Studying and tackling noisy fitness in evolutionary design of game characters

Merelo, Castillo, Mora, Fernández-Ares, Esparcia-Alcázar, Cotta, Rico

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We live in a noisy world

And games are even noisier

Image by James Davies

The outcome of a game is uncertain

"Eleven against eleven, and Germany wins"

How can you optimize game strategies

If you don't even know which strategy is the best

Noises have colors

fitness distribution

Can we use the statistical properties of fitness for selection in EAs?

We will use Wilcoxon paired test for comparing chromosomes.

Testing 3 different methods

  1. 0-memory: reevaluate.
  2. Incremental temporal average: keep fitness and average.
  3. Wilcoxon partial order: compare using Wilcoxon test.

How WPO works every generation

For every individual

  1. Computes fitness again
  2. Does 10 comparisons with other individuals. Score +1 if better, -1 if not, 0 if not statistically significant.
  3. Rescale to [0,20]

Noisy experiments done this way

  • Two multimodal functions, Trap and MMDP
  • Additive gaussian noise with center in 0 and σ = 1,2,4
  • Using Algorithm::Evolutionary in Perl

ITA wins with low noise

Evaluations sigma 0

WP beats it with loud noise

Evaluations all sigms

Different situation for MMDP

Evaluations with MMDP

It's great to remember

Memory-based systems beat 0-memory.

WPO ~ ITA evaluation-wise, but more robust

Some way to go

  • Find a more general model for noise in the fitness of games.
  • Use Wilcoxon comparison in a different way: Wilcoxon Tournament
  • Test in which conditions each strategy performs the best.

Open Science!

All source, parameters for experiments, data available from

Thanks a lot for your attention

Any question?

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