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

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• Obj i∈�1...n� ∈ {T rue, F alse}: adequacy of direction i with the objective (given by a higher rank model). In our StarCraft AI, we use the scalar product between the direction i and the objective vector (output of the pathfinding) with a minimum value (0.3 in move mode for instance) so that the probability to go in a given direction is proportional to its alignment with the objective. – For flee(), the objective is set in the direction which flees the potential damage gradient (corresponding to the unit type: ground or air). – For fightMove(), the objective is set (by the units group) either to retreat, to fight freely or to march aggressively towards the goal (see 5.3.3). – For the scout behavior, the objective (�o) is set to the next pathfinder waypoint. • Dmg i∈�1...n� ∈ {no, low, medium, high}: potential damage value in direction i, relative to the unit base health points, in direction i. In our StarCraft AI, this is directly drawn from two constantly updated potential damage maps (air, ground). • A i∈�1...n� ∈ {free, small, big}: occupation of the direction i by an allied unit. The model can effectively use many values (other than “occupied/free”) because directions may be multi-scale (for instance we indexed the scale on the size of the unit) and, in the end, small and/or fast units have a much smaller footprint, collision wise, than big and/or slow. In our AI, instead of direct positions of allied units, we used their (linear) interpolation dist(unit, � di) unit.speed (time it takes the unit to go to � di) frames later (to avoid squeezing/expansion). • E i∈�1...n� ∈ {free, small, big}: occupation of the direction i by an enemy unit. As above. • Occ i∈�1...n� ∈ {free, building, staticterrain}: Occupied, repulsive effect of buildings and terrain (cliffs, water, walls). There is basically one set of (sensory) variables per perception in addition to the Diri values. Decomposition The joint distribution (JD) over these variables is a specific kind of fusion called inverse programming [Le Hy et al., 2004]. The sensory variables are considered conditionally independent knowing the actions, contrary to standard naive Bayesian fusion, in which the sensory variables are considered independent knowing the phenomenon. P(Dir1:n, Obj1:n, Dmg1:n, A1:n, E1:n, Occ1:n) (5.1) = JD = n� P(Diri)P(Obji|Diri) (5.2) i=1 P(Dmgi|Diri)P(Ai|Diri) (5.3) P(Ei|Diri)P(Occi|Diri) (5.4) We assume that the i directions are independent depending on the action because dependency is already encoded in (all) sensory inputs. 80
Forms • P(Diri) prior on directions, unknown, so unspecified/uniform over all i. P(diri) = 0.5. • P(Obji|Diri) for instance, “probability that this direction is the objective knowing that we go there” P(obji|diri) = threshold + (1.0 − threshold) × max(0, veco · � di). We could have different thresholds depending on the mode, but this was not the case in our handspecified tables: threshold = 0.3. The right diagram on Figure 5.4 shows P(Obji|Diri) for each of the possible directions (inside the thick big square boundaries of atomic directions) with red being higher probabilities. • P(Dmgi|Diri) probability of damages values in direction i knowing this is the direction that we are headed to. P(Dmgi = high|Diri = T ) has to be small in many cases for the unit to avoid going to positions it could be killed instantly. Probability table: Dmgi diri diri ¯ no 0.9 0.25 low 0.06 0.25 medium 0.03 0.25 high 0.01 0.25 • P(Ai|Diri) probability that there is an ally in direction i knowing this is the unit direction. It is used to avoid collisions by not going where allied units could be in the near future. Probability table: Ai diri diri ¯ free 0.9 0.333 small 0.066 0.333 big 0.033 0.333 • P(Ei|Diri) same explanation and use as above but with enemy units, it can have different parameters as we may want to be stucking enemy units, or avoid them (mostly depending on the unit type). In a repulsive setting (what we mostly want), the left diagram in Figure 5.4 can be seen as P(Ai, Ei| ¯ Diri) if red corresponds to high probabilities (P(Ai, Ei|Diri) if red corresponds to lower probabilities). In our hand-specified implementation, for flee() and fightMove(), this is the same probability table as above (for P(Ai|Diri)). • P(Occi|Diri) probability table that there is a blocking building or terrain element is some direction, knowing this is the unit direction, P(Occi = Static|Diri = T ) will be very low, whereas P(Occi = Building|Diri = T ) will also be very low but triggers building attack (and destruction) when there are no other issues. Probability table: Occi diri diri ¯ free 0.999899 0.333 building 0.001 0.333 static 0.000001 0.333 81
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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
Page 30 and 31: 2.6.2 State of the art Methods used
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Page 34 and 35: Strategy Tactics Action Strategic d
Page 36 and 37: 2.8.4 Time constant(s) For novice t
Page 38 and 39: effects. In RTS games, there is a l
Page 41 and 42: Chapter 3 Bayesian modeling of mult
Page 43 and 44: programmer-specified states, the (m
Page 45 and 46: which derives the laws of probabili
Page 47 and 48: Indeed, when evaluating two models
Page 49 and 50: • energy/mana/stamina regenerator
Page 51 and 52: • The probability that the ith un
Page 53 and 54: 3.3.4 Example This model has been a
Page 55 and 56: and P(Ai = false|T = i) = 0.6. To m
Page 57 and 58: Chapter 4 RTS AI: StarCraft: Broodw
Page 59 and 60: eplay is shown in appendix in Table
Page 61 and 62: Supply/Max supply Build Note (popul
Page 63 and 64: Figure 4.3: Military moves from a S
Page 65 and 66: Technology Strategy Army How? Econo
Page 67: • Robotic player (bot): chapter 8
Page 70 and 71: • Complexity: pspace-complete [Pa
Page 72 and 73: educing the complexity (no communic
Page 74 and 75: (grid-based) pathfinding was recent
Page 76 and 77: U A E Figure 5.4: In both figures,
Page 78 and 79: Fire Reload Figure 5.6: Fight FSM o
Page 82 and 83: Identification Parameters and proba
Page 84 and 85: ⎧⎪ Bayesian program ⎨ ⎧⎪
Page 86 and 87: 36 units setup vs OAI. For Bayesian
Page 88 and 89: we learned, by optimizing the effic
Page 90 and 91: Probabilistic modality Finally, we
Page 92 and 93: • Type: prediction is problem of
Page 94 and 95: can possibly be in the future. In t
Page 96 and 97: 6.3.2 Evaluating regions Partial ob
Page 98 and 99: Pylon Gate Core Range Gate Core Pyl
Page 100 and 101: events (detected by a heuristic, se
Page 102 and 103: • AD1:n ∈ {no, low, med, high}:
Page 104 and 105: The model is highly modular, and so
Page 106 and 107: attacked: P(ei�=r, ti�=r, tai
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
Page 114 and 115: Finally, our approach is not exclus
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
Page 125 and 126: • Variables: - X i∈�1...n�
Page 127 and 128: Figure 7.3: Protoss vs Terran distr
Page 129 and 130: 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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