I am working on a chess-like-game engine (its the same as chess except each player gets to make 2 moves), and would like to be able to calculate a search to around depth 8(which i guess translates to around depth 16 for regular chess or more since there is no pruning of the 2-moves). I am running alphaBeta pruning.
Currently I seem to be able to get depth 6 (12+ for regular chess) within 20-30ish minutes. Relatively speaking how bad is this performance?
Any tips would be appreciated.
Each ply costs you a multiple of time equal to the number of moves being considered.
If you need 20-30 mins to reach only depth 6, it'll take exponential more time to reach depth 8. So the answer is NO.
You should go back to your algorithm and check for any possible improvement. Null-move reduction, heavy pruning etc are required.
Related
I know that my question is general, but I'm new to AI area.
I have an experiment with some parameters (almost 6 parameters). Each one of them is independent one, and I want to find the optimal solution for maximum or minimum the output function. However, if I want to do it in traditional programming technique it will take much time since i will use six nested loops.
I just want to know which AI technique to use for this problem? Genetic Algorithm? Neural Network? Machine learning?
Update
Actually, the problem could have more than one evaluation function.
It will have one function that we should minimize it (Cost)
and another function the we want to maximize it (Capacity)
Maybe another functions can be added.
Example:
Construction a glass window can be done in a million ways. However, we want the strongest window with lowest cost. There are many parameters that affect the pressure capacity of the window such as the strength of the glass, Height and Width, slope of the window.
Obviously, if we go to extreme cases (Largest strength glass, with smallest width and height, and zero slope) the window will be extremely strong. However, the cost for that will be very high.
I want to study the interaction between the parameters in specific range.
Without knowing much about the specific problem it sounds like Genetic Algorithms would be ideal. They've been used a lot for parameter optimisation and have often given good results. Personally, I've used them to narrow parameter ranges for edge detection techniques with about 15 variables and they did a decent job.
Having multiple evaluation functions needn't be a problem if you code this into the Genetic Algorithm's fitness function. I'd look up multi objective optimisation with genetic algorithms.
I'd start here: Multi-Objective optimization using genetic algorithms: A tutorial
First of all if you have multiple competing targets the problem is confused.
You have to find a single value that you want to maximize... for example:
value = strength - k*cost
or
value = strength / (k1 + k2*cost)
In both for a fixed strength the lower cost wins and for a fixed cost the higher strength wins but you have a formula to be able to decide if a given solution is better or worse than another. If you don't do this how can you decide if a solution is better than another that is cheaper but weaker?
In some cases a correctly defined value requires a more complex function... for example for strength the value could increase up to a certain point (i.e. having a result stronger than a prescribed amount is just pointless) or a cost could have a cap (because higher than a certain amount a solution is not interesting because it would place the final price out of the market).
Once you find the criteria if the parameters are independent a very simple approach that in my experience is still decent is:
pick a random solution by choosing n random values, one for each parameter within the allowed boundaries
compute target value for this starting point
pick a random number 1 <= k <= n and for each of k parameters randomly chosen from the n compute a random signed increment and change the parameter by that amount.
compute the new target value from the translated solution
if the new value is better keep the new position, otherwise revert to the original one.
repeat from 3 until you run out of time.
Depending on the target function there are random distributions that work better than others, also may be that for different parameters the optimal choice is different.
Some time ago I wrote a C++ code for solving optimization problems using Genetic Algorithms. Here it is: http://create-technology.blogspot.ro/2015/03/a-genetic-algorithm-for-solving.html
It should be very easy to follow.
I've got a system that takes 15 points out of a 17 by 17 grid as input (order doesn't matter), and generates a single scalar as output. The system is not representable by a formal function.
The goal is to find the optimal 15 points so that the output scalar is minimum. Solving this problem exhaustively simply takes too much time to be practical as each run takes 14 seconds.
I've started taking a machine learning course online. But this problem does seem to be rather unsophisticated and I wonder if anyone can point me to the right direction. Any help is greatly appreciated!
Use simulated annealing. I guess this will be close to optimal here.
Therefore, start with a random distribution of the 15 points. Then, in each iteration change one and accept the new state if the resulting scalar value is lower. If it is larger, accept with a certain probability (a Boltzmann factor). Eventually you have to try this for a small number of randomly chosen initial states and afterwards accept the lowest value.
and thanks for reading my thread.
I have read some of the previous posts on formatting/normalising input data for a Neural Network, but cannot find something that addresses my queries specifically. I apologise for the long post.
I am attempting to build a radial basis function network for analysing horse racing data. I realise that this has been done before, but the data that I have is "special" and I have a keen interest in racing/sportsbetting/programming so would like to give it a shot!
Whilst I think I understand the principles for the RBFN itself, I am having some trouble understanding the normalisation/formatting/scaling of the input data so that it is presented in a "sensible manner" for the network, and I am not sure how I should formulate the output target values.
For example, in my data I look at the "Class change", which compares the class of race that the horse is running in now compared to the race before, and can have a value between -5 and +5. I expect that I need to rescale these to between -1 and +1 (right?!), but I have noticed that many more runners have a class change of 1, 0 or -1 than any other value, so I am worried about "over-representation". It is not possible to gather more data for the higher/lower class changes because thats just 'the way the data comes'. Would it be best to use the data as-is after scaling, or should I trim extreme values, or something else?
Similarly, there are "continuous" inputs - like the "Days Since Last Run". It can have a value between 1 and about 1000, but values in the range of 10-40 vastly dominate. I was going to scale these values to be between 0 and 1, but even if I trim the most extreme values before scaling, I am still going to have a huge representation of a certain range - is this going to cause me an issue? How are problems like this usually dealt with?
Finally, I am having trouble understanding how to present the "target" values for training to the network. My existing results data has the "win/lose" (0 or 1?) and the odds at which the runner won or lost. If I just use the "win/lose", it treats all wins and loses the same when really they're not - I would be quite happy with a network that ignored all the small winners but was highly profitable from picking 10-1 shots. Similarly, a network could be forgiven for "losing" on a 20-1 shot but losing a bet at 2/5 would be a bad loss. I considered making the results (+1 * odds) for a winner and (-1 / odds) for a loser to capture the issue above, but this will mean that my results are not a continuous function as there will be a "discontinuity" between short price winners and short price losers.
Should I have two outputs to cover this - one for bet/no bet, and another for "stake"?
I am sorry for the flood of questions and the long post, but this would really help me set off on the right track.
Thank you for any help anyone can offer me!
Kind regards,
Paul
The documentation that came with your RBFN is a good starting point to answer some of these questions.
Trimming data aka "clamping" or "winsorizing" is something I use for similar data. For example "days since last run" for a horse could be anything from just one day to several years but tends to centre in the region of 20 to 30 days. Some experts use a figure of say 63 days to indicate a "spell" so you could have an indicator variable like "> 63 =1 else 0" for example. One clue is to look at outliers say the upper or lower 5% of any variable and clamp these.
If you use odds/dividends anywhere make sure you use the probabilities ie 1/(odds+1) and a useful idea is to normalize these to 100%.
The odds or parimutual prices tend to swamp other predictors so one technique is to develop separate models, one for the market variables (the market model) and another for the non-market variables (often called the "fundamental" model).
I have in game currency in my game. For a user to buy the next upgrade I currently use a very simple method whereby the Nth upgrade costs N*1000 coins.
Im not a massive fan of using this at the moment as I'd like it to be a bit easier to start off with and possibly scale better so its not quite as hard to get upgrades.
One solution would be to use Fibonnacci which gives great early results but would make later upgrades nigh on impossible.
Can anyone offer a solution as my maths knowledge is pretty limited
What about sigmoid function? It starts to rise slowly, then it rises nearly linearly and at the end it starts to slow down.
If you look at the graph at wolfram alpha, you can calculate your price like this:
price = a_bit_more_than_maximum_upgrade_price * sigmoid( x )
You have to choose what multiple of the maximum price will be the price of the starting upgrade, if you choose starting x=-4 you'll get some price less than 5% of maximum. Ending x could be equal to 4. You'll reach around 95% of maximum price. Then you have number of upgrades. You could calculate the input for sigmoid like this:
x = (upgrade_index / (number_of_upgrades-1)) * 8.0 - 4.0
Upgrade index is starting from zero and you have to have at least 2 upgrades :)
You can trim off last few digits or round them up to get nicer looking numbers.
This seems like a question more related for http://programmers.stackoverflow.com
But anyway, I would say try use an exponential function, something like
f(n) = 1000 * 1.1^n
Obviously once you have 100 or more upgrades the price gets a bit ridiculous, you can then perhaps use a condition to check if n is larger than a certain number, then resume with your linear function to calculate the price of the next upgrade.
Im trying to analyse data from cycle accidents in the UK to find statistical black spots. Here is the example of the data from another website. http://www.cycleinjury.co.uk/map
I am currently using SQLite to ~100k store lat / lon locations. I want to group nearby locations together. This task is called cluster analysis.
I would like simplify the dataset by ignoring isolated incidents and instead only showing the origin of clusters where more than one accident have taken place in a small area.
There are 3 problems I need to overcome.
Performance - How do I ensure finding nearby points is quick. Should I use SQLite's implementation of an R-Tree for example?
Chains - How do I avoid picking up chains of nearby points?
Density - How to take cycle population density into account? There is a far greater population density of cyclist in london then say Bristol, therefore there appears to be a greater number of backstops in London.
I would like to avoid 'chain' scenarios like this:
Instead I would like to find clusters:
London screenshot (I hand drew some clusters)...
Bristol screenshot - Much lower density - the same program ran over this area might not find any blackspots if relative density was not taken into account.
Any pointers would be great!
Well, your problem description reads exactly like the DBSCAN clustering algorithm (Wikipedia). It avoids chain effects in the sense that it requires them to be at least minPts objects.
As for the differences in densities across, that is what OPTICS (Wikipedia) is supposed do solve. You may need to use a different way of extracting clusters though.
Well, ok, maybe not 100% - you maybe want to have single hotspots, not areas that are "density connected". When thinking of an OPTICS plot, I figure you are only interested in small but deep valleys, not in large valleys. You could probably use the OPTICS plot an scan for local minima of "at least 10 accidents".
Update: Thanks for the pointer to the data set. It's really interesting. So I did not filter it down to cyclists, but right now I'm using all 1.2 million records with coordinates. I've fed them into ELKI for analysis, because it's really fast, and it actually can use the geodetic distance (i.e. on latitude and longitude) instead of Euclidean distance, to avoid bias. I've enabled the R*-tree index with STR bulk loading, because that is supposed to help to get the runtime down a lot. I'm running OPTICS with Xi=.1, epsilon=1 (km) and minPts=100 (looking for large clusters only). Runtime was around 11 Minutes, not too bad. The OPTICS plot of course would be 1.2 million pixels wide, so it's not really good for full visualization anymore. Given the huge threshold, it identified 18 clusters with 100-200 instances each. I'll try to visualize these clusters next. But definitely try a lower minPts for your experiments.
So here are the major clusters found:
51.690713 -0.045545 a crossing on A10 north of London just past M25
51.477804 -0.404462 "Waggoners Roundabout"
51.690713 -0.045545 "Halton Cross Roundabout" or the crossing south of it
51.436707 -0.499702 Fork of A30 and A308 Staines By-Pass
53.556186 -2.489059 M61 exit to A58, North-West of Manchester
55.170139 -1.532917 A189, North Seaton Roundabout
55.067229 -1.577334 A189 and A19, just south of this, a four lane roundabout.
51.570594 -0.096159 Manour House, Picadilly Line
53.477601 -1.152863 M18 and A1(M)
53.091369 -0.789684 A1, A17 and A46, a complex construct with roundabouts on both sides of A1.
52.949281 -0.97896 A52 and A46
50.659544 -1.15251 Isle of Wight, Sandown.
...
Note, these are just random points taken from the clusters. It may be sensible to compute e.g. cluster center and radius instead, but I didn't do that. I just wanted to get a glimpse of that data set, and it looks interesting.
Here are some screenshots, with minPts=50, epsilon=0.1, xi=0.02:
Notice that with OPTICS, clusters can be hierarchical. Here is a detail:
First, your example is quite misleading. You have two different sets of data, and you don't control the data. If it appears in a chain, then you will get a chain out.
This problem is not exactly suitable for a database. You'll have to write code or find a package that implements this algorithm on your platform.
There are many different clustering algorithms. One, k-means, is an iterative algorithm where you look for a fixed number of clusters. k-means requires a few complete scans of the data, and voila, you have your clusters. Indexes are not particularly helpful.
Another, which is usually appropriate on slightly smaller data sets, is hierarchical clustering -- you put the two closest things together, and then build the clusters. An index might be helpful here.
I recommend though that you peruse a site such as kdnuggets in order to see what software -- free and otherwise -- is available.