Author: Ratko V Tomic
Date: 07:05:45 10/18/00
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> I disagree. From you main points later, I think you disagree mainly with my definition of "evaluation terms" not the substance of the objection to Bob's post. Let me explain. > There is no need to go so far as to assume the need for multiple points > of view of the position and so multiple evaluation functions, non-linear > terms etc. > > You tacitly assume Bob's argument: That being a piece down cannot be > justified by position terms. This is certainly true for a wishy-washy, > inexact evaluation, but I don't believe it to be true when the > evaluation becomes better. I assume only Bob's _definition_ of evaluation terms (in order to argue against his subsequent conclusions), i.e. largely orthogional (independent, not significantly entangled or correlated) components which then get added. Material values are the most typical example of such independent terms (with small violation of independence for Bishop pair). In fact, if you define your "positional evaluation" as some arbitrary mapping from a position to a value V, then the total "evaluation" is the simplest posible "linear" function, Total=V. So, whether there is non-linearity, depends on how you draw your semantic lines, how you label components of computation, what is the separate evaluation term, and what you call the combination of terms. The trivial extreme case above, Total=V, shows that with large enough concept of "evaluation function term" you can always make it appear a simple combination, a linear function. Now, consider Bob's objection to Gambit Tiger's evaluation -- he sees GT display +3 value in a position Crafty may take as 0.0. He concludes GT could drop a piece here and think it is equal. Obviously, Bob doesn't have in mind an evaluation function which could depend on presence of pieces in any more complex way than linear additive term, with no (statistically) significant entanglement between the terms. If you now take Bob's implicit definition of evaluation terms, you can only point out that the full evaluation may combine such simple terms in a nonlinear way, ranging from ultimately the Samuels style arbitrary mapping to some milder intermediate form of nonlinearity or almost linearity. One most concrete way to see the problem with Bob's objection was in the example I gave there of the king attack which won't evaluate as +3 if you were to take one of GT's pieces away, i.e. the key component of the king attack or defense (say of the queen side) is missing, and the total attack evaluation term fizzles away to 0, while the material due to the piece removal drops by 3, and the total result is -3, not 0 as Bob suggested. That was my counterpoint to Bob's assertion given in terms of down-to-earth chess reasoning (the angle a practical chess player may take). But there are other angles on the same phenomenon, differing in their proximity to the most concrete (over the board) resoning, and that was what made up the rest of my comment. It was meant to offer a different perspective on the same phenomenon, not to diminish or negate the other possible perspectives. > I don't see any reason to focus on some aspect of the game and ignore the > others, i.e. because there's a king attack going on, there's no need > to discount pawn weaknesses or such stuff. It's just a question of giving > the correct weight to everything. > Again here, I think what you see as disagreement is largely a matter of definitions (and I had used Bob's implicit definitions of simple and essentially orthogonal evaluation terms). When you say "It's just a question of giving the correct weight to everything" this perfectly agrees with what I am saying, provided the "correct weight" (or correct scale) could mean that the weights (or scales) used with Bob's type of evaluation terms are effectively sensitive to the (larger) context. Or if one speaks in terms of what you define as individual evaluation components (which allows for complex interdependence of the components), one might say that one component may overshadow and override the advice from others in some positions, but not in others. Thus the king-side attack evaluation component may override the pawn weakness terms (which by themselves would advise the program not to attack here). Even more, the king-side attack component could override the material "value" terms to any degree (e.g. the queen sacrifice, without specifically being able to see the payback node). It doesn't matter (for the substance of the argument against Bob's objection to GT) whether you package semantically your nonlinearity inside your evaluation term or your combination of such terms, the net effect is the same, it is there and it gets accounted for when all is said and done. I agree with all of that, and that was essentially contained in the first aspect I covered in the earlier message. Now the question is how can one go about producing such complex terms. One way (as suggested in the first part of the message) is building ever more complex evaluation functions in basically ad hoc manner, testing them and thus empirically tuning the terms and weights (the line between being largely a matter of definition) and their context dependence. In the second aspect I covered earlier, I suggested that there is a better, more systematic (and in the long term more effective) way of getting there, the way pointed out by Botvinnik. What Botvinnik realized is that there is a much finer structure and pattern in the evaluation function complexities. They are not mere expanding amorphous blobs of computation but have an additional pattern, a fine skeleton, as it were, guiding this growth. Instead of an ad hoc growth of evaluation complexity via inspired trial and error (as most programs still follow, and which often hits a wall of no returns at certain level of complexity), he suggested using multilevel decision system (a two level in his Pioneer project), where the lowest level is a regular alpha-beta search, but the components used for the leaf evaluation of this search are being set and changed by a higher level reasoning/knowledge layer (which in turn feeds itself and its cretive output on the input from the previous iterations of the lower level searches). The regular a-b search layer can thus be seen as helping answer specific question posed by the reasoning (guiding-, knowledge-) layer. Multiple a-b searches are initiated from the same higher level node (individual stepping stone of the higher level search), each a-b search using a highly costraining leaf evaluation function, specialized to answer a single specific question the higher layer wishes to know at the moment (e.g. can my queen side pawns and rook resist/block counterattack by opponent's forces within the time I plan to use for my king-side attack), yielding thus very high efficiency cutoffs. While it is common among the present-day experts to dismiss Botvinnik's approach as at best ineffective, and at worst as a fraud, I think the time is on his side. While there is indeed a much greater startup cost in putting his method into action compared to the prevailing ad hoc methods of growth of evaluation complexity, when complexity reaches certain levels the ad hoc methods hit a wall of diminishing returns, while Botvinnik's method at that point is merely beginning to pick up a speed. It is the kind of difference one may have between a car factory and a machanic's garrage. It may take much longer to come up with a car factory idea (e.g. Ford's production line), design it and gather resources to build it, and before it all happens a machanic in his little garrage may have built several cars in an ad hoc way. But once the factory has overcome its startup overhead, it will quickly and vastly outproduce the little garrage. I think the chess programming is at present in an analogous position to the car production before the mass scale production lines, with lots of small garrages and few skilled mechanics (most often, just one real brain behind the operation) in each putting together the cars in an ad hoc ways. > In other words, good evaluation is all that is needed, and the magic will > follow. Getting it is quite a trick in itself, of course, and the first > step is to understand what is meant by "good evaluation". It is "a trick" right now, but it won't be once the additional patterns to its growth are used to the full extent.
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