There are a number of questions to ask:
- do you have the appropriate number of neurons in each layer
- are you using the appropriate types of transfer functions?
- are you using the appropriate type of learning algorithm
- do you have a large enough sample size
- can you confirm that your samples have the right sorts of relationship with each other to be informative? (not redundant, of relevant dimension, etc...)
What can you give in the way of ephemeris? Can you tell us something about the nature of the data?
You could make a gradient boosted tree of neural networks.
You asked what happens if you stop early.
You can try yourself. Run 300x where you start with random initialized weights, and then stop at a specified number of iterations, lets say 100. At that point compute your ensemble error, your training-subset error, and your test-set error. Repeat. After you have 300 values to tell you what the error is, you can get an idea of your error distribution given 100 learning iterations. If you like, you can then sample that distribution at several other values of learning. I suggest 200, 500, and 1000 iterations. This will give you an idea how your SNR changes over time. A plot of the SNR vs iteration count can give you an idea about "cliffs" or "good enough". Sometimes there are cliffs where error collapses. Sometimes the error is acceptable at that point.
It takes "relatively simple" data or "pretty good" luck for your system to consistently converge in under 100 iterations. Both of which are not about repeatability nor are they generalizable.
Why are you thinking in terms of weights converging and not error being below a particular threshold. Have you ever heard of a voting paradox? (link) When you have cyclic interactions in your system (like feedback in Neural Networks) then you can have voting paradoxes - coupled changes. I don't know if weights alone is a sufficient indicator for convergence of the network.
You can think of the weights as a space. It has more than 3 dimensions, but it is still a space. In the "centroid" of that space is your "best fit" region. Far from the centroid is a less good fit. You can think of the current setting of your weights as a single point in that space.
Now you don't know where the "good" actually is. What you do have is a local "slope". You can perform gradient descent toward local "better" given where your point is right now. It doesn't tell you the "universal" better, but local is better than nothing.
So you start iterating, walking downhill toward that valley of betterness. You iterate until you think you are done. Maybe the value of your weights are large. Maybe they are bouncing all over the place. Maybe the compute is "taking too long". You want to be done.
So how do you know whether where you are is "good enough"?
Here is a quick test that you could do:
Take 30 uniform random subsets of the data (like a few percent of the data each) and retrain the network on them. It should be much faster. Observe how long it takes them to converge and compare it with the convergence history of the big set. Test the error of the network for the entire data on these subsets and see how that distribution of errors compares to your big error. Now bump the subset sizes up to maybe 5% of your data and repeat. See what this teaches you.
This is a variation on particle swarm optimization(see reference) modeled on how honeybees make decisions based on scouting.
You asked what happens if weights do not converge.
Neural Networks are one tool. They are not the only tool. There are others. I would look at using one of them.
I work in terms of information criteria, so I look at both the weights (parameter count) and the error. You might try one of those.
There are some types of preprocessing that can be useful. Center and Scale. Rotate using principal components. If you look at the eigenvalues in your principal components you can use skree plot rules to estimate the dimension of your data. Reducing the dimension can improve convergence. If you know something about the 'underlying physics' then you can smooth or filter the data to remove noise. Sometimes convergence is about noise in the system.
I find the idea of Compressed sensing to be interesting. It can allow radical sub-sampling of some systems without loss of generalization. I would look at some bootstrap re-sampled statistics and distributions of your data to determine if and at what level of sub-sampling the training set becomes representative. This gives you some measure of the "health" of your data.
Sometimes it is a good thing that they not converge
Have you ever heard of a voting paradox? You might think of it as a higher-count cousin to a two-way impasse. It is a loop. In a 2-person voting paradox the first person wants candidate "A" while the second wants candidate "B" (or not-A or such). The important part is that you can think of it as a loop.
Loops are important in neural networks. Feedback. Recursion. It made the perceptron able to resolve XOR-like problems. It makes loops, and sometimes the loops can act like the voting paradox, where they will keep changing weights if you had infinite iterations. They aren't meant to converge because it isn't the individual weight that matters but the interaction of the weights in the loop.
Note:
Using only 500 iterations can be a problem. I have had NN's where 10,000 iterations was barely enough. The number of iterations to be "enough" is dependent, as I have already indicated, on data, NN-topology, node-transfer functions, learning/training function, and even computer hardware. You have to have a good understanding of how they all interact with your iteration count before saying that there have been "enough" or "too many" iterations. Other considerations like time, budget, and what you want to do with the NN when you are done training it should also be considered.
Chen, R. B., Chang, S. P., Wang, W., & Wong, W. K., (2011, September). Optimal Experimental Designs via Particle Swarm Optimization Methods (preprint), Retrieved March 25, 2012, from http://www.math.ntu.edu.tw/~mathlib/preprint/2011-03.pdf
Q1. You're definitely on the right track, but a few changes could help immensely. Some people use one output unit per action so that they only have to run their network once for action selection (you have to run your net once for each possible action). But this shouldn't make a difference with regards to learning, and is only worth implementing if you're planning on scaling your model up significantly.
Q2. Generally, people use a linear activation function for the last layer of their neural network, especially for reinforcement learning. There are a variety of reasons for this, but the most pertinent is that a linear activation function allows you to represent the full range of real numbers as your output. Thus, even if you don't know the bounds on the rewards for your task, you're still guaranteed to be able to represent that range.
Q3. Unfortunately, the theoretical guarantees for combining neural networks (and non-linear function approximation for generally) with reinforcement learning are pretty much non-existent. There are a few fancier versions of reinforcement learning (mainly out of the Sutton lab) that can make the sorts of convergence claims you mention, but I've never really seen those algorithms applied 'in the wild'. The reason for this is that while great performance can't be promised, it is typically obtained in practice, with proper attention to hyper-parameters and initial conditions.
One final point that bears mentioning for neural networks in general: don't use sigmoid activation functions for networks with a lot of hidden layers! They're cursed with the problem of 'vanishing gradients'; the error signal hardly reaches the earlier layers (looking at the derivative of the function should make it clear why this is the case). Instead, try using rectified linear units (RELU) or 'soft plus' units, as they generally exhibit much better performance in deep networks.
See this paper for a great implementation of neural networks trained with reinforcement learning:
Mnih, Volodymyr, et al. "Playing Atari with deep reinforcement learning." arXiv preprint arXiv:1312.5602 (2013).
Best Answer
Setting a seed is a good start. It should ensure that you will always get the same results from the same code. It would also be worth noting the version of R and the version of nnet that you're using (as well as any other relevant packages), in case something changes in later versions. If you want to be really careful, you could even archive the current versions so you can go back to them if CRAN ever goes down.
The best evaluation approach usually involves some kind of out-of-sample prediction. Cross-validation is one very good option, as is a simple holdout approach. The
caretpackage automates some of these tools. You have so much data that holding some of it out probably won't hurt you much.nnetalways has one hidden layer. Perhaps you meant the number of hidden units? Cross-validation can be a good option here as well. Just make sure that you don't use the same data for improving the model fit that you plan on using to evaluate model performance (as in question #2).Convergence means that the parameters aren't changing anymore. It means that the
nnethas done as well as it can, given the setup you chose and the random seed used. If you want it to run for more iterations, try increasing the size of the hidden layer or starting from a different set of initial conditions.