In Q-learning with function approximation, is it possible to avoid hand-crafting features? - machine-learning

I have little background knowledge of Machine Learning, so please forgive me if my question seems silly.
Based on what I've read, the best model-free reinforcement learning algorithm to this date is Q-Learning, where each state,action pair in the agent's world is given a q-value, and at each state the action with the highest q-value is chosen. The q-value is then updated as follows:
Q(s,a) = (1-α)Q(s,a) + α(R(s,a,s') + (max_a' * Q(s',a'))) where α is the learning rate.
Apparently, for problems with high dimensionality, the number of states become astronomically large making q-value table storage infeasible.
So the practical implementation of Q-Learning requires using Q-value approximation via generalization of states aka features. For example if the agent was Pacman then the features would be:
Distance to closest dot
Distance to closest ghost
Is Pacman in a tunnel?
And then instead of q-values for every single state you would only need to only have q-values for every single feature.
So my question is:
Is it possible for a reinforcement learning agent to create or generate additional features?
Some research I've done:
This post mentions A Geramifard's iFDD method
http://www.icml-2011.org/papers/473_icmlpaper.pdf
http://people.csail.mit.edu/agf/Files/13RLDM-GQ-iFDD+.pdf
which is a way of "discovering feature dependencies", but I'm not sure if that is feature generation, as the paper assumes that you start off with a set of binary features.
Another paper that I found was apropos is Playing Atari with Deep Reinforcement Learning, which "extracts high level features using a range of neural network architectures".
I've read over the paper but still need to flesh out/fully understand their algorithm. Is this what I'm looking for?
Thanks

It seems like you already answered your own question :)
Feature generation is not part of the Q-learning (and SARSA) algorithm. In a process which is called preprocessing you can however use a wide array of algorithms (of which you showed some) to generate/extract features from your data. Combining different machine learning algorithms results in hybrid architectures, which is a term you might look into when researching what works best for your problem.
Here is an example of using features with SARSA (which is very similar to Q-learning).
Whether the papers you cited are helpful for your scenario, you'll have to decide for yourself. As always with machine learning, your approach is highly problem-dependent. If you're in robotics and it's hard to define discrete states manually, a neural network might be helpful. If you can think of heuristics by yourself (like in the pacman example) then you probably won't need it.

Related

Is reinforcement learning applicable to a RANDOM environment?

I have a fundamental question on the applicability of reinforcement learning (RL) on a problem we are trying to solve.
We are trying to use RL for inventory management - where the demand is entirely random (it probably has a pattern in real life but for now let us assume that we have been forced to treat as purely random).
As I understand, RL can help learn how to play a game (say chess) or help a robot learn to walk. But all games have rules and so does the ‘cart-pole’ (of OpenAI Gym) – there are rules of ‘physics’ that govern when the cart-pole will tip and fall over.
For our problem there are no rules – the environment changes randomly (demand made for the product).
Is RL really applicable to such situations?
If it does - then what will improve the performance?
Further details:
- The only two stimuli available from the ‘environment’ are the currently available level of product 'X' and the current demand 'Y'
- And the ‘action’ is binary - do I order a quantity 'Q' to refill or do I not (discrete action space).
- We are using DQN and an Adam optimizer.
Our results are poor - I admit I have trained only for about 5,000 or 10,000 - should I let it train on for days because it is a random environment?
thank you
Rajesh
You are saying random in the sense of non-stationary, so, no, RL is not the best here.
Reinforcement learning assumes your environment is stationary. The underlying probability distribution of your environment (both transition and reward function) must be held constant throughout the learning process.
Sure, RL and DRL can deal with some slightly non-stationary problems, but it struggles at that. Markov Decision Processes (MDPs) and Partially-Observable MDPs assume stationarity. So value-based algorithms, which are specialized in exploiting MDP-like environments, such as SARSA, Q-learning, DQN, DDQN, Dueling DQN, etc., will have a hard time learning anything in non-stationary environments. The more you go towards policy-based algorithms, such as PPO, TRPO, or even better gradient-free, such as GA, CEM, etc., the better chance you have as these algorithms don't try to exploit this assumption. Also, playing with the learning rate would be essential to make sure the agent never stops learning.
Your best bet is to go towards black-box optimization methods such as Genetic Algorithms, etc.
Randomness can be handled by replacing single average reward output with a distribution with possible values. By introducing a new learning rule, reflecting the transition from Bellman’s (average) equation to its distributional counterpart, the Value distribution approach has been able to surpass the performance of all other comparable approaches.
https://www.deepmind.com/blog/going-beyond-average-for-reinforcement-learning

Is supervised learning synonymous to classification and unsupervised learning synonymous to clustering?

I am a beginner in machine learning and recently read about supervised and unsupervised machine learning. It looks like supervised learning is synonymous to classification and unsupervised learning is synonymous to clustering, is it so?
No.
Supervised learning is when you know correct answers (targets). Depending on their type, it might be classification (categorical targets), regression (numerical targets) or learning to rank (ordinal targets) (this list is by no means complete, there might be other types that I either forgot or unaware of).
On the contrary, in unsupervised learning setting we don't know correct answers, and we try to infer, learn some structure from data. Be it cluster number or low-dimensional approximation (dimensionality reduction, actually, one might think of clusterization as of extreme 1D case of dimensionality reduction). Again, this might be far away from completeness, but the general idea is about hidden structure, that we try to discover from data.
Supervised learning is when you have labeled training data. In other words, you have a well-defined target to optimize your method for.
Typical (supervised) learning tasks are classification and regression: learning to predict categorial (classification), numerical (regression) values or ranks (learning to rank).
Unsupservised learning is an odd term. Because most of the time, the methods aren't "learning" anything. Because what would they learn from? You don't have training data?
There are plenty of unsupervised methods that don't fit the "learning" paradigm well. This includes dimensionality reduction methods such as PCA (which by far predates any "machine learning" - PCA was proposed in 1901, long before the computer!). Many of these are just data-driven statistics (as opposed to parameterized statistics). This includes most cluster analysis methods, outlier detection, ... for understanding these, it's better to step out of the "learning" mindset. Many people have trouble understanding these approaches, because they always think in the "minimize objective function f" mindset common in learning.
Consider for example DBSCAN. One of the most popular clustering algorithms. It does not fit the learning paradigm well. It can nicely be interpreted as a graph-theoretic construct: (density-) connected components. But it doesn't optimize any objective function. It computes the transitive closure of a relation; but there is no function maximized or minimized.
Similarly APRIORI finds frequent itemsets; combinations of items that occur more than minsupp times, where minsupp is a user parameter. It's an extremely simple definition; but the search space can be painfully large when you have large data. The brute-force approach just doesn't finish in acceptable time. So APRIORI uses a clever search strategy to avoid unnecessary hard disk accesses, computations, and memory. But there is no "worse" or "better" result as in learning. Either the result is correct (complete) or not - nothing to optimize on the result (only on the algorithm runtime).
Calling these methods "unsupervised learning" is squeezing them into a mindset that they don't belong into. They are not "learning" anything. Neither optimizes a function, or uses labels, or uses any kind of feedback. They just SELECT a certain set of objects from the database: APRIORI selects columns that frequently have a 1 at the same time; DBSCAN select connected components in a density graph. Either the result is correct, or not.
Some (but by far not all) unsupervised methods can be formalized as an optimization problem. At which point they become similar to popular supervised learning approaches. For example k-means is a minimization problem. PCA is a minimization problem, too - closely related to linear regression, actually. But it is the other way around. Many machine learning tasks are transformed into an optimization problem; and can be solved with general purpose statistical tools, which just happen to be highly popular in machine learning (e.g. linear programming). All the "learning" part is then wrapped into the way the data is transformed prior to feeding it into the optimizer. And in some cases, like for PCA, a non-iterative way to compute the optimum solution was found (in 1901). So in these cases, you don't need the usual optimization hammer at all.

What are some effective techniques for learning heuristic weights?

I have a minimax game playing program that sums together different heuristics to return a value for each state of the game. I would like to implement learning. I want the program to learn weights for each heuristic. What is the most effective means of having the program learn the weights for each heuristic? Of course, it would only know if a certain weight was effective for a certain heuristic after trying it. Is the only option some kind of trial and error system?
Thank you for your help!
I've not applied minimax much in practice - but in general its preferable to have an intrinsic measure of score/goodness/badness to base it off of. The first step would be to try and define such a score for you game - and expose that as an interface that is implemented for each supported game.
Is the only option some kind of trial and error system?
No! Genetic algorithms are popular for this kind of thing (at least among hobbyists), and can be used successfully for many problems (given sufficient time). You can find a lot of information related to this in early AI research, especially related to chess programs.
You can look up some of the research in hyperparameter optimization to find more machine learning style ways to do it. Unfortunately its not as well studied an area as it probably should be.
There are more possibilities depending on the specifics of the game being implemented / the nature of the heuristics.
Reinforcement Learning (RL), in particual Temporal Difference (TD) methods, deal with learning weights for heuristics in non-adversarial setting. How to learn weights for heuristics in a game setting, depends on what algorithms you use to play the game. The major classes of algorithms are alpha-beta minimax and UpperConfidenceTree. For minimax, you can look at the updates to values on the tree nodes as you increase the depth of the tree. I recommend starting by learning about RL-TD, and then reading Bootstrapping from Game Tree Search
by Joel Veness et. al.

What is machine learning? [closed]

Closed. This question is off-topic. It is not currently accepting answers.
Want to improve this question? Update the question so it's on-topic for Stack Overflow.
Closed 10 years ago.
Improve this question
What is machine learning ?
What does machine learning code do ?
When we say that the machine learns, does it modify the code of itself or it modifies history (database) which will contain the experience of code for given set of inputs?
What is a machine learning ?
Essentially, it is a method of teaching computers to make and improve predictions or behaviors based on some data. What is this "data"? Well, that depends entirely on the problem. It could be readings from a robot's sensors as it learns to walk, or the correct output of a program for certain input.
Another way to think about machine learning is that it is "pattern recognition" - the act of teaching a program to react to or recognize patterns.
What does machine learning code do ?
Depends on the type of machine learning you're talking about. Machine learning is a huge field, with hundreds of different algorithms for solving myriad different problems - see Wikipedia for more information; specifically, look under Algorithm Types.
When we say machine learns, does it modify the code of itself or it modifies history (Data Base) which will contain the experience of code for given set of inputs ?
Once again, it depends.
One example of code actually being modified is Genetic Programming, where you essentially evolve a program to complete a task (of course, the program doesn't modify itself - but it does modify another computer program).
Neural networks, on the other hand, modify their parameters automatically in response to prepared stimuli and expected response. This allows them to produce many behaviors (theoretically, they can produce any behavior because they can approximate any function to an arbitrary precision, given enough time).
I should note that your use of the term "database" implies that machine learning algorithms work by "remembering" information, events, or experiences. This is not necessarily (or even often!) the case.
Neural networks, which I already mentioned, only keep the current "state" of the approximation, which is updated as learning occurs. Rather than remembering what happened and how to react to it, neural networks build a sort of "model" of their "world." The model tells them how to react to certain inputs, even if the inputs are something that it has never seen before.
This last ability - the ability to react to inputs that have never been seen before - is one of the core tenets of many machine learning algorithms. Imagine trying to teach a computer driver to navigate highways in traffic. Using your "database" metaphor, you would have to teach the computer exactly what to do in millions of possible situations. An effective machine learning algorithm would (hopefully!) be able to learn similarities between different states and react to them similarly.
The similarities between states can be anything - even things we might think of as "mundane" can really trip up a computer! For example, let's say that the computer driver learned that when a car in front of it slowed down, it had to slow down to. For a human, replacing the car with a motorcycle doesn't change anything - we recognize that the motorcycle is also a vehicle. For a machine learning algorithm, this can actually be surprisingly difficult! A database would have to store information separately about the case where a car is in front and where a motorcycle is in front. A machine learning algorithm, on the other hand, would "learn" from the car example and be able to generalize to the motorcycle example automatically.
Machine learning is a field of computer science, probability theory, and optimization theory which allows complex tasks to be solved for which a logical/procedural approach would not be possible or feasible.
There are several different categories of machine learning, including (but not limited to):
Supervised learning
Reinforcement learning
Supervised Learning
In supervised learning, you have some really complex function (mapping) from inputs to outputs, you have lots of examples of input/output pairs, but you don't know what that complicated function is. A supervised learning algorithm makes it possible, given a large data set of input/output pairs, to predict the output value for some new input value that you may not have seen before. The basic method is that you break the data set down into a training set and a test set. You have some model with an associated error function which you try to minimize over the training set, and then you make sure that your solution works on the test set. Once you have repeated this with different machine learning algorithms and/or parameters until the model performs reasonably well on the test set, then you can attempt to use the result on new inputs. Note that in this case, the program does not change, only the model (data) is changed. Although one could, theoretically, output a different program, but that is not done in practice, as far as I am aware. An example of supervised learning would be the digit recognition system used by the post office, where it maps the pixels to labels in the set 0...9, using a large set of pictures of digits that were labeled by hand as being in 0...9.
Reinforcement Learning
In reinforcement learning, the program is responsible for making decisions, and it periodically receives some sort of award/utility for its actions. However, unlike in the supervised learning case, the results are not immediate; the algorithm could prescribe a large sequence of actions and only receive feedback at the very end. In reinforcement learning, the goal is to build up a good model such that the algorithm will generate the sequence of decisions that lead to the highest long term utility/reward. A good example of reinforcement learning is teaching a robot how to navigate by giving a negative penalty whenever its bump sensor detects that it has bumped into an object. If coded correctly, it is possible for the robot to eventually correlate its range finder sensor data with its bumper sensor data and the directions that sends to the wheels, and ultimately choose a form of navigation that results in it not bumping into objects.
More Info
If you are interested in learning more, I strongly recommend that you read Pattern Recognition and Machine Learning by Christopher M. Bishop or take a machine learning course. You may also be interested in reading, for free, the lecture notes from CIS 520: Machine Learning at Penn.
Machine learning is a scientific discipline that is concerned with the design and development of algorithms that allow computers to evolve behaviors based on empirical data, such as from sensor data or databases. Read more on Wikipedia
Machine learning code records "facts" or approximations in some sort of storage, and with the algorithms calculates different probabilities.
The code itself will not be modified when a machine learns, only the database of what "it knows".
Machine learning is a methodology to create a model based on sample data and use the model to make a prediction or strategy. It belongs to artificial intelligence.
Machine learning is simply a generic term to define a variety of learning algorithms that produce a quasi learning from examples (unlabeled/labeled). The actual accuracy/error is entirely determined by the quality of training/test data you provide to your learning algorithm. This can be measured using a convergence rate. The reason you provide examples is because you want the learning algorithm of your choice to be able to informatively by guidance make generalization. The algorithms can be classed into two main areas supervised learning(classification) and unsupervised learning(clustering) techniques. It is extremely important that you make an informed decision on how you plan on separating your training and test data sets as well as the quality that you provide to your learning algorithm. When you providing data sets you want to also be aware of things like over fitting and maintaining a sense of healthy bias in your examples. The algorithm then basically learns wrote to wrote on the basis of generalization it achieves from the data you have provided to it both for training and then for testing in process you try to get your learning algorithm to produce new examples on basis of your targeted training. In clustering there is very little informative guidance the algorithm basically tries to produce through measures of patterns between data to build related sets of clusters e.g kmeans/knearest neighbor.
some good books:
Introduction to ML (Nilsson/Stanford),
Gaussian Process for ML,
Introduction to ML (Alpaydin),
Information Theory Inference and Learning Algorithms (very useful book),
Machine Learning (Mitchell),
Pattern Recognition and Machine Learning (standard ML course book at Edinburgh and various Unis but relatively a heavy reading with math),
Data Mining and Practical Machine Learning with Weka (work through the theory using weka and practice in Java)
Reinforcement Learning there is a free book online you can read:
http://www.cs.ualberta.ca/~sutton/book/ebook/the-book.html
IR, IE, Recommenders, and Text/Data/Web Mining in general use alot of Machine Learning principles. You can even apply Metaheuristic/Global Optimization Techniques here to further automate your learning processes. e.g apply an evolutionary technique like GA (genetic algorithm) to optimize your neural network based approach (which may use some learning algorithm). You can approach it purely in form of a probablistic machine learning approach for example bayesian learning. Most of these algorithms all have a very heavy use of statistics. Concepts of convergence and generalization are important to many of these learning algorithms.
Machine learning is the study in computing science of making algorithms that are able to classify information they haven't seen before, by learning patterns from training on similar information. There are all sorts of kinds of "learners" in this sense. Neural networks, Bayesian networks, decision trees, k-clustering algorithms, hidden markov models and support vector machines are examples.
Based on the learner, they each learn in different ways. Some learners produce human-understandable frameworks (e.g. decision trees), and some are generally inscrutable (e.g. neural networks).
Learners are all essentially data-driven, meaning they save their state as data to be reused later. They aren't self-modifying as such, at least in general.
I think one of the coolest definitions of machine learning that I've read is from this book by Tom Mitchell. Easy to remember and intuitive.
A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E
Shamelessly ripped from Wikipedia: Machine learning is a scientific discipline that is concerned with the design and development of algorithms that allow computers to evolve behaviors based on empirical data, such as from sensor data or databases.
Quite simply, machine learning code accomplishes a machine learning task. That can be a number of things from interpreting sensor data to a genetic algorithm.
I would say it depends. No, modifying code is not normal, but is not outside the realm of possibility. I would also not say that machine learning always modifies a history. Sometimes we have no history to build off of. Sometime we simply want to react to the environment, but not actually learn from our past experiences.
Basically, machine learning is a very wide-open discipline that contains many methods and algorithms that make it impossible for there to be 1 answer to your 3rd question.
Machine learning is a term that is taken from the real world of a person, and applied on something that can't actually learn - a machine.
To add to the other answers - machine learning will not (usually) change the code, but it might change it's execution path and decision based on previous data or new gathered data and hence the "learning" effect.
there are many ways to "teach" a machine - you give weights to many parameter of an algorithm, and then have the machine solve it for many cases, each time you give her a feedback about the answer and the machine adjusts the weights according to how close the machine answer was to your answer or according to the score you gave it's answer, or according to some results test algorithm.
This is one way of learning and there are many more...

Best approach to what I think is a machine learning problem [closed]

Closed. This question is opinion-based. It is not currently accepting answers.
Want to improve this question? Update the question so it can be answered with facts and citations by editing this post.
Closed 4 years ago.
Improve this question
I am wanting some expert guidance here on what the best approach is for me to solve a problem. I have investigated some machine learning, neural networks, and stuff like that. I've investigated weka, some sort of baesian solution.. R.. several different things. I'm not sure how to really proceed, though. Here's my problem.
I have, or will have, a large collection of events.. eventually around 100,000 or so. Each event consists of several (30-50) independent variables, and 1 dependent variable that I care about. Some independent variables are more important than others in determining the dependent variable's value. And, these events are time relevant. Things that occur today are more important than events that occurred 10 years ago.
I'd like to be able to feed some sort of learning engine an event, and have it predict the dependent variable. Then, knowing the real answer for the dependent variable for this event (and all the events that have come along before), I'd like for that to train subsequent guesses.
Once I have an idea of what programming direction to go, I can do the research and figure out how to turn my idea into code. But my background is in parallel programming and not stuff like this, so I'd love to have some suggestions and guidance on this.
Thanks!
Edit: Here's a bit more detail about the problem that I'm trying to solve: It's a pricing problem. Let's say that I'm wanting to predict prices for a random comic book. Price is the only thing I care about. But there are lots of independent variables one could come up with. Is it a Superman comic, or a Hello Kitty comic. How old is it? What's the condition? etc etc. After training for a while, I want to be able to give it information about a comic book I might be considering, and have it give me a reasonable expected value for the comic book. OK. So comic books might be a bogus example. But you get the general idea. So far, from the answers, I'm doing some research on Support vector machines and Naive Bayes. Thanks for all of your help so far.
Sounds like you're a candidate for Support Vector Machines.
Go get libsvm. Read "A practical guide to SVM classification", which they distribute, and is short.
Basically, you're going to take your events, and format them like:
dv1 1:iv1_1 2:iv1_2 3:iv1_3 4:iv1_4 ...
dv2 1:iv2_1 2:iv2_2 3:iv2_3 4:iv2_4 ...
run it through their svm-scale utility, and then use their grid.py script to search for appropriate kernel parameters. The learning algorithm should be able to figure out differing importance of variables, though you might be able to weight things as well. If you think time will be useful, just add time as another independent variable (feature) for the training algorithm to use.
If libsvm can't quite get the accuracy you'd like, consider stepping up to SVMlight. Only ever so slightly harder to deal with, and a lot more options.
Bishop's Pattern Recognition and Machine Learning is probably the first textbook to look to for details on what libsvm and SVMlight are actually doing with your data.
If you have some classified data - a bunch of sample problems paired with their correct answers -, start by training some simple algorithms like K-Nearest-Neighbor and Perceptron and seeing if anything meaningful comes out of it. Don't bother trying to solve it optimally until you know if you can solve it simply or at all.
If you don't have any classified data, or not very much of it, start researching unsupervised learning algorithms.
It sounds like any kind of classifier should work for this problem: find the best class (your dependent variable) for an instance (your events). A simple starting point might be Naive Bayes classification.
This is definitely a machine learning problem. Weka is an excellent choice if you know Java and want a nice GPL lib where all you have to do is select the classifier and write some glue. R is probably not going to cut it for that many instances (events, as you termed it) because it's pretty slow. Furthermore, in R you still need to find or write machine learning libs, though this should be easy given that it's a statistical language.
If you believe that your features (independent variables) are conditionally independent (meaning, independent given the dependent variable), naive Bayes is the perfect classifier, as it is fast, interpretable, accurate and easy to implement. However, with 100,000 instances and only 30-50 features you can likely implement a fairly complex classification scheme that captures a lot of the dependency structure in your data. Your best bet would probably be a support vector machine (SMO in Weka) or a random forest (Yes, it's a silly name, but it helped random forest catch on.) If you want the advantage of easy interpretability of your classifier even at the expense of some accuracy, maybe a straight up J48 decision tree would work. I'd recommend against neural nets, as they're really slow and don't usually work any better in practice than SVMs and random forest.
The book Programming Collective Intelligence has a worked example with source code of a price predictor for laptops which would probably be a good starting point for you.
SVM's are often the best classifier available. It all depends on your problem and your data. For some problems other machine learning algorithms might be better. I have seen problems that neural networks (specifically recurrent neural networks) were better at solving. There is no right answer to this question since it is highly situationally dependent but I agree with dsimcha and Jay that SVM's are the right place to start.
I believe your problem is a regression problem, not a classification problem. The main difference: In classification we are trying to learn the value of a discrete variable, while in regression we are trying to learn the value of a continuous one. The techniques involved may be similar, but the details are different. Linear Regression is what most people try first. There are lots of other regression techniques, if linear regression doesn't do the trick.
You mentioned that you have 30-50 independent variables, and some are more important that the rest. So, assuming that you have historical data (or what we called a training set), you can use PCA (Principal Componenta Analysis) or other dimensionality reduction methods to reduce the number of independent variables. This step is of course optional. Depending on situations, you may get better results by keeping every variables, but add a weight to each one of them based on relevant they are. Here, PCA can help you to compute how "relevant" the variable is.
You also mentioned that events that are occured more recently should be more important. If that's the case, you can weight the recent event higher and the older event lower. Note that the importance of the event doesn't have to grow linearly accoding to time. It may makes more sense if it grow exponentially, so you can play with the numbers here. Or, if you are not lacking of training data, perhaps you can considered dropping off data that are too old.
Like Yuval F said, this does look more like a regression problem rather than a classification problem. Therefore, you can try SVR (Support Vector Regression), which is regression version of SVM (Support Vector Machine).
some other stuff you can try are:
Play around with how you scale the value range of your independent variables. Say, usually [-1...1] or [0...1]. But you can try other ranges to see if they help. Sometimes they do. Most of the time they don't.
If you suspect that there are "hidden" feature vector with a lower dimension, say N << 30 and it's non-linear in nature, you will need non-linear dimensionality reduction. You can read up on kernel PCA or more recently, manifold sculpting.
What you described is a classic classification problem. And in my opinion, why code fresh algorithms at all when you have a tool like Weka around. If I were you, I would run through a list of supervised learning algorithms (I don't completely understand whey people are suggesting unsupervised learning first when this is so clearly a classification problem) using 10-fold (or k-fold) cross validation, which is the default in Weka if I remember, and see what results you get! I would try:
-Neural Nets
-SVMs
-Decision Trees (this one worked really well for me when I was doing a similar problem)
-Boosting with Decision trees/stumps
-Anything else!
Weka makes things so easy and you really can get some useful information. I just took a machine learning class and I did exactly what you're trying to do with the algorithms above, so I know where you're at. For me the boosting with decision stumps worked amazingly well. (BTW, boosting is actually a meta-algorithm and can be applied to most supervised learning algs to usually enhance their results.)
A nice thing aobut using Decision Trees (if you use the ID3 or similar variety) is that it chooses the attributes to split on in order of how well they differientiate the data - in other words, which attributes determine the classification the quickest basically. So you can check out the tree after running the algorithm and see what attribute of a comic book most strongly determines the price - it should be the root of the tree.
Edit: I think Yuval is right, I wasn't paying attention to the problem of discretizing your price value for the classification. However, I don't know if regression is available in Weka, and you can still pretty easily apply classification techniques to this problem. You need to make classes of price values, as in, a number of ranges of prices for the comics, so that you can have a discrete number (like 1 through 10) that represents the price of the comic. Then you can easily run classification it.

Resources