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

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The model is highly modular, and some parts are more important than others. We can separate three main parts: P(E, T, T A, B|A), P(AD, GD, ID|H) and P(H|HP ). In prediction, P(E, T, T A, B|A) uses the inferred (uncertain) economic (E), tactical (T ) and belonging (B) scores of the opponent while knowing our own tactical position fully (T A). In decision-making, we know E, T, B (for us) and estimate T A. In our prediction benchmarks, P(AD, GD, ID|H) has the lesser impact on the results of the three main parts, either because the uncertainty from the attacker on AD, GD, ID is too high or because our heuristics are too simple, though it still contributes positively to the score. In decision-making, it allows for reinforcement learning to have tuple values for AD, GD, ID at which to switch attack types. In prediction, P(H|HP ) is used to take P(T T ) (coming from strategy prediction [Synnaeve and Bessière, 2011], chapter 7) into account and constraints H to what is possible. For the use of P(H|HP )P(HP |T T )P(T T ) in decision-making, see the results section (6.6) or the appendix B.2.1. Questions For a given region i, we can ask the probability to attack here, and the mean by which we should attack, P(Ai = ai|ei, ti, tai, bi) (6.5) = P(ei, ti, tai, bi|ai)P(ai) � Ai P(ei, ti, tai, bi|Ai)P(Ai) (6.6) ∝ P(ei, ti, tai, Bi|ai)P(ai) (6.7) P(Hi = hi|adi, gdi, idi) (6.8) ∝ � [P(adi, gdi, idi|hi)P(hi|HP )P(HP |T T )P(T T )] (6.9) T T,HP We always sum over estimated, inferred variables, while we know the one we observe fully. In prediction mode, we sum over T A, B, T T, HP ; in decision-making, we sum over E, T, B, AD, GD, ID (see appendix B.2.1). The complete question that we ask our model is P(A, H|F ullyObserved). The maximum of P(A, H) = P(A)×P(H) may not be the same as the maximum of P(A) or P(H) take separately. For instance think of a very important economic zone that is very well defended, it may be the maximum of P(A), but not once we take P(H) into account. Inversely, some regions are not defended against anything at all but present little or no interest. Our joint distribution 6.3 can be rewritten: P(Searched, F ullyObserved, Estimated), so we ask: ∝ P(A1:n, H1:n|F ullyObserved) (6.10) � P(A1:n, H1:n, Estimated, F ullyObserved) (6.11) Estimated The Bayesian program of the model is as follows: 104
⎧⎪ Bayesian program ⎨ ⎧⎪ Description ⎨ Specification (π) ⎧ V ariables A1:n, E1:n, T1:n, T A1:n, B1: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, H1:n, GD1:n, AD1:n, ID1:n, HP, T T ) = ⎪⎨ �n i=1 [P(Ai)P(Ei, Ti, T Ai, Bi|Ai) P(ADi, GDi, IDi|Hi)P(Hi|HP )] P(HP |T T )P(T T ) F orms P(Ai) prior on attack in region i P(E, T, T A, B|A) covariance/probability table 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(A = true) = P(AD = ad, GD = gd, ID = id|H = h) = ⎪⎩ P(H = h|HP = hp) = ∀i ∈ regionsP(Hi|adi, gdi, idi) ⎪⎩ P(A, H|F ullyObserved) nbattles nbattles+nnot battles = µ battles/game µ (probability to attack a region) regions/map it could be learned online (preference of the opponent) : P(Ai = true) = 1+nbattles(i) 2+ � j∈regions P(E = e, T = t, T A = ta, B = b|A = T rue) = Questions ∀i ∈ regionsP(Ai|ei, ti, tai) 6.6 Results on StarCraft nbattles(i) (online for each game ∀r) 1+nbattles(h,hp) |H|+ � H nbattles(H,hp) 6.6.1 Learning and posterior analysis 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) To measure fairly the prediction performance of such a model, we applied “leave-100-out” crossvalidation from our dataset: as we had many games (see Table 6.2), we set aside 100 games of each match-up for testing (with more than 1 battle per match: rather ≈ 15 battles/match) and train our model on the rest. We write match-ups XvY with X and Y the first letters of the factions involved (Protoss, Terran, Zerg). Note that mirror match-ups (PvP, TvT, ZvZ) have fewer games but twice as many attacks from a given faction (it is twice the same faction). Learning was performed as explained in section 6.5.1: for each battle in r we had one observation for: P(er, tr, tar, br|A = true), and #regions − 1 observations for the i regions which were not 105
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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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Page 55 and 56: and P(Ai = false|T = i) = 0.6. To m
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Page 76 and 77: U A E Figure 5.4: In both figures,
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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
Page 88 and 89: we learned, by optimizing the effic
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Page 96 and 97: 6.3.2 Evaluating regions Partial ob
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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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shows a brutal transition from the
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Chapter 8 BroodwarBotQ Dealing with
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8.1.2 Tactical goals The decision t
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• X t i∈�1...n� ∈ �r1 .
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3 2 player 1 1 6 4 resources 8 play
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the construction plan as our Produc
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Figure 8.5: Crops of screenshots of
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anking). We consider that this rati
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This is an extension of the work on
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• differences in situations: as t
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9.2.4 Inter-game Adaptation (Meta-g
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fog of war hiding of some of the fe
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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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