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[Ma Chao]

Hi, all.

These days I was thinking about using reinforcement learning to train my evaluation function. I came up with a question about how to understand the relationship between evaluation and the search.

Let us go back to the original definition of evaluation and minimax search. We know that for each position, the evaluation gives us an estimation of the current position. If this estimation is exactly enough (which means this evaluation is *perfect*), the engine should be strong even only search for just 1 depth to pick a best move whose leading position has the maximum evaluation. Unfortunately, it is impossible to make such a 100% exact estimation. However, a minimax search with depth D can make the evaluation more exactly. It is intuitive to believe that the value of a minimax search with depth D (D > 1) should be more accurate than calling the evaluation function directly.

Now the question is coming: if we have an evaluation function Eval() which is not accurate enough (for example, an evaluation that only make the summation of all material values in that position), firstly we use this evaluation function to evaluate a position, suppose the value return by Eval(pos) is H. Then we run a minimax search of depth D with the same evaluation function (which is called when the search reach the leaf nodes) and the position above is the root position. The search use qsearch and check extension to avoid horizon effect. The search will also return a value for this position, say V. My question is: “Can we say that V is more accurate than H respectively?”

Notice that the evaluation function itself is not accurate at all. So the search result may also not be accurate.

Another more interesting topic is about the delta between V and H. Suppose Delta = |V – H|, what conclusion can we get from this Delta? Can we say that Delta reflect the degree of accuracy of an evaluation function? Or it is just a essential condition for an accurate evaluation function, but not sufficient (we can say “an accurate evaluation => a small Delta”, but can not say “a small Delta => an accurate evaluation”)? Or neither?

Dose the evaluation of Stockfish or Crafty has such a property of “small Delta”? Have someone made such a test? (The comparison may need some normalization to the percentage pawn score scale)
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