Artificial data

The next logical step is to investigate the possibility to infer both the search strategy and the evaluation function simultaneously. The first step is to use artificial data to see if the results would match the known strategy and evaluation function. The process works as in the last section for the random lambda values, but this time instead of a fixed inferred evaluation function, the lambda values are inferred at each strategy. It is impossible to show all the inferred evaluation functions in Table 13, so all discussion of the evaluation functions will be from the raw data, which is not shown. Trials were done inferring with only two games at a time, this was due to the immense memory requirements. Ten games were infeasible, as now the inference cannot be accomplished incrementally. Before the message lengths for each strategy of each game can be calculated; these message lengths need then be simply added up and an inference on the search strategy could be made. Now the whole ten games would be required so as to infer the evaluation functions. This places huge requirements on the PC and even with virtual memory, the gigabytes worth of memory needed could not be obtained. Thus only the inference of small numbers of games is possible until computing hardware improves.

 

Table: Inference results from inferring both the search strategies and random $\lambda$ values.

	Actual Strategy
Inferred	min1max1	min1max2	min1max3	min1max4	min2max2
min1max1	98%	6%	15%	32%	4%
min1max2	0%	94%	0%	0%	0%
min1max3	0%	0%	85%	0%	0%
min1max4	0%	0%	0%	68%	0%
min2max2	2%	0%	0%	0%	96%

The inference of the search strategies is extremely good. With impressively high prediction rates, it would appear that this method is robust and accurate. The problems with the prediction of the min1max3 and min1max4 strategies being not as accurate in the results, should improve with a greater number of games. Time restrictions and the large amount of computations required meant that this theory could not be substantiated.

 

Table 14: Inference results from inferring evaluating function when true search strategy is min1max1.

	Inferred $\lambda$
Strategy	$\lambda_{MAT}$	$\lambda_{MOB}$	$\lambda_{CENT}$	$\lambda_{ATT}$	I-Inferred
min1max1	0.9375	1.75	0.0625	11.5625	56.8651
min1max2	0	0.187406	0.6875	2.375	333.5
min1max3	0	0.9375	2.5625	8.125	226.001
min1max4	0	0.25	2.05838	4.05438	316.913
min2max2	0	0.1875	1.0625	2.875	322.487
Actual	0.887478	1.33811	0.913724	9.93347

A typical example of the inference of the evaluation function is shown in Table 14. The interesting thing is that the only evaluation function that has weights like the actual ones is the true search strategy. This same pattern occurs for most of the data, and is most probably due to the different strategies having a very large effect on the values used for the inference of the evaluation function. Although the results found here are not perfect they do indicate that it is quite possible to find both the evaluation strategy and the search strategy at the same time. The memory usage and processor power needed for these tests is huge. The artificial data tends to be a lot less computer intensive than the real world data yet it pushes the computer to the limit in terms of power and memory.