Modelling Learning as Modelling

In table 1, we summarize the relevant characteristics of the alternative formal (as distinct from "soft") learning paradigms found in the economics and management literature.

The two particular aspects of these models which are of greatest interest here are the model selection criteria and the model adaptation methods. On the criterion of model selection methods alone, network representations of learning and learning as statistical estimation differ fundamentally from the modelling representation and genetic algorithms in that there is only one model and, so, no selection to be made. On the criterion of model adaptation methods, modelling has most in common with neural networks and logics in relation to model specification and shares with rational expectations and least-squares learning a reliance on the estimation of model parameters.

Genetic algorithms and evolutionary methods engage in some sort of random search which generates new models which are selected with increasing frequency if they do well and with less frequency until they are discarded if they do badly. Genetic algorithms become increasingly local in their model adaptations as they identify the areas of the model space which systematically yield the fittest models.There is a single process by means of which genetic algorithms identify the best models and the estimate the best values of the parameters of those models.

The closeness among modelling, neural networks, genetic algorithms and logics in model specification is that all of them modify the hypothesized relationships among variables by marginal changes resulting from specific failures of the incumbent models.

In summary, the modelling representation of learning differs from all of the others but logics and genetic algorithms in allowing for multiple models and for adapting models only by local searches of the space of possible models.

Some logics can be used to represent learning as modelling. Several of these have been devised and implemented (e.g., Masuch and Huang [15]; Fox, Krause and Elvang Goransson [9]. Others (e.g. Fagin and Halpern [10]; Fox [8]) have been well explored.

It seems reasonable to require a representation of learning as modelling to be sound and consistent. In general, completeness and decidability are desirable for the (real, i.e. not simulated) model-builder but only be obtainable at the expense of the expressive power of the formal framework.

This is in contrast to the situation with the internal models of the agent. Here the logic paradigm has more problems, principally logical omniscience, and the common tolerance of inconsistency. There are logic formalism which get round these problems (for example step logics and paraconsistent logics), but still do not map naturally into learning as it is preformed by real economic agents.

Having said this, there is clearly an affinity between logics and modelling representations of learning. It might nonetheless be possible that the strict formalism of logical systems will not be compatible with the description of key elements in a decision-making problem or procedure. In that case, there will be a trade-off between the rigour of logic and the relevance of modelling representations that do not resemble logics.

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