An information theoretic landscape analysis of neuro-controlled embodied organisms

I was searching for "information theory" and "environment" and ended up with this, an info-theoretic approach to characterizing the multidimensional search spaces common in the pursuit of evolved robots.

They look at four topologies of neural networks (ANN's) with four info theoretic metrics. They determine that the four ANN's aren't significantly different from each other. The four are all feed forward networks, just with some that have more forward connections or recurrent connections. It is the metrics that were interesting, though not so interesting that I put enough time to understand them. But I know where to find them now.

This article introduced me to the ideas of epistasis and modality, to measures of fitness landscape 'ruggedness' which correlates with difficulty of search. They weren't clear on whether difficulty meant inherent unreliability, inherent uncertainty, or just long search times.

epistatis "refers to the situation where the fitness of a genotype is dependant on multiple gene interactions". In other words, it is trouble if the genes interact. Modality "regers to the situation where the search space has large numbers of optima".

"The structure of an evolutionary algorithm is thus tied intimately to the structure of its fitness landscape" Is this true more than for any other search algorithm? In my understanding genetic search is more different than the other mains types of search (hills, annealing) than they are from each other. So that could make it vulnerable to different kinds of landscape features.

Here are the metrics they used:

• Information Content: indicates the ruggedness of the landscape path
• Partial Information Content: indicates the modality of the landscape path
• Information Stability: indicates the magnitude of the landscape path's optima
• Density-Basin Information: characterises the landscape structure around the optima

"To characterize the fitness landscape, a random walk was performed using all four ANN architectures."

• A random walk of the agent, the ANN, or the fitness landscape?
• I'm pretty sure it is of the agent. But why a random walk, they want to evolve an agent that can random walk? Why not straight walking?

"As such, the ability for search algorithms to find increasingly better solutions may be highly dependent on the initialisation and trajectory of the search on the fitness landscape."

• This suggests parallels to non-linear dynamics and chaos.

Conclusions

• They determine that the four ANN's aren't significantly different from each other. Recurrent and direct connections did not provide any significant advantage for evolving better creatures.
• The fitness landscapes of the search spaces have both rugged and smooth sections depending on the sub-spaces being explored. High epistatis and high modality.
• "There are serious deficiencies associated with current landscape analysis methodologies, expecially for analysing non-homogenous and anisotropic search spaces"

Questions

• Is there a course at IU that will expose me to issues brought up in the paper: characterization of search spaces and algorithms?
• In what way is evolutionary search more vulnerable to landscape structure than an other search algorithm?

• ".. the neighborhood operator plays a vital role in simplifying the finess landscape only when epistatis is low. If epistatis is high(that is when almost all genes depend on all other genes), the connectivity in the genotype space becomes maximal. Thus, every solution appears to be within the neighborhood of every other solution. It is still an open question of how to choose the right genotype to phenotype mapping that will reduce the degree of epistatis in the genotype space."
  • Ok, This paragraph was great. A few questions:
  • There exists a neighborhood operator that can simplify landscapes?
  • Is there any use in maximal connectivity of genotype space?
  • Is connectivity a technical term in this context? What field is being invoked?
  • What do you mean by neighborhood?
  • You can choose genotype-to-phenotype mappings to reduce the degree of epistatis?

• What is 'landscape path'?
• What are "non-homogenous and anisotropic search spaces"?

Readings

• "The idea of fitness landscapes was first proposed by Wright" The roles of mutation, inbreeding, crossbreeding and selection in evolution 1932