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9 An Example Model - Utility Learning Agents

9.1 General Description

A simple application of the above approach is that of an economic agent that seeks to maximise its utility by dividing its spending of a fixed budget between two goods in each time period. Unlike classical economic agents, this one does not know its utility function (even its form) but tries to induce it from past experience. To do this it attempts to model its utility with a function using +, -, *, /, max, min, log, exp, average, "cutbetween" (A three-argument function which takes the second value if the first value is less than 1 and the third value thereafter, i.e. it is a graft of two functions at a point determined by a third - a sort of functional cross-over.), a selection of random constants and variables representing the amounts bought of the two products.

The advantage in this model is that we can introduce a severe structural change in the agent's utility function and observe the result (imagine the agent has suddenly developed an allergy to the combination of the two products concerned).

Each time period it:

  1. carries over its previous functional models;

  2. produces some new ones by either combining the previous models with a new operator or by growing a new random one;

  3. it then evaluates all its current models using past known data on amount it spent and the utility it gained (considerations such as the predictivity and depth of the model are also factors in the fitness function);

  4. it then selects the best models in terms of fitness for carrying over in the next period

  5. it finds the fittest such model;

  6. it then performs a limited binary search on this model to find a reasonable spending pattern in terms of increasing its utility;

  7. finally it takes that action and observes its resulting utility.

Modelling Learning as Modelling - 23 FEB 98
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