Some of the strategies I can think of for implementing an AI player for simple 2-player games like Tic-tac-toe, Connect 4 etc. are:
Random play
Use of a heuristic (e.g. play the center or corners when possible)
Minimax
Monte Carlo methods
Are there any other approaches which are commonly used please?
The list of approaches you have is a reasonable start - especially for two-player perfect information games. If you allow a broader range of games you get a broader set of algorithms:
Learning algorithm (either reinforcement learning or supervised learning) can be used for play on their own, although they are often combined with some type of search for even stronger game play.
Expectiminimax is used in games with chance elements but no hidden information.
Counter-factual Regret (CFR) is used for computing Nash equilibria in games like Poker with hidden information. (Fictitious play is a similar alternate.)
Perfect-Information Monte-Carlo (PIMC) is an approximation algorithm for games with imperfect information that can be used on top of other search algorithms. This is usually used for trick-based card games.
Multi-player games are usually based on the max^n algorithm instead of minimax. (There is a similar variant of MCTS.)
When you get to more complex games, there are a broader range of algorithms available because they need to deal with the complexities of a specific game in different ways.
I want to develop a two player game with imperfect information - "Stratego".
The game is "somewhat" like chess but initially we don't know anything about the ranks of the opponent's pieces. When a piece attacks or is attacked by some opponent's piece, their ranks are revealed and the higher rank piece kills/captures the lower rank piece.
More detail on the game can be found here.
I did a little research. I read "Opponent Modeling in Stratego" by J.A. Stankiewicz. But I couldn't find a complete tutorial on how to develop the game. I have successfully developed before a two player game - "Othello" a.k.a. Reversi, and I'm familiar with MINIMAX algorithm and alpha-beta pruning.
I found somewhere that Monte-Carlo Tree Search is also used in developing zero-sum two player games. Can it be used for games like stratego? Can I get a complete tutorial for the same?
Any other tutorial not involving Monte-Carlo Tree Search would also be useful :)
I think MCTS would have a difficult time in Stratego since the initial spreading function is so large while the best play is very dependent on the ground-truth of the game. That is to say, MCTS would, in the best case, give you a play that's statistically good amongst all the possible variations of your opponent's pieces, but the best next move is highly dependent on which particular variation they've chosen.
I'm still developing a solid understanding of MCTS, but it seems to me that MCTS does not do well in games where multi-round deceptive play involving hidden information is important (poker, canonically, but stratego, I would say, also). In such games, you really need to develop a model of the other player(s) situation/strategy and MCTS by its nature is going to give you an answer that is statistically related to all trees, not just the ground-truth tree.
MCTS works fine with games involving large amounts of chance (backgammon and other board games involving dice and many card games) and seems to me an excellent general-purpose solution that could be rapidly adopted to a large number of modern "European-style" board games. (The interesting thing with those is that although they involve "deceptive strategy" they generally involve relatively little hidden information.)
I don't know of any MCTS for incomplete information off the top of my had, and it seems like it would take substantial modification to the algorithm to get it to work.
Even in a very restricted type of Stratego where there are only ten pieces on each side, only two types of piece, and only one of the "stronger" piece, you're still playing one of ten possible actual games. In a full game of stratego there is far more uncertainty than that because of the large number of combinations of starting position, which all look alike.
It seems like you would also have to augment the algorithm to capture "revealed knowledge," as it happens, e.g., in our toy example, every encounter between pieces reveals some information about the enemy position.
It seems like it would be interesting to try, but only for a very restricted Stratego-like problem at first, and with the understanding that off the shelf MCTS is not sufficient and that you'd have to think carefully and deeply about the right extensions to the algorithm.
For my bachelor's thesis I want to write a genetic algorithm that learns to play the game of Stratego (if you don't know this game, it's probably safe to assume I said chess). I haven't ever before done actual AI projects, so it's an eye-opener to see how little I actually know of implementing things.
The thing I'm stuck with is coming up with a good representation for an actual strategy. I'm probably making some thinking error, but some problems I encounter:
I don't assume you would have a representation containing a lot of
transitions between board positions, since that would just be
bruteforcing it, right?
What could branches of a decision tree look
like? Any representation I come up with don't have interchangeable
branches... If I were to use a bit string, which is apparently also
common, what would the bits represent?
Do I assign scores to the distance between certain pieces? How would I represent that?
I think I ought to know these things after three+ years of study, so I feel pretty stupid - this must look likeI have no clue at all. Still, any help or tips on what to Google would be appreciated!
I think, you could define a decision model and then try to optimize the parameters of that model. You can create multi-stage decision models also. I once did something similar for solving a dynamic dial-a-ride problem (paper here) by modeling it as a two stage linear decision problem. To give you an example, you could:
For each of your figures decide which one is to move next. Each figure is characterized by certain features derived from its position on the board, e.g. ability to make a score, danger, protecting x other figures, and so on. Each of these features can be combined (e.g. in a linear model, through a neural network, through a symbolic expression tree, a decision tree, ...) and give you a rank on which figure to act next with.
Acting with the figure you selected. Again there are a certain number of actions that can be taken, each has certain features. Again you can combine and rank them and one action will have the highest priority. This is the one you choose to perform.
The features you extract can be very simple or insanely complex, it's up to what you think will work best vs what takes how long to compute.
To evaluate and improve the quality of your decision model you can then simulate these decisions in several games against opponents and train the parameters of the model that combines these features to rank the moves (e.g. using a GA). This way you tune the model to win as many games as possible against the specified opponents. You can test the generality of that model by playing against opponents it has not seen before.
As Mathew Hall just said, you can use GP for this (if your model is a complex rule), but this is just one kind of model. In my case a linear combination of the weights did very well.
Btw, if you're interested we've also got a software on heuristic optimization which provides you with GA, GP and that stuff. It's called HeuristicLab. It's GPL and open source, but comes with a GUI (Windows). We've some Howto on how to evaluate the fitness function in an external program (data exchange using protocol buffers), so you can work on your simulation and your decision model and let the algorithms present in HeuristicLab optimize your parameters.
Vincent,
First, don't feel stupid. You've been (I infer) studying basic computer science for three years; now you're applying those basic techniques to something pretty specialized-- a particular application (Stratego) in a narrow field (artificial intelligence.)
Second, make sure your advisor fully understands the rules of Stratego. Stratego is played on a larger board, with more pieces (and more types of pieces) than chess. This gives it a vastly larger space of legal positions, and a vastly larger space of legal moves. It is also a game of hidden information, increasing the difficulty yet again. Your advisor may want to limit the scope of the project, e.g., concentrate on a variant with full observation. I don't know why you think this is simpler, except that the moves of the pieces are a little simpler.
Third, I think the right thing to do at first is to take a look at how games in general are handled in the field of AI. Russell and Norvig, chapters 3 (for general background) and 5 (for two player games) are pretty accessible and well-written. You'll see two basic ideas: One, that you're basically performing a huge search in a tree looking for a win, and two, that for any non-trivial game, the trees are too large, so you search to a certain depth and then cop out with a "board evaluation function" and look for one of those. I think your third bullet point is in this vein.
The board evaluation function is the magic, and probably a good candidate for using either a genetic algorithm, or a genetic program, either of which might be used in conjunction with a neural network. The basic idea is that you are trying to design (or evolve, actually) a function that takes as input a board position, and outputs a single number. Large numbers correspond to strong positions, and small numbers to weak positions. There is a famous paper by Chellapilla and Fogel showing how to do this for a game of Checkers:
http://library.natural-selection.com/Library/1999/Evolving_NN_Checkers.pdf
I think that's a great paper, tying three great strands of AI together: Adversarial search, genetic algorithms, and neural networks. It should give you some inspiration about how to represent your board, how to think about board evaluations, etc.
Be warned, though, that what you're trying to do is substantially more complex than Chellapilla and Fogel's work. That's okay-- it's 13 years later, after all, and you'll be at this for a while. You're still going to have a problem representing the board, because the AI player has imperfect knowledge of its opponent's state; initially, nothing is known but positions, but eventually as pieces are eliminated in conflict, one can start using First Order Logic or related techniques to start narrowing down individual pieces, and possibly even probabilistic methods to infer information about the whole set. (Some of these may be beyond the scope of an undergrad project.)
The fact you are having problems coming up with a representation for an actual strategy is not that surprising. In fact I would argue that it is the most challenging part of what you are attempting. Unfortunately, I haven't heard of Stratego so being a bit lazy I am going to assume you said chess.
The trouble is that a chess strategy is rather a complex thing. You suggest in your answer containing lots of transitions between board positions in the GA, but a chess board has more possible positions than the number of atoms in the universe this is clearly not going to work very well. What you will likely need to do is encode in the GA a series of weights/parameters that are attached to something that takes in the board position and fires out a move, I believe this is what you are hinting at in your second suggestion.
Probably the simplest suggestion would be to use some sort of generic function approximation like a neural network; Perceptrons or Radial Basis Functions are two possibilities. You can encode weights for the various nodes into the GA, although there are other fairly sound ways to train a neural network, see Backpropagation. You could perhaps encode the network structure instead/as well, this also has the advantage that I am pretty sure a fair amount of research has been done into developing neural networks with a genetic algorithm so you wouldn't be starting completely from scratch.
You still need to come up with how you are going to present the board to the neural network and interpret the result from it. Especially, with chess you would have to take note that a lot of moves will be illegal. It would be very beneficial if you could encode the board and interpret the result such that only legal moves are presented. I would suggest implementing the mechanics of the system and then playing around with different board representations to see what gives good results. A few ideas top of the head ideas to get you started could be, although I am not really convinced any of them are especially great ways to do this:
A bit string with all 64 squares one after another with a number presenting what is present in each square. Most obvious, but probably a rather bad representation as a lot of work will be required to filter out illegal moves.
A bit string with all 64 squares one after another with a number presenting what can move to each square. This has the advantage of embodying the covering concept of chess where you what to gain as much coverage of the board with your pieces as possible, but still has problems with illegal moves and dealing with friendly/enemy pieces.
A bit string with all 32 pieces one after another with a number presenting the location of that piece in each square.
In general though I would suggest that chess is rather a complex game to start with, I think it will be rather hard to get something playing to standard which is noticeably better than random. I don't know if Stratego is any simpler, but I would strongly suggest you opt for a fairly simple game. This will let you focus on getting the mechanics of the implementation correct and the representation of the game state.
Anyway hope that is of some help to you.
EDIT: As a quick addition it is worth looking into how standard chess AI's work, I believe most use some sort of Minimax system.
When you say "tactic", do you mean you want the GA to give you a general algorithm to play the game (i.e. evolve an AI) or do you want the game to use a GA to search the space of possible moves to generate a move at each turn?
If you want to do the former, then look into using Genetic programming (GP). You could try to use it to produce the best AI you can for a fixed tree size. JGAP already comes with support for GP as well. See the JGAP Robocode example for an instance of this. This approach does mean you need a domain specific language for a Stratego AI, so you'll need to think carefully how you expose the board and pieces to it.
Using GP means your fitness function can just be how well the AI does at a fixed number of pre-programmed games, but that requires a good AI player to start with (or a very patient human).
#DonAndre's answer is absolutely correct for movement. In general, problems involving state-based decisions are hard to model with GAs, requiring some form of GP (either explicit or, as #DonAndre suggested, trees that are essentially declarative programs).
A general Stratego player seems to me quite challenging, but if you have a reasonable Stratego playing program, "Setting up your Stratego board" would be an excellent GA problem. The initial positions of your pieces would be the phenotype and the outcome of the external Stratego-playing code would be the fitness. It is intuitively likely that random setups would be disadvantaged versus setups that have a few "good ideas" and that small "good ideas" could be combined into fitter-and-fitter setups.
...
On the general problem of what a decision tree, even trying to come up with a simple example, I kept finding it hard to come up with a small enough example, but maybe in the case where you are evaluation whether to attack a same-ranked piece (which, IIRC destroys both you and the other piece?):
double locationNeed = aVeryComplexDecisionTree();
if(thatRank == thisRank){
double sacrificeWillingness = SACRIFICE_GENETIC_BASE; //Assume range 0.0 - 1.0
double sacrificeNeed = anotherComplexTree(); //0.0 - 1.0
double sacrificeInContext = sacrificeNeed * SACRIFICE_NEED_GENETIC_DISCOUNT; //0.0 - 1.0
if(sacrificeInContext > sacrificeNeed){
...OK, this piece is "willing" to sacrifice itself
One way or the other, the basic idea is that you'd still have a lot of coding of Stratego-play, you'd just be seeking places where you could insert parameters that would change the outcome. Here I had the idea of a "base" disposition to sacrifice itself (presumably higher in common pieces) and a "discount" genetically-determined parameter that would weight whether the piece would "accept or reject" the need for a sacrifice.
I have a typical AI Problem to solve. Customers gonna submit comments about a product. I have to be able to create a program that classify these comment as either good,bad or neutral.
Surely, Neural Network gonna play a great role in it.
Also, I think fuzzy logic can play some role in it. Such as how far a comment is good,bad or neutral!!
Some more ideas about how to solve it??
This problem is usually referred to as Sentiment Analysis. You can check out the wikipedia entry about Sentiment Analysis for a brief review, or Liu Bing's page on sentiment analysis for more detailed resources and tutorials.
You can use some form of supervised learning.
The most important thing for classification is then choosing the right features. "Features" means you extract some values from the review that still capture the essence with respect to the classification task. Things that come to my mind are
number of words
average number of words per sentence
number of words from some set like {crap, shit, damn, viagra, ...}
Then you can use any available machine learning algorithm (neural networks, SVM) and train a classifier given you have enough reviews that are labeled with good/neutral/bad.
Neural networks would certainly work for it, however I would be supicious about introducing new words, and languages. I would go for a Bayes net approach for determining the probability of being in a "good/neutral/bad" state. You should consider cleaning the data [stemming, etc] before putting it through the bayes net.
Additionally: The meta attributes [what ziggy mentioned] are more of an indicator to boost the performance of the approach you take.
EDIT: Bayes-Nets are a form of supervised learning.
I have coded some AI for connect-4. I would like to adjust the weights in certain evaluation functions. I have limited time and hardware so my question is this: Is it very bad with respect to quality of the evaluation to perform the "training" and adjustment of weights based on results obtained from using lower-depth searches than those that will be used when the AI has to perform its best later in a situation where it has more time and hence can search the game tree at deeper levels ?
Well, if you have limited time, you have to adjust the weights using a lower depth search. This is very similar to the idea of temporal difference learning that is used to make games like backgammon. That is, you might want to use the idea of reinforcement learning. Temporal difference is a flavour of reinforcement learning.