Good afternoon, I used q-learning to model the following problem: a set of agents have the access to 2 access points (AP) states to upload data. S={1,2} the set of states which refers to the connection to AP1 or 2. A={remain, change}. We suppose that during the total duration of simulation, the agents can access to the 2 APs. The goal is to upload the maximum of data during the simulation. The reward is a function that depends on time, which is defined as follows: R(t)= alpha*T+b, where T is the length of the interval of time and b varies over time.
In this situation, is it true to define the terminal condition as the convergence of q-tables to a pre-defined value? How the exploitation phase can be expressed (because there is not a step defined as a final goal)?
Thank you in advance for your help.
Related
I write a custom gym environment, and trained with PPO provided by stable-baselines3. The ep_rew_mean recorded by tensorboard is as follow:
the ep_rew_mean curve for total 100 million steps, each episode has 50 steps
As shown in the figure, the reward is around 15.5 after training, and the model converges. However, I use the function evaluate_policy() for the trained model, and the reward is much smaller than the ep_rew_mean value. The first value is mean reward, the second value is std of reward:
4.349947246664763 1.1806464511030819
the way I use function evaluate_policy() is:
mean_reward, std_reward = evaluate_policy(model, env, n_eval_episodes=10000)
According to my understanding, the initial environment is randomly distributed in an area when using reset() fuction, so there should not be overfitting problem.
I have also tried different learning rate or other parameters, and this problem is not solved.
I have checked my environment, and I think there is no error.
I have searched on the internet, read the doc of stable-baselines3 and issues on github, but did not find the solution.
evaluate_policy has deterministic to True by default (https://stable-baselines3.readthedocs.io/en/master/common/evaluation.html).
If you sample from the distribution during training, it may help to evaluate the policy without it selecting the actions with an argmax (by passing in deterministic=False).
I have a confusion about the way the LSTM networks work when forecasting with an horizon that is not finite but I'm rather searching for a prediction in whatever time in future. In physical terms I would call it the evolution of the system.
Suppose I have a time series $y(t)$ (output) I want to forecast, and some external inputs $u_1(t), u_2(t),\cdots u_N(t)$ on which the series $y(t)$ depends.
It's common to use the lagged value of the output $y(t)$ as input for the network, such that I schematically have something like (let's consider for simplicity just lag 1 for the output and no lag for the external input):
[y(t-1), u_1(t), u_2(t),\cdots u_N(t)] \to y(t)
In this way of thinking the network, when one wants to do recursive forecast it is forced to use the predicted value at the previous step as input for the next step. In this way we have an effect of propagation of error that makes the long term forecast badly behaving.
Now, my confusion is, I'm thinking as a RNN as a kind of an (simple version) implementation of a state space model where I have the inputs, my output and one or more state variable responsible for the memory of the system. These variables are hidden and not observed.
So now the question, if there is this kind of variable taking already into account previous states of the system why would I need to use the lagged output value as input of my network/model ?
Getting rid of this does my long term forecast would be better, since I'm not expecting anymore the propagation of the error of the forecasted output. (I guess there will be anyway an error in the internal state propagating)
Thanks !
Please see DeepAR - a LSTM forecaster more than one step into the future.
The main contributions of the paper are twofold: (1) we propose an RNN
architecture for probabilistic forecasting, incorporating a negative
Binomial likelihood for count data as well as special treatment for
the case when the magnitudes of the time series vary widely; (2) we
demonstrate empirically on several real-world data sets that this
model produces accurate probabilistic forecasts across a range of
input characteristics, thus showing that modern deep learning-based
approaches can effective address the probabilistic forecasting
problem, which is in contrast to common belief in the field and the
mixed results
In this paper, they forecast multiple steps into the future, to negate exactly what you state here which is the error propagation.
Skipping several steps allows to get more accurate predictions, further into the future.
One more thing done in this paper is predicting percentiles, and interpolating, rather than predicting the value directly. This adds stability, and an error assessment.
Disclaimer - I read an older version of this paper.
I have a question about my own project for testing reinforcement learning technique. First let me explain you the purpose. I have an agent which can take 4 actions during 8 steps. At the end of this eight steps, the agent can be in 5 possible victory states. The goal is to find the minimum cost. To access of this 5 victories (with different cost value: 50, 50, 0, 40, 60), the agent don't take the same path (like a graph). The blue states are the fail states (sorry for quality) and the episode is stopped.
enter image description here
The real good path is: DCCBBAD
Now my question, I don't understand why in SARSA & Q-Learning (mainly in Q learning), the agent find a path but not the optimal one after 100 000 iterations (always: DACBBAD/DACBBCD). Sometime when I compute again, the agent falls in the good path (DCCBBAD). So I would like to understand why sometime the agent find it and why sometime not. And there is a way to look at in order to stabilize my agent?
Thank you a lot,
Tanguy
TD;DR;
Set your epsilon so that you explore a bunch for a large number of episodes. E.g. Linearly decaying from 1.0 to 0.1.
Set your learning rate to a small constant value, such as 0.1.
Don't stop your algorithm based on number of episodes but on changes to the action-value function.
More detailed version:
Q-learning is only garranteed to converge under the following conditions:
You must visit all state and action pairs infinitely ofter.
The sum of all the learning rates for all timesteps must be infinite, so
The sum of the square of all the learning rates for all timesteps must be finite, that is
To hit 1, just make sure your epsilon is not decaying to a low value too early. Make it decay very very slowly and perhaps never all the way to 0. You can try , too.
To hit 2 and 3, you must ensure you take care of 1, so that you collect infinite learning rates, but also pick your learning rate so that its square is finite. That basically means =< 1. If your environment is deterministic you should try 1. Deterministic environment here that means when taking an action a in a state s you transition to state s' for all states and actions in your environment. If your environment is stochastic, you can try a low number, such as 0.05-0.3.
Maybe checkout https://youtu.be/wZyJ66_u4TI?t=2790 for more info.
Learner might be in training stage, where it update Q-table for bunch of epoch.
In this stage, Q-table would be updated with gamma(discount rate), learning rate(alpha), and action would be chosen by random action rate.
After some epoch, when reward is getting stable, let me call this "training is done". Then do I have to ignore these parameters(gamma, learning rate, etc) after that?
I mean, in training stage, I got an action from Q-table like this:
if rand_float < rar:
action = rand.randint(0, num_actions - 1)
else:
action = np.argmax(Q[s_prime_as_index])
But after training stage, Do I have to remove rar, which means I have to get an action from Q-table like this?
action = np.argmax(self.Q[s_prime])
Once the value function has converged (values stop changing), you no longer need to run Q-value updates. This means gamma and alpha are no longer relevant, because they only effect updates.
The epsilon parameter is part of the exploration policy (e-greedy) and helps ensure that the agent visits all states infinitely many times in the limit. This is an important factor in ensuring that the agent's value function eventually converges to the correct value. Once we've deemed the value function converged however, there's no need to continue randomly taking actions that our value function doesn't believe to be best; we believe that the value function is optimal, so we extract the optimal policy by greedily choosing what it says is the best action in every state. We can just set epsilon to 0.
Although the answer provided by #Nick Walker is correct, here it's some additional information.
What you are talking about is closely related with the concept technically known as "exploration-exploitation trade-off". From Sutton & Barto book:
The agent has to exploit what it already knows in order to obtain
reward, but it also has to explore in order to make better action
selections in the future. The dilemma is that neither exploration nor
exploitation can be pursued exclusively without failing at the task.
The agent must try a variety of actions and progressively favor those
that appear to be best.
One way to implement the exploration-exploitation trade-off is using epsilon-greedy exploration, that is what you are using in your code sample. So, at the end, once the agent has converged to the optimal policy, the agent must select only those that exploite the current knowledge, i.e., you can forget the rand_float < rar part. Ideally you should decrease the epsilon parameters (rar in your case) with the number of episodes (or steps).
On the other hand, regarding the learning rate, it worths noting that theoretically this parameter should follow the Robbins-Monro conditions:
This means that the learning rate should decrease asymptotically. So, again, once the algorithm has converged you can (or better, you should) safely ignore the learning rate parameter.
In practice, sometimes you can simply maintain a fixed epsilon and alpha parameters until your algorithm converges and then put them as 0 (i.e., ignore them).
I want to use IFFT to obtain the time signal from freqency data, being response amplitude operators (RAO's) and phase shifts of a vessel over frequency range 0.1-2.6 RAd/s, having 200 samples. I first used a very unrefined method to obtain the time domain response as follows:
for i=1:length(t)
surgedisp(:,i)=surge_amp(:,1).*cos(g(:,i)+surge_phase(:,1)+phase(:,1));
surge(1,i)=sum(surgedisp(:,i));
end
Here, g represents w*t, surge phase is the phase shift of the surge motion wrt the waves, phase is a random phase (multiple of 2pi) of the random (ocean)wave. (The values at each frequency)
For the use of IFFT, I needed to represent the surge_amplitudes and surge_phases into the complex form in order to use IFFT:
Z=surge_amp.*exp(j*surge_phase+j*phase), followed by IFFT(Z), and obtain the time signal.
I think I get totally wrong results and I don't know in which direction to look for. Can it have something to do with the j*wt part that I should incorporate into Z? And can someone tell me if the first method is equivalent to the IFFT method?