> -----Original Message----- > From: Jason House <[EMAIL PROTECTED]> > On Jun 26, 2008, at 3:23 PM, [EMAIL PROTECTED] wrote:
Cool! Now for the cases where I'd want a Kalman filter, I'd need it to predict the future state of a non-stationary, multimodal distribution. A typical pattern is for a node to start out with optimistic scores but to experience a strong pessimistic trend later as UCT starts to focus more on effective enemy counter moves. Or the reverse, or sometimes a see-saw. > The drift term is intended to take care of that kind of behavior.? My limited experience is with objects moving in space, so please bear with me. The win rate is a 1 dimensional value analogous to a car moving on a road. If it has a constant velocity, we can model that with a Kalman filter having a drift rate. But if we assume a constant drift rate, we'll wind up with win rates greater than 1 or less than zero, right? When a car is at point A, for a while, then moves?to a final destination?point B, it has to (at least) accelerate for a while, then decelerate. In UCT, a new node will start with an initial win rate reflecting the fact that UCT is exploring moves fairly randomly, then settle eventually at a "final"?win rate where UCT would put it if it ran for a very long while. Closer to the root, we are?seeing a superposition of many such distributions. My gut feeling is that the UCT tree is already doing a better job of what I'm asking the Kalman filter to do. But it's a nagging question for me. > There's no way for a single floating point value to capture deeper structure. Well, yes and no. There is more available than a single floating point number. You can, in fact, look at Monte Carlo go as a source separation problem. The sources are the values of the moves at the root, and the signals, the playouts, are mixtures of those sources. AMAF is a model that assumes very simple mixing of the sources in the playouts. But, maybe, this is a discussion for another day. - Dave Hillis
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