i,T ′ i E i,E ′ i P(Ei, Ti, tai, Bi|Ai)P(Ai)P(B ′ i)P(T ′ i )P(E ′ i) ∀i ∈ regions P(Hi|tt, λID,i = 1, λGD,i = 1, λAD,i = 1) � � � � ID i,ID ′ i GD i,GD ′ i ADi,AD ′ i HP P(ADi, GDi, IDi|Hi)P(Hi|HP )P(HP |tt)P(ID ′ i)P(AD ′ i)P(GD ′ i) 199
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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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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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Page 180 and 181: RTS Real-Time Strategy games are (m
Page 182 and 183: Sander C. J. Bakkes, Pieter H. M. S
Page 184 and 185: Julien Diard, Pierre Bessière, and
Page 186 and 187: Damian Isla. Handling complexity in
Page 188 and 189: Kinshuk Mishra, Santiago Ontañón,
Page 190 and 191: Mark Riedl, Boyang Li, Hua Ai, and
Page 192 and 193: Adrien Treuille, Seth Cooper, and Z
Page 194 and 195: • 0 (not at all, or irrelevant)
Page 197: Appendix B StarCraft AI B.1 Micro-m
Page 201 and 202: Figure B.2: Top: StarCraft’s Lost
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