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

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Notations Symbols ← assignment of value to the left hand operand ∼ the right operand is the distribution of the left operand (random variable) ∝ proportionality ≈ approximation # cardinal of a space or dimension of a variable ∩ intersection ∪ union ∧ and ∨ or M T M transposed � � integers interval Variables X and V ariable random variables (or logical propositions) x and value values #s = |s| cardinal of the set s #X = |X| shortcut for “cardinal of the set of the values of X” X1:n the set of n random variables X1 . . . Xn {x ∈ Ω|Q(x)} the set of elements from Ω which verify Q Probabilities P(X) = Distribution is equivalent to X ∼ Distribution P(x) = P(X = x) = P([X = x]) Probability (distribution) that X takes the value x P(X, Y ) = P(X ∧ Y ) Probability (distribution) of the conjunction of X and Y P(X|Y ) Probability (distribution) of X knowing Y Conventions ⎛ ⎞ X1 ⎜ P ⎝ . Xk ⎟ ⎠ = P(X) = N (µ, σ) ↔ P(X = x) = 1 (2π) k/2 exp(−1 1/2 |Σ| P(X) = Categorical 1 (K, p) ↔ P(X = i) = pi, such that 1 also sometimes called Multinomial or Histogram 8 2 (x − µ)T Σ −1 (x − µ)) K� pi = 1 i=1
Chapter 1 Introduction Every game of skill is susceptible of being played by an automaton. Charles Babbage 1.1 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Reading map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.1 Context 1.1.1 Motivations There is more to playing than entertainment, particularly, playing has been found to be a basis for motor and logical learning. Real-time video games require skill and deep reasoning, attributes respectively shared by music playing and by board games. On many aspects, high-level realtime strategy (RTS) players can be compared to piano players, who would write their partition depending on how they want to play a Chess match, simultaneously to their opponent. Research on video games rests in between research on real-world robotics and research on simulations or theoretical games. Indeed artificial intelligences (AI) evolve in a simulated world that is also populated with human-controlled agents and other AI agents on which we have no control. Moreover, the state space (set of states that are reachable by the players) is much bigger than in board games. For instance, the branching factor* in StarCraft is greater than 1.10 6 , compared to approximatively 35 in Chess and 360 in Go. Research on video games thus constitutes a great opportunity to bridge the gap between real-world robotics and simulations. Another strong motivation is that there are plenty of highly skilled human video game players, which provides inspiration and incentives to measure our artificial intelligences against them. For RTS* games, there are professional players, whose games are recorded. This provides datasets consisting in thousands human-hours of play, by humans who beat any existing AI, which enables machine learning. Clearly, there is something missing to classical AI approaches to be able to handle video games as efficiently as humans do. I believe that RTS AI is where Chess AI was in the early 70s: we have RTS AI world competitions but even the best entries cannot win against skilled human players. 9
Page 1: THÈSE Pour obtenir le grade de DOC
Page 4 and 5: Contents Contents 4 1 Introduction
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Page 10 and 11: Complexity, real-time constraints a
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Page 18 and 19: 3 2 1 1 Figure 2.1: A Tic-tac-toe b
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Page 24 and 25: 2.4.1 Monopoly In Monopoly, there i
Page 26 and 27: 2.4.3 Poker Poker 4 is a zero-sum (
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Page 41 and 42: Chapter 3 Bayesian modeling of mult
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Page 47 and 48: Indeed, when evaluating two models
Page 49 and 50: • energy/mana/stamina regenerator
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Page 55 and 56: and P(Ai = false|T = i) = 0.6. To m
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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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(tt) if it allows for building all
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7.7.2 Results We did not evaluate d
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forces scores PvP PvT PvZ TvT TvZ Z
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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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