The document discusses the need for effective geospatial modeling in complex games, focusing on learning high-level abstractions from environment attributes. It presents methods for discretizing game space and evaluating clustering techniques to categorize biomes based on observed characteristics. The authors conclude that predictive, interpretable, and efficient models are crucial for enhancing non-player character intelligence and overall game design.

1. Discretization of Game
Space by Environment
Attributes
Alex Braylan and Risto Miikkulainen
The University of Texas at Austin

2. Introduction
▪ Games are becoming more complex
▪ Many characteristics of the game are not explicitly coded
▪ Need for learning high-level abstraction
▪ Non-player character (NPC) intelligence
▪ Analytics for player
▪ Analytics for designer
▪ Focus of this work is on geo-spatial environment
▪ What can be learned about xy coordinates

3. Prior work on learning
representations of game
characteristics
▪ Tomai 2018
▪ Graph structure of interactions between agents and objects
▪ Fulda et al 2018
▪ Interaction modes, or subsets of possible actions that are reasonable in
a given situation
▪ Winder and desJardins 2018
▪ Hierarchies of concepts formed from observations of game objects and
their attributes
▪ Many others

4. Geospatial modeling:
what makes it special?
▪ Small input
▪ XY coordinates
▪ Continuous input
▪ (In the non-discrete sense) nearby locations assumed similar
▪ (In the non-sporadic sense) large amount of observed input
▪ Big output
▪ What kinds of objects might I find?
▪ What kinds of enemies might I encounter?
▪ Are there quest-givers, vendors, inns, etc?
▪ How likely am I to die?
▪ Output generally discrete and sporadic

5. Geospatial modeling goals
▪ Usefulness
▪ Predictive power
▪ Interpretability
▪ Efficiency
▪ Memory requirement
▪ Compute time

6. Evaluation measures:
usefulness
▪ Predictive power
▪ How accurate are model’s predictions?
▪ Cross-entropy loss for categorical outcomes
▪ Interpretability
▪ NPC should communicate clearly with player
▪ Analytics should be transparent to designer
▪ Kernel (non-parametric) example:
“I am at coordinates (x, y), where by interpolation from observations at (x − 3,
y − 2), (x − 1, y + 1), (x + 2, y + 4) ... the probability of encountering a wolf
each minute is 0.12”
▪ Cluster (parametric) example:
“I am at coordinates (x, y), which are in biome type 7, where the probability of
encountering a wolf each minute is 0.12”

7. Evaluation measures:
efficiency
▪ Memory requirement
▪ Model output can be as complex as observation dimensionality
▪ Probability of encountering each type of enemy/object/etc
▪ Concrete measure in next slide
▪ Compute time
▪ Measure in seconds? CPU usage? Number of operations?

8. Biomes: simplifying complex
observation spaces
▪ Discretization of game space by environment attributes
▪ Map XY coordinates to biome IDs
▪ Biome IDs in observation probability table
▪ Store biome boundary definitions
▪ Memory efficiency measures
▪ Number of biomes
▪ Non-overlap, average fraction of nearest neighbors in geographical
space belonging to same biome
Biome 1 Biome 2 Biome 8
Wolf 0.05 0.36 0.00
Turtle 0.21 0.11 0.04
Shield 0.01 0.05 0.02
… … … …
Pirate 0.01 0.00 0.17

9. Learning biomes by clustering
▪ Geospatial input XY, observation attribute output Z
▪ Baselines:
K-means on XY K-means on Z
Ignored attributes Undefined boundaries

10. Learning biomes by clustering
▪
W
1 0 0
W
1 0 0
T
0 1 0
W
.5 .5 0
W
1 0 0
T
.5 .5 0
W: 0.87
T: 0.44
W
XY
proximit
y
check?

11. Learning biomes by clustering
▪ GCC/GAC define biomes according to characteristic inhabitants
▪ GCC/GAC enforce contiguity of biomes to minimize representation complexity
GCC GAC
Contiguous biomes Partially contiguous biomes

12. Evaluation of clustering
methods
Overlap Cross-entropy Seconds
K-means XY 1% 34.07 2.00
K-means Z 44% 5.33 1.17
GCC 2% 27.00 3.07
GAC 4% 27.83 6.87
▪ Modern multi-player first-person shooter game
▪ Three maps with 5000-18000 observations of 200-400 types of creatures
Least predictive
No compression
Slowest
Winner

13. Conclusion
▪ Geospatial modeling: an important part of a larger picture
▪ Models should be predictive, interpretable, compact, tractable
▪ Biome concept: maximize information, constrain complexity
▪ GCC & GAC: methods for learning biomes
▪ Future work:
▪ Integration with larger models
▪ Usefulness as explanatory variable should be dependent on other explanatory variables
▪ Z as residuals rather than observations?
▪ Defining boundaries
▪ Interpolating between biomes near boundaries
▪ Additional dimensions in space and time