Hi Mark,
You should run a lot more test games. The 95% confidence interval on the result is at least sqrt(1/num_games), so you need 400 or more games to know the win rate within 5%. I've seen many anomalous win rates when I used to test with 20 games. Now I use 200 games minimum, and I try to get 500 before I make any conclusion. I think mogo is the only strong program that uses the UCB1-tuned formula. The others use the same formula you use. I found a thesis where they measured many different formulas and found little difference. If any strong program other than mogo uses some formula other than the basic one, can you please let us know? The reason to only initialize the nodes after a certain count is to save memory. The simple uct algorithm visits each child once before using uct to choose one. If you create all child nodes before any are visited you end up with most of the nodes in the tree having zero visits. How many playouts per second are you getting (from the start of the game on a 9x9 board), and on what hardware? Regards, David From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Mark Boon Sent: Tuesday, February 05, 2008 7:54 AM To: computer-go Subject: [computer-go] More UCT / Monte-Carlo questions Although most of my time has been eaten up by implementing/improving some general framework parts I did get a chance to play a bit with a simple UCT search. Some things that I found puzzled me a bit and I hoped someone had an explanation or similar experiences. I implemented a very basic UCT / MC program first using pseudo-liberties. I figured this should be the base-line against which I can test some ideas. To test if the program actually worked properly I first let it play against Orego. The speed of my playouts are similar to Orego so I figured the level of play should be similar. (I switched off pondering and multiple-threading in Orego to get an apples-to-apples comparison.) To my surprise my program seemed to be winning the majority of the games (after a few dozen games). When looking at Orego's output I couldn't help noticing that at the start of the game it prints much smaller numbers of 'runs' than my program, whereas by the end of the game the numbers are similar. This may be the reason for my program performing better. When I looked at the code of Orego I noticed there are two main differences: - It computes the UCT value in a completely different way. A comment in the code refers to a paper called "Modification of UCT with Patterns in Monte-Carlo Go". I haven't studied this yet, but whatever it does it apparently doesn't do wonders over the standard C * sqrt( (2*ln(N)) / (10*n) ) that I use. - It only initialises the list of untried moves in the tree after a node had a minimum run-count of 81 (on 9x9). For the life of me I couldn't figure out what the effect of this was or what it actually does. I was wondering if this has an effect of what is counted as a 'run' but I'm not sure. Then I found a paragraph (4.2) in Remi Coulomn's paper about ELO raings in patterns. It briefly describes it as "As soon as a number of simulations is equal to the number of points on the board, this node is promoted to internal node, and pruning is applied." I can't help feeling that the implementation in Orego is doing this. But I can't figure out where it does any pruning or applying patterns of any kind. Is there supposedly a general benefit to this even without pruning or patterns? As stated before, at least it doesn't seem to provide any benefit over my more primitive implementation. Maybe Peter Drake or someone else familiar with Orego knows more about this? Anyway, reading the same paragraph mentioned above again I was struck by another detail I thought surprising: after doing the required number of runs, the candidates are pruned to a certain number 'n' based on patterns. Does that mean from then on the win-ratio is ignored? What if the by far most successful move so far does not match any pattern? Am I misunderstanding something here? The paragraph is very brief and does not elaborate much detail. On to my next step I introduced some very basic tactics to save stones with one liberty, capture the opponent's stones with one liberty and capturing the opponent's stones in a ladder. There are many possible choices here. Just doing this near the last move and/or over the whole board. Doing this in the simulation and/or during the selection. Just doing this near the last move during simulation caused a slow-down of a factor 4 or 5 but improves play considerably. Also doing this near the last move during selection doesn't affect speed much but deteriorated play! Doing this first near the last move and then look for tactics over the whole board as a next step affected results negatively even more. Number of playouts are still in the same ball-park. Thinking it over, since I don't use this to prune the selection but just to order the candidates I could see that after many runs the ordering suggested by the tactics get overriden by the UCT selection. So I could see the effect of using this for selection reduced steadily with the number of runs through a node. But still I didn't expect a considerable reduction in strength. So what could be happening here? - I could have a bug. - I didn't run enough games (about 50) - Using knowledge to order the initial selection is counter-productive when not accompanied with pruning. The last one I find very hard to believe. Did anyone else run into something like this? Finally, I also looked a bit at using more threads to make use of more than one processor. I figure this can wait and it's better to keep things simple at this early stage but still it's something I want to keep in mind. When looking at what I need to do to enable multiple threads during search it seems to me I'll be required to lock substantial parts of the UCT-tree. This means traversing the tree when looking for the best node to expand is going to be the main bottle-neck. Maybe not with just two to four processors, but I foresee substantial diminishing returns after that. Is this correct? Is there experience with many processors? Maybe a different expansion algorithm will be required? Mark
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