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Figure 7.8: Evolution of P(BT |observations, time, λ = 1) in time (seen/observed buildings on the x-axis). Only BT with a probability > 0.01 are shown. The numbers in the legend correspond to build trees identifier numbers. The interpolation was obtained by fitting a second order polynomial. The robustness to noise is measured by the distance d to the real build tree with increasing levels of noise, for k = 0. The predictive power of our model is measured by the k > 0 next buildings for which we have “good enough” prediction of future build trees in: P(BT t+k |T = t, O1:N = o1:N, λ = 1) “Good enough” is measured by a distance d to the actual build tree of the opponent that � � we tolerate. We used a set distance: d(bt1, bt2) = card(bt1∆bt2) = card((bt1 bt2)\(bt1 bt2)). One less or more building in the prediction is at a distance of 1 from the actual build tree. The same set of buildings except for one replacement is at a distance of 2 (that would be 1 is we used tree edit distance with substitution). • We call d(best, real) =“best” the distance between the most probable build tree and the one that actually happened. • We call d(bt, real) ∗ P(bt)=“mean” the marginalized distance between what was inferred balanced (variable bt) by the probability of inferences (P(bt)). Note that this distance is always over the complete build tree, and not only the newly inferred buildings. This distance metric was counted only after the fourth (4th) building so that the first buildings would not penalize the prediction metric (the first building can not be predicted 4 buildings in advance). For information, the first 4 buildings for a Terran player are more often amongst his first supply depot, barracks, refinery (gas), and factory or expansion or second barracks. For Zerg, the first 4 buildings are is first overlord, zergling pool, extractor (gas), and expansion or lair tech. For Protoss, it can be first pylon, gateway, assimilator (gas), cybernectics core, and sometimes robotics center, or forge or expansion. 132
Table 7.4 shows the full results, the first line has to be interpreted as “without noise, the average of the following measures are” (columns): • d for k = 0: – d(best, real) = 0.535, it means that the average distance from the most probable (“best”) build tree to the real one is 0.535 building. – d(bt, real) ∗ P(bt) = 0.870, it means that the average distance from each value bt of the distribution on BT , weighted by its own probability (P(bt)), to the real one is 0.87 building. • k for d = 1: – best k = 1.193, it means that the average number of buildings ahead (of their construction) that the model predicts at a fixed maximum error of 1 (d = 1) for the most probable build tree (“best”) is 1.193 buildings. – “mean” k = 3.991, it means that the average number of buildings ahead (of their construction) that the model predicts at a fixed maximum error 1 (d = 1), summed for bt in BT value and weighted by P(bt) is 3.991 5 • idem that the bullet above but k for d = 2 and d = 3. The second line (“min”) is the minimum across the different match-ups* (as they are detailed for noise = 10%), the third (“max”) is for the maximum across match-ups, both still at zero noise. Subsequent sets of lines are for increasing values of noise (i.e. missing observations). Predictive power To test the predictive power of our model, we are interested at looking at how big k is (how much “time” before we can predict a build tree) at fixed values of d. We used d = 1, 2, 3: with d = 1 we have a very strong sense of what the opponent is doing or will be doing, with d = 3, we may miss one key building or the opponent may have switched of tech path. We can see in Table 7.4 that with d = 1 and without noise (first line), our model predicts in average more than one building in advance (k > 1) what the opponent will build next if we use only its best prediction. If we marginalize over BT (sum on BT weighted by P(bt)), we can almost predict four buildings in advance. Of course, if we accept more error, the predictive power (number of buildings ahead that our model is capable to predict) increases, up to 6.122 (in average) for d = 3 without noise. Robustness to missing informations (“noise”) The robustness of our algorithm is measured by the quality of the predictions of the build trees for k = 0 (reconstruction, estimation) or k > 0 (prediction) with missing observations in: P(BT t+k |T = t, O1:N = partial(o1:N), λ = 1) 5 This shows that when the most probable build tree is mistaken, there is 1) not much confidence in it (otherwise we would have P(btbest) ≈ 1.0 and the “mean” k for fixed d values would equal the “best” one). 2) much information in the distribution on BT , in the subsequent P(bt¬best) values. 133
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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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Page 84 and 85: ⎧⎪ Bayesian program ⎨ ⎧⎪
Page 86 and 87: 36 units setup vs OAI. For Bayesian
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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
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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
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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
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Page 129 and 130: 7.5 Build tree prediction The work
Page 131: Questions The question that we will
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Page 137 and 138: 7.6 Openings 7.6.1 Bayesian model W
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Page 143 and 144: Table 7.5: Prediction probabilities
Page 145 and 146: 7.6.3 Possible uses We recall that
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Page 149 and 150: (tt) if it allows for building all
Page 151 and 152: 7.7.2 Results We did not evaluate d
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Page 163 and 164: 3 2 player 1 1 6 4 resources 8 play
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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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