Preliminary Evaluation of Brownian Noise as a Suitable Environment Modification

This is the (very) preliminary results of running evolvability experiments using various amounts of Brownian noise.  In all cases, the starting value for A is 3.0, and at the end of each epoch a uniform amount of noise in the range [-Var, +Var] is added.

Also included is the results of Experiment 4, which so far best shows the effects we're looking for.  It uses uniform random values in the range [-3, 9] to replace the value of A at each epoch end.

Here are the results so far:

Experiment 9 (Brownian, Var = 0)

 Fitnesses
 Fitness Differences
 Sizes
 

Experiment 3 (Brownian, Var = 1)

 Fitnesses
 Fitness Differences
 Sizes
 

Experiment 11 (Brownian, Var = 3)

 Fitnesses
 Fitness Differences
 Sizes
 

Experiment 8 (Brownian, Var = 6)

 Fitnesses
 Fitness Differences
 Sizes
 

Experiment 10 (Brownian, Var = 10)

 Fitnesses
 Fitness Differences
 Sizes
 

Experiment 4 (Uniform, Range = [-3, 9])

 Fitnesses
 Fitness Differences
 Sizes
 

Experiment 12 (Uniform, Range = [0, 6])

 Fitnesses
 Fitness Differences
 Sizes
 

Discussion

So far, nothing in the Brownian experiments with non-zero variance has beaten Uniform noise in terms of fitness differences.  Experiment 4 includes gains of over 100.  Experiment 3 gets close to that a couple of times.  One could argue that the separation of ADF and non-ADF hit differentials is more pronounced in experiments 8 and 10, but this is mostly because non-ADF does so crappy in these experiments.

Uniform also beats Brownian with non-zero variance when we look at the highest fitness level attained.  "ADF, end" in the Uniform case frequently exceeds 150 hits.  In the Brownian case it never does.

In terms of tree sizes, we see code bloat in all Brownian cases, but not in the Uniform case.

About the only thing we can say so far for Brownian is that the results are less noisy.

Conclusion

Right now I'm leaning towards using Uniform noise for A, not Brownian.  Let me know if you think it's worthwhile to start runs on uniform noise with varying window widths.