I am working currently on a project to optimize heater performance using MATLAB neural network tool, I read the manuals and got the guidance from MATLAB manual.
I have configured the network and tested it, what I need is two points:
1. Am I on the right track? is my network correct? I need an expert advise
2. I need to (Optimize) the performance of the heater, I have defined my function but I don't have a clue how to integrate the network in the optimization of the function.
my network is as follows
3 inputs x1 x2 x3
one out put
load input1
load input2
load input3
x1= importdata('input1.txt'); (similar the other inputs and output)
[x1n,x1min,x1max]=norm_nn(x1); ( I worte my own normalization function)
IN=[x1n x2n x3n]';
OUT=[y1n]';
INTRAIN = IN(:,1:1307);
OUTTRAIN = OUT(:,1:1307);
INTEST =IN(:,1308 : 1634);
OUTTEST = OUT(:,1308:1634);
NETWORKNet1 = newff(IN,OUT,[20 20 20], {'tansig' 'tansig' }, 'trainbr');
net = init (NETWORKNet1);
NETWORKNet1 = trainbr(NETWORKNet1,INTRAIN,OUTTRAIN);
YtestNwt1 = sim(NETWORKNet1,INTEST);
y1testd=denorm_nn7(YtestNet1(1,:),y1min,y1max);
e1=er8(y1testd,y1(1308:1634));
save Net1
I have used (1634 data points and divided it for training (80%) and test (20%))
Here is some advice:
(A) Use feedforwardnet as newff is deprecated
(B) Plot the training, test data and the network result to make it easier to visualize what's going on.
(C) By writing [20 20 20] your network has 3 hidden layers. The vast majority of problems require only 1 hidden layer. Only if all other avenues have been exhausted should you move to multiple hidden layers.
(D) Test the network (ie, the sim command) on the training data first. This is an 'easy' test for a neural network and should be working first before you move on. Then you can test it with the test data (which the network was not trained on). This will show if the network has generalized the shape of the data it is trying to learn.
Validation is also another important factor which helps the network to generalize. If you look at the matlab neural network training window (nntraintool) and click 'performance', one of the graphs should be labelled 'validation'.
Regarding your specific questions:
1. Is my network correct? - difficult to say without seeing the dataset.
2. Optimizing performance of the heater - on a simple level you would have a single output neuron, a number between 0 and 1 which denotes heater performance. The input neurons then contain any other parameters involved.
But now, the network can only predict what the performance will be, given any combination of inputs. It won't be able to tell you which inputs will give you maxmimum output. For only 3 inputs, with low resolution / granularity, you could try an exhaustive / brute force search. Otherwise, look into genetic algorithms to quickly find a good solution.
Related
I'm trying to navigate an agent in a n*n gridworld domain by using Q-Learning + a feedforward neural network as a q-function approximator. Basically the agent should find the best/shortest way to reach a certain terminal goal position (+10 reward). Every step the agent takes it gets -1 reward. In the gridworld there are also some positions the agent should avoid (-10 reward, terminal states,too).
So far I implemented a Q-learning algorithm, that saves all Q-values in a Q-table and the agent performs well.
In the next step, I want to replace the Q-table by a neural network, trained online after every step of the agent. I tried a feedforward NN with one hidden layer and four outputs, representing the Q-values for the possible actions in the gridworld (north,south,east, west).
As input I used a nxn zero-matrix, that has a "1" at the current positions of the agent.
To reach my goal I tried to solve the problem from the ground up:
Explore the gridworld with standard Q-Learning and use the Q-map as training data for the Network once Q-Learning is finished
--> worked fine
Use Q-Learning and provide the updates of the Q-map as trainingdata
for NN (batchSize = 1)
--> worked good
Replacy the Q-Map completely by the NN. (This is the point, when it gets interesting!)
-> FIRST MAP: 4 x 4
As described above, I have 16 "discrete" Inputs, 4 Output and it works fine with 8 neurons(relu) in the hidden layer (learning rate: 0.05). I used a greedy policy with an epsilon, that reduces from 1 to 0.1 within 60 episodes.
The test scenario is shown here. Performance is compared beetween standard qlearning with q-map and "neural" qlearning (in this case i used 8 neurons and differnt dropOut rates).
To sum it up: Neural Q-learning works good for small grids, also the performance is okay and reliable.
-> Bigger MAP: 10 x 10
Now I tried to use the neural network for bigger maps.
At first I tried this simple case.
In my case the neural net looks as following: 100 input; 4 Outputs; about 30 neurons(relu) in one hidden layer; again I used a decreasing exploring factor for greedy policy; over 200 episodes the learning rate decreases from 0.1 to 0.015 to increase stability.
At frist I had problems with convergence and interpolation between single positions caused by the discrete input vector.
To solve this I added some neighbour positions to the vector with values depending on thier distance to the current position. This improved the learning a lot and the policy got better. Performance with 24 neurons is seen in the picture above.
Summary: the simple case is solved by the network, but only with a lot of parameter tuning (number of neurons, exploration factor, learning rate) and special input transformation.
Now here are my questions/problems I still haven't solved:
(1) My network is able to solve really simple cases and examples in a 10 x 10 map, but it fails as the problem gets a bit more complex. In cases where failing is very likely, the network has no change to find a correct policy.
I'm open minded for any idea that could improve performace in this cases.
(2) Is there a smarter way to transform the input vector for the network? I'm sure that adding the neighboring positons to the input vector on the one hand improve the interpolation of the q-values over the map, but on the other hand makes it harder to train special/important postions to the network. I already tried standard cartesian two-dimensional input (x/y) on an early stage, but failed.
(3) Is there another network type than feedforward network with backpropagation, that generally produces better results with q-function approximation? Have you seen projects, where a FF-nn performs well with bigger maps?
It's known that Q-Learning + a feedforward neural network as a q-function approximator can fail even in simple problems [Boyan & Moore, 1995].
Rich Sutton has a question in the FAQ of his web site related with this.
A possible explanation is the phenomenok known as interference described in [Barreto & Anderson, 2008]:
Interference happens when the update of one state–action pair changes the Q-values of other pairs, possibly in the wrong direction.
Interference is naturally associated with generalization, and also happens in conventional supervised learning. Nevertheless, in the reinforcement learning paradigm its effects tend to be much more harmful. The reason for this is twofold. First, the combination of interference and bootstrapping can easily become unstable, since the updates are no longer strictly local. The convergence proofs for the algorithms derived from (4) and (5) are based on the fact that these operators are contraction mappings, that is, their successive application results in a sequence converging to a fixed point which is the solution for the Bellman equation [14,36]. When using approximators, however, this asymptotic convergence is lost, [...]
Another source of instability is a consequence of the fact that in on-line reinforcement learning the distribution of the incoming data depends on the current policy. Depending on the dynamics of the system, the agent can remain for some time in a region of the state space which is not representative of the entire domain. In this situation, the learning algorithm may allocate excessive resources of the function approximator to represent that region, possibly “forgetting” the previous stored information.
One way to alleviate the interference problem is to use a local function approximator. The more independent each basis function is from each other, the less severe this problem is (in the limit, one has one basis function for each state, which corresponds to the lookup-table case) [86]. A class of local functions that have been widely used for approximation is the radial basis functions (RBFs) [52].
So, in your kind of problem (n*n gridworld), an RBF neural network should produce better results.
References
Boyan, J. A. & Moore, A. W. (1995) Generalization in reinforcement learning: Safely approximating the value function. NIPS-7. San Mateo, CA: Morgan Kaufmann.
André da Motta Salles Barreto & Charles W. Anderson (2008) Restricted gradient-descent algorithm for value-function approximation in reinforcement learning, Artificial Intelligence 172 (2008) 454–482
In my project, one of my objectives is to find outliers in aeronautical engine data and chose to use the Replicator Neural Network to do so and read the following report on it (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.12.3366&rep=rep1&type=pdf) and am having a slight understanding issue with the step-wise function (page 4, figure 3) and the prediction values due to it.
The explanation of a replicator neural network is best described in the above report but as a background the replicator neural network I have built works by having the same number of outputs as inputs and having 3 hidden layers with the following activation functions:
Hidden layer 1 = tanh sigmoid S1(θ) = tanh,
Hidden layer 2 = step-wise, S2(θ) = 1/2 + 1/(2(k − 1)) {summation each variable j} tanh[a3(θ −j/N)]
Hidden Layer 3 = tanh sigmoid S1(θ) = tanh,
Output Layer 4 = normal sigmoid S3(θ) = 1/1+e^-θ
I have implemented the algorithm and it seems to be training (since the mean squared error decreases steadily during training). The only thing I don't understand is how the predictions are made when the middle layer with the step-wise activation function is applied since it causes the 3 middle nodes' activations to be become specific discrete values (e.g. my last activations on the 3 middle were 1.0, -1.0, 2.0 ) , this causes these values to be forward propagated and me getting very similar or exactly the same predictions every time.
The section in the report on page 3-4 best describes the algorithm but i have no idea what i have to do to fix this, i don't have much time either :(
Any help would be greatly appreciated.
Thank you
I'm facing the problem of implementing this algorithm and here is my insight into the problem that you might have had: The middle layer, by utilizing a step-wise function, is essentially performing clustering on the data. Each layer transforms the data into a discrete number which could be interpreted as a coordinate in a grid system. Imagine we use two neurons in the middle layer with step-wise values ranging from -2 to +2 in increments of 1. This way we define a 5x5 grid where each set of features will be placed. The more steps you allow, the more grids. The more grids, the more "clusters" you have.
This all sounds good and all. After all, we are compressing the data into a smaller (dimensional) representation which then is used to try to reconstruct into the original input.
This step-wise function, however, has a big problem on itself: back-propagation does not work (in theory) with step-wise functions. You can find more about this in this paper. In this last paper they suggest switching the step-wise function with a ramp-like function. That is, to have almost an infinite amount of clusters.
Your problem might be directly related to this. Try switching the step-wise function with a ramp-wise one and measure how the error changes throughout the learning phase.
By the way, do you have any of this code available anywhere for other researchers to use?
I used ntstool to create NAR (nonlinear Autoregressive) net object, by training on a 1x1247 input vector. (daily stock price for 6 years)
I have finished all the steps and saved the resulting net object to workspace.
Now I am clueless on how to use this object to predict the y(t) for example t = 2000, (I trained the model for t = 1:1247)
In some other threads, people recommended to use sim(net, t) function - however this will give me the same result for any value of t. (same with net(t) function)
I am not familiar with the specific neural net commands, but I think you are approaching this problem in the wrong way. Typically you want to model the evolution in time. You do this by specifying a certain window, say 3 months.
What you are training now is a single input vector, which has no information about evolution in time. The reason you always get the same prediction is because you only used a single point for training (even though it is 1247 dimensional, it is still 1 point).
You probably want to make input vectors of this nature (for simplicity, assume you are working with months):
[month1 month2; month2 month 3; month3 month4]
This example contains 2 training points with the evolution of 3 months. Note that they overlap.
Use the Network
After the network is trained and validated, the network object can be used to calculate the network response to any input. For example, if you want to find the network response to the fifth input vector in the building data set, you can use the following
a = net(houseInputs(:,5))
a =
34.3922
If you try this command, your output might be different, depending on the state of your random number generator when the network was initialized. Below, the network object is called to calculate the outputs for a concurrent set of all the input vectors in the housing data set. This is the batch mode form of simulation, in which all the input vectors are placed in one matrix. This is much more efficient than presenting the vectors one at a time.
a = net(houseInputs);
Each time a neural network is trained, can result in a different solution due to different initial weight and bias values and different divisions of data into training, validation, and test sets. As a result, different neural networks trained on the same problem can give different outputs for the same input. To ensure that a neural network of good accuracy has been found, retrain several times.
There are several other techniques for improving upon initial solutions if higher accuracy is desired. For more information, see Improve Neural Network Generalization and Avoid Overfitting.
strong text
I have created a neural network with 2 inputs nodes, 4 hidden nodes and 3 output nodes. The initial weights are random between -1 to 1. I used backpropagation method to update the network with TD error. However, the performance is not good.
I want to know, where the problem might be?
1. Is a bias node necessary?
2. Are eligibility traces necessary?
If anyone can provide me any sample code, I'm very grateful.
Yes, you should include the bias nodes, and yes you should use eligibility traces. The bias nodes just give one additional tunable parameter. Think of the neural network as a "function approximator" as described in Sutton and Barto's book (free online). If the neural network has parameters theta (a vector containing all of the weights in the network), then the Sarsa update is just (using LaTeX notation):
\delta_t = r_t + \gamma*Q(s_{t+1},a_{t+1},\theta_t) - Q(s_t,a_t, \theta_t)
\theta_{t+1} = \theta_t + \alpha*\delta_t*\frac{\partial Q(s,a,\theta)}{\partial \theta}
This is for any function approximator Q(s,a,\theta), which estimates Q(s,a) by tuning its parameters, \theta.
However, I must ask why you're doing this. If you're just trying to get Q learning working really well, then you should use the Fourier Basis instead of a neural network:
http://all.cs.umass.edu/pubs/2011/konidaris_o_t_11.pdf
If you really want to use a neural network for RL, then you should use a natural actor-critic (NAC). NACs follow something called the "natural gradient," which was developed by Amari specifically to speed up learning using neural networks, and it makes a huge difference.
We need more information. What is the problem domain. What are the inputs? What are the outputs?
RL can take a very long time to train and, depending on how you're training, can go from good to great to good to not-so-good during training. Therefore, you should plot the performance of your agent during learning, not just the end result.
You always should use bias nodes. Eligibility traces? Probably not.
I have created a neural network and the performance is good. By using nprtool, we are allow to test the network with an input data and target data. Here is my question, what is the purpose of testing a neural network with target data provided? Isn't it testing should not hav e target data so that we can know how well can the trained neural network perform without target data is given? Hope someone will respond to this, thanks =)
I'm not familiar with nprtool, but I suspect it would give the input data to your neural network, and then compare your NN's output data with the target data (and compute some kind of success rate based on that).
So your NN will never see the target data, it's just used to measure the performance.
It's like the "teacher's edition" of the exercise books in school. The student (i.e. the NN) doesn't have the solutions, but her/his answers will be compared against them by the teacher (i.e. nprtool). (Okay, the teacher probably/hopefully knows the subject, but you get the idea.)
The "target" data t is the desired y of y=net(x) used as example to train the network.
What nprtool do is to divide the training set into three groups: the training set, the validation set and the test set.
The first one is used to actually update the network.
The second one is used to determine the performances of the net (note: this set is NOT used in any way to update the network): as the NN "learns" the error (as difference between the t and net(x)) over the validation set decreases. The trend will eventually stop or even reverse: this phenomena is called "overfitting", which means the NN is now chasing the training set, "memorizing" it at the cost of the ability to generalize (meaning: to perform well with unseen data). So the purpose of this validation set is to determine when to stop the training before the NN starts overfitting. This should answer your question.
Finally third set is for external testing, to leave you a set of data untouched by the training procedure.
Even though the total data set [training, validation and testing] are inputs to the training algorithm, the testing data is in no way used to design (i.e., train and validate) the net
total = design + test
design = train + validate
The training data is used to estimate weights and biases
The validation data is used to monitor the design performance on nontraining data. REGARDLESS OF THE PERFORMANCE ON TRAINING DATA, if validation performance degrades continuously for 6 (default) epochs, training is terminated (VALIDATION STOPPING).
This mitigates the dreaded phenomenon of OVERTRAINING AN OVERFIT NET where performance on nontraining data degrades even if the training set performance is improving.
An overfit net has more unknown weights and biases than training equations, thereby allowing an infinite number of solutions. A simple example of overfitting with two unknowns but only one equation:
KNOWN: a, b, c
FIND: unique x1 and x2
USING: a * x1 + b * x2 = c
Hope this helps.
Greg