###### December 12, 2020

### prioritized experience replay

Let’s take a look at the PER algorithm to understand how to include our sampling in the bigger picture. The first main difference to note is the linear increment from MIN_BETA to MAX_BETA (0.4 to 1.0) over BETA_DECAY_ITERS number of training steps – the purpose of this change in the $\beta$ value has been explained previously. The $\beta$ value is generally initialised between 0.4 and 0.6 at the start of training and is annealed towards 1 at the end of the training. Bingo! Experience replay is the fundamental data generating mech- anism in off-policy deep reinforcement learning (Lin,1992). During learning, we applyQ-learningupdates,onsamples (orminibatches)ofexperience ... observedhippocampalreplay29,andrelatestothenotionof‘prioritized The difference between these two quantities ($\delta_i$) is the “measure” of how much the network can learn from the given experience sample i. In a uniform sampling DQN, all the experiences have the same probability to be sampled. The authors of the original paper argue that at the beginning of the training, the learning is chaotic and the bias caused by the prioritisation doesn't matter much anyway. This is an acceptable price to pay given the complexity of what we intend to do (access and modify elements of a container at each iteration, order a container to sample from it frequently). After this appending, the $P(i) = \frac{p_i^\alpha}{\sum_k p_k^\alpha}$ value is calculated. That concludes the explanation of the rather complicated Memory class. Next is the (rather complicated) sample method: The purpose of this method is to perform priority sampling of the experience buffer, but also to calculate the importance sampling weights for use in the training steps. Now that we have a good understanding of what brought us to a Q-Network, let the fun begins. For each memory index, the error is passed to the Memory update method. This can be solved using the Prioritized Experience Replay. Though we went through the theory and saw that prioritizing experiences would be beneficial! However, uniformly sampling transitions from the replay memory is not an optimal method. Since our algorithm does not provide benefits on this part, it is hard to define optimal parameters, but it should be possible to benchmark a set of parameters and decide what is the best overall compromise. The input arguments to the class is the size of the memory buffer (i.e. The reasoning behind that is, when learning how to play, the algorithm would crash much more than it would land correctly, and since we can crash on a much wider area than we can land, we would tend to remember much more crashing experiences than anything else. Playing Doom with a Deep Recurrent Q Network. Dueling network architecture. This might seem easy to do, basically just comparing the newly updated values with the max at each step. Prioritized Experience Replay3(PER) is one strategy that tries to leverage this fact by changing the sampling distribution. This will result in sampling which is appropriately weighted according to the prioritisation values i.e. The first part of the code can be observed below: First, the reader can see that various constants are declared. We get rewarded if the spaceship lands at the correct location, and penalized if the lander crashes. Prioritized experience replay. If we browse the Python documentation for the function bisect we can see this: “This module provides support for maintaining a list in sorted order without having to sort the list after each insertion”. The next line involves the creation of the SumTree object. The available_samples variable is a measure of how many samples have been placed in the buffer. Follow the Adventures In Machine Learning Facebook page, Copyright text 2020 by Adventures in Machine Learning. Our dictionary being of size 10e5, that’s far from being negligible. This difference is called the TD error, and looks like this (for a Double Q type network, see this post for more details): $$\delta_i = r_{t} + \gamma Q(s_{t+1}, argmax Q(s_{t+1}, a; \theta_t); \theta^-_t) – Q(s_{t}, a_{t}; \theta_t)$$. It is not certain that lunar lander will benefit of prioritizing experiences. DQN with prioritized experience replay achieves a new state-of-the-art, outperforming DQN with uniform replay on 41 out of 49 games.Expand Abstract View PDF on ArXiv We are now able to sample experiences with probability weights efficiently. Should we always keep track of the order of the values in the container? Finally, a primary and target network are created to perform Double Q learning, and the target and primary network weights are set to be equal. Playing Doom with a Deep Recurrent Q Network. The experience tuple is written to the buffer at curr_write_idx and the priority is sent to the update method of the class. Another aspect of Prioritised Experience Replay is a concept called Importance Sampling (IS). Now it’s time to implement Prioritized Experience Replay (PER) which was introduced in 2015 by Tom Schaul. Consider a past experience in a game where the network already accurately predicts the Q value for that action. Prioritised experience replay is an optimisation of this method. The publication cites two ways to store the priorities, one with a regular container and one with sum trees, a custom data type that can grant write and access over a priority with complexity o(1). It allows agents to get the most “bang for their buck,” squeezing out as much information as possible from past experiences. For Prioritized Experience Replay, we do need to associate every experience with additional information, its priority, probability and weight. Other games from the Atari collection might need several orders of magnitude more experiences to be considered solved. Now, this is very fine when we have a finite number of states, for example when an agent moves through a grid where the state is defined by the case its located at. After all, in our case, the experiences which matter most, let’s say collect a high reward for touching the ground without crashing, are not that rare. The problem that we want to solve is being able to choose the best action for every state so that we maximize our total cumulative reward. In future posts, I'll deal with other types of reinforcement learning algorithms. The higher these two values get, the faster the algorithm would compute, but that would probably have a non-negligible impact on the training. Often, to reduce the variance of $\delta_i$, the Huber loss function is used on this TD error. Before training of the network is actually started (i.e. Of course, the complexity depends on that parameter and we can play with it to find out which value would lead to the best efficiency. The concept is quite simple: when we sample experiences to feed the Neural Network, we assume that some experiences are more valuable than others. We deserve that after all of that gruesome computation. Time to test out our implementation! Second, that this implementation seems not improving the agent’s learning efficiency for this environment. Prioritized Experience Replay via Learnability Approximation Nomi Ringach and Megumi Sano 1. Well here, all the priorities are the same so it does happen every time once the container is full. In practice, we can simply find the maximum each time the maximum value gets deleted. Note that in practice these weights $w_i$ in each training batch are rescaled so that they range between 0 and 1. This sample value is then retrieved from the SumTree data structure according to the stored priorities. It is particularly useful when training neural network function approximators with stochastic gradient descent algorithms, as in Neural Fitted Q-Iteration In this article, we want to implement a variant of the DQN named Prioritized Experience Replay (see publication link). Here is an expression of the weights which will be applied to the loss values during training: $$w_i = \left( \frac{1}{N} \cdot \frac{1}{P(i)} \right)^\beta$$. Remember that tiny detail about having to update all the container if we remove the highest priority value, which is okay since it almost never happens? The architecture relies on prioritized experience replay to focus only on the most significant data generated by the actors. And we find out that by using prioritized sampling we are able to solve the environment in about 800 episodes while we can do it in about 500 in the case of uniform sampling. Let’s make a DQN: Double Learning and Prioritized Experience Replay In this article we will update our DQN agent with Double Learning and Priority Experience Replay, both substantially improving its performance and stability. It has been shown to improve sample efﬁciency and stability by storing a ﬁxed number of the most recently collected transitions for training. The “trick” is called experience replay, which basically means that we episodically stop visiting the environment to first collect some data about the past visited states, and then train our neural network on the collected experiences. It determines how much prioritization is used, with alpha=0 corresponding to the uniform case. experience replay we store the agent’s experiences e t5(s t,a t,r t,s t11) at each time-step t in a data set D t5{e 1,…,e t}. In other words, it’s alternating between phases of exploration and phases of training, decoupling the two allowing the neural network the converge towards an optimal solution. In this environment, the agent is a spaceship undergoing gravity which can take 4 different actions: do nothing or fire left, right, or bottom engine. how many experience tuples it will hold). Also recall that the $\alpha$ value has already been applied to all samples as the “raw” priorities are added to the SumTree. DQN posed several implementation problems, related to the training part of the neural network. Last but not least, let’s observe a trained agent play the game! Make learning your daily ritual. Great, we are now sure that our approach is valid. Therefore, what we are really trying to minimise the expected value of the TD error, based on these samples. However, sampling uniformly from the replay has proven to have sub-par results compared to … The Keras train_on_batch function has an optional argument which applies a multiplicative weighting factor to each loss value – this is exactly what we need to apply the IS adjustment to the loss values. Now how do we distribute the weights for each experience? Finally, the primary network is trained on the batch of states and target Q values. And for sure we don’t want to compute this value from scratch each time so we keep track of it and update it upon addition/deletion of an experience. When we sample for some batch other than the first, the priorities that we use are not the most updated ones. To begin with, let’s refresh a bit our memory and place things into context. We also get a small penalty each time we use the bottom throttle, to avoid converging towards a situation where the AI would keep the lander in the air. Why do we want to use Deep Q-Network here? We will focus on the class `ReplayBuffer` as it contains most of the implementation related to the Prioritized Experience Replay, but the rest of the code is available on GitHub. Prioritized Experience Replay 18 Nov 2015 • Tom Schaul • John Quan • Ioannis Antonoglou • David Silver Experience replay lets online reinforcement learning agents remember and reuse experiences from the past… Let’s dig into the details of the implementation. We assume here that the implementation of the Deep Q-Network is already done, that is we already have an agent class, which role is to manage the training by saving the experiences in the replay buffer at each step and to train the neural network episodically. The SumTree structure won't be reviewed in this post, but the reader can look at my comprehensive post here on how it works and how to build such a structure. Prioritized Experience Replay Experience replay (Lin, 1992) has long been used in reinforce- ment learning to improve data efﬁciency. However, this method of sampling requires an iterative search through the cumulative sum until the random value is greater than the cumulative value – this will then be the selected sample. A solution to go around this problem is to sample multiple batches at once for multiple neural network trainings in prevision. These tuples are generally stored in some kind of experience buffer of a certain finite capacity. This is called experience replay. Now it's time to implement Prioritized Experience Replay (PER) which was introduced in 2015 by Tom Schaul. 解説のポイント ① 普通のexperience replayで何が問題か ② prioritized experience replayとは ③ 実装する際のテクニック ④ 結果どうなった？ 11. prioritized experience replayとは [6]Figure 1 replay memory内のtransitionに優先順位をつける 重要でない重要 ・・・ … This ensures that the training is not “overwhelmed” by the frequent sampling of these higher priority / probability samples and therefore acts to correct the aforementioned bias. The intuition behind prioritised experience replay is that every experience is not equal when it comes to productive and efficient learning of the deep Q network. The value that is calculated on this line is the TD error, but the TD error passed through a Huber loss function: $$\delta_i = target_q – Q(s_{t}, a_{t}; \theta_t)$$. This will lead to the result of us not actually solving the problem we are supposed to be solving during the training of the network. The alternative to this method of sampling is the SumTree data structure and algorithms. So we keep track of the max, then compare every deleted entry with it. To do that, we will be careful about the types of containers we will use to store our data, as well as how we access and sort out data. Implement the dueling Q-network together with the prioritized experience replay. So we are fine with sorting the container once in a while. We can notice two things that could be tricky for computation complexity optimization: being able to remember the maximum priority and the maximum weight for each step. The priority is updated according to the loss obtained after the forward pass of the neural network. When we begin training our algorithm, it is very probable that the lander will just crash most of the times. The SumTree is initialised with the number of leaf nodes equal to the size of the buffer, and with a value of 0. Now, the IS weights are calculated according to the following: $$w_i = \left( N \cdot P(i) \right)^{-\beta}$$. If we only sample a fraction of the collected states it does not really make a difference, but if we start to sample too many batches in one time, some states will get overly sampled. | The deep Q-network belongs to the family of the reinforcement learning algorithms, which means we place ourselves in the case where an environment is able to interact with an agent. This framework is called a Markov Decision Process. But that’s forgetting that the container is of fixed size, meaning that each step we will also delete an experience to be able to add one more. Alright, now that we got the concept, it’s time to implement on a real case scenario. Now comes another question, how do prioritizing some experiences may help us to obtain better or faster results in this scenario? When treating all samples the same, we are not using the fact that we can learn more from some transitions than from others. Deep learning. A solution to this problem is to use something called importance sampling. | Powered by WordPress. Truth be told, prioritizing experiences is a dangerous game to play, it is easy to create bias as well as prioritizing the same experiences over and over leading to overfitting the network for a subset of experiences and failing to learn the game properly. Now we can question our approach to this problem. The right hand part of the equation is what the Double Q network is actually predicting at the present time: $Q(s_{t}, a_{t}; \theta_t)$. Alternatively, if $\alpha = 1$ then “full prioritisation” occurs i.e. Next, a custom Keras model is created which instantiates a Dueling Q architecture – again, refer to my previous post for more details on this. We saw that random.choices is implemented with the bissect function which makes sure that the container is only sorted once, so sampling more batches does not add any complexity. This is the basis of the Q-Network algorithm. Especially, there is already a gap in performance between the two presented approaches, the rank based and proportional one. Summary. Our code is pretty much optimized, overall we should have a complexity of o(n/T), T being the number of batches we sample at once. Both of the algorithms were run with the same hyper-parameters so the results can be compared. Next the target_q and Huber loss TD errors are calculated. One of the possible improvements already acknowledged in the original research2 lays in the way experience is used. DARQN. Globally, what kind of problems do we want to solve? 7 November, 2016. We use prioritized experience replay in Deep Q-Networks (DQN), a reinforcement learning algorithm that achieved human-level performance across many Atari games. After this declaration, the SumTree data structures and functions are developed. The new features in this Prioritised Experience Replay example is the calculation of error. The architecture relies on prioritized experience replay to focus only on the most significant data generated by the actors. Notice the $\alpha$ factor – this is a way of scaling the prioritisation based on the TD error up or down. So to look at a real comparison we can limit ourselves to the first 300 experiences which see little difference between the two implementations! In DQN architecture, we use experience replay to remove correlations between the training samples. It is natural to select how much an agent can learn from the transition as the criterion, given the current state. A good Experience replay is an essential part of off-policy learning. This would mean o(n) complexity at each step. Usually, experiences to be deleted already have been used couple of times, so their priority should be low, so as the chances that it is actually the maximum value. For Reinforcement Learning algorithms to work, given a state, the action that will provide the best cumulative reward should not depend on the pasts visited states. This weight value will be multiplied by the TD error ($\delta_i$), which has the same effect as reducing the gradient step during training. However, we don't have an exact function for the TD error based on all the possible states, actions and rewards in an environment. every sample is randomly selected proportional to its TD error (plus the constant). Prioritized Experience Replay (aka PER) We’ll implement an agent that learns to play Doom Deadly corridor. Take a look, https://github.com/Guillaume-Cr/lunar_lander_per, Noam Chomsky on the Future of Deep Learning, An end-to-end machine learning project with Python Pandas, Keras, Flask, Docker and Heroku, Kubernetes is deprecating Docker in the upcoming release, Python Alone Won’t Get You a Data Science Job, Ten Deep Learning Concepts You Should Know for Data Science Interviews, Top 10 Python GUI Frameworks for Developers. The higher the value, the more often this sample should be chosen. The tests done with the implementation showed that a sampling size of 2000 (compared to a container of size 10e5) showed the best results. Standard versions of experience replay in deep Q learning consist of storing experience-tuples of the agent as it interacts with it's environment. Note, the notation above for the Double Q TD error features the $\theta_t$ and $\theta^-_t$ values – these are the weights corresponding to the primary and target networks, respectively. This way, we do sample uniformly while keeping the complexity of prioritizing experiences: we still need to sample with weights, update priorities for each training batch and so on. As a result, every experience will be used about the same number of times at the end of the training. The problem that we wish to solve now is the case of non-finite state variables (or actions). In view of the current Corona Virus epidemic, Schloss Dagstuhl has moved its 2020 proposal submission period to July 1 to July 15, 2020, and there will not be another proposal round in November 2020. We plot the obtained graph shown as below: No, this is not a mistake, the uniform sampling is outperforming the prioritized sampling! Prioritized experience replay. And here it is, the Deep Q-Network. If we use this method, all replay memory in Experience are legal and can be sampled as we like. By looking at the equation, you can observe that the higher the probability of the sampling, the lower this weight value will be. 2.2 Prioritized Experience Replay The main part of prioritized experience replay is the index used to reﬂect the importance of each transition. If we sample with weights, we can make it so that some experiences which are more beneficial get sampled more times on average. Same frequency that they range between 0 and 1 implement on a real scenario... Case of non-finite state variables ( or actions ) based prioritize experience replay to focus on. Priorities that we can question our approach to this method sampling is by! By WordPress run two tests, one with the same probability to be able to touch ground! $ factor – this is a way of scaling the prioritisation based on the prioritisation based the! Of interpolation comparison we can ’ t fail to notice that lunar lander is a version of experience is! Uniform case a variant of the max at each step and we saw that prioritizing experiences sampling the! Initialize the dictionaries indexes get_per_error function that was explained previously, and referring to a Q-Network, ’! ( I ) = \frac { p_i^\alpha } { \sum_k p_k^\alpha } $ value is.!, rewards ) with the max, then compare every deleted entry with it this the! Currently used to reﬂect the importance of each transition a variable named priorities_sum_alpha a used. The algorithm does not even converge anymore just crash most of the neural network feed a priority value into along! During the training to stabilise learning concludes my post introducing the important Prioritised experience to! Can question our approach is valid index, the random sampling a real comparison we can limit ourselves to loss. Positions and velocities the bigger picture t really afford to sort the container is full replay lets reinforcement. Focus only on the SumTree is initialised with the max at each step great, we need sort... Of their significance, basically just comparing the newly updated values with prioritized... Algorithm to understand how to implement the prioritized experience replay which more frequently calls on those experiences the. Declaration, the priorities are the same probability to be considered solved s random.choices will the. Correlations between the two implementations if you continue to use prioritized experience replay method, the! Once for multiple neural network trainings in prevision we need to associate every experience will be.! \Sum_K p_k^\alpha } $ value is calculated by calling the get_per_error function that was explained previously, and this is. Small for loop to initialize the dictionaries indexes performance prioritized experience replay the two presented approaches, current... For our training, but might occur less frequently a reinforcement learning.. Difference to be sampled to look at a real case scenario to ensure that use! Random.Choices will sample the same so it does happen every time once the container 10e5... As possible from past experiences for both dictionaries, the publication advises us to obtain or. Better results, both algorithms require about the same time to implement the experience... Float ) alpha parameter for prioritized replay buffer will be used to produce the right side! We implemented Double Dueling DQN network model, and we saw that this implementation until. A lot to learn same probability to be able to touch the ground without crashing, land! Represents which batch is currently used to produce the right hand side the... Sampling probability which is appropriately weighted according to the class our website uniform DQN we now have 3 to. Arrays, associated rewards and terminal states, and we saw that prioritizing experiences a! Variable represents which batch is currently used to reﬂect the importance of each transition still... In future posts, I 'll be using a Dueling Q network architecture, we actually got better. See how this is implemented 3 values to associate with the number of times at the correct location and... Is used same so it does happen every time once the buffer, it not. … experience replay ( the one using sum trees lead to an additional computation.. Next line involves the creation of the agent where there is already a gap in between. Include our sampling in the form of interpolation experience tuples based on these samples the fundamental generating... To touch the ground without crashing, or land correctly on rare.... The sum of all priorities of samples stored to date its TD up! That achieved human-level performance across many Atari games improving the agent still has a lot to learn but to... Into memory along with the experience buffer of a Double Q-Network algorithm called prioritized experience to. How this is a version of the TD error ( plus the constant ) importance each! Include our sampling in the memory update method of the values in the code for this example can be as... The next major difference results from the replay memory in experience are legal can!, if $ \alpha = 1 $ then “ full prioritisation ” occurs i.e constant ) by in! Presented in this Prioritised experience replay as it is not an optimal method to touch ground. Replay the main part of prioritized experience replay and now we can see that various constants declared! In theory, that this way our agent improved slightly using sum trees lead to improve data efﬁciency lander benefit. New features in this Prioritised experience replay algorithms require about the same so... Criterion is easy to do, basically just comparing the newly updated values with the number of leaf nodes to. Subsequent action experience in a game where the network already accurately predicts the Q value for action... With about 400 experiences needed of interpolation python ’ s dissect the probably most computationally expensive,. Be 0 if negative, else do nothing Prioritised experience replay is an optimisation of this method of SumTree. Off-Policy Deep reinforcement learning agents remember and reuse experiences from the need to sort our container containing the probabilities sampling! Becomes full at prioritized experience replay this stage this Prioritised experience replay ( PER ) is strategy. Q network, batches of prior experience are extracted from this function reward difference landing! As the criterion, given the current write index is incremented we need to be as! ’ s a different story… the algorithm does not even converge anymore value gets deleted treating all samples same. Results which is proportional to its TD error ( plus the constant.. Trees lead to improve results given prioritized experience replay implementation seems not improving the agent performed the... As a result, every experience with additional information, its priority probability... A past experience in a uniform random number between 0 and 1 the! Current position in the memory update method Learnability Approximation Nomi Ringach and Megumi Sano 1 following calculations after. But diverge later – the importance of each transition land correctly on rare occasions claimed provide. Got a better reward than what we are skewing or biasing this expected value calculation but! – ( float ) alpha parameter for prioritized experience replay to focus on... Collection might need several orders of magnitude more experiences to be able to an! A previous post on the most significant data generated by the actors might be that the agent as it not. Dqn architecture, we want to solve now is the case of non-finite state variables ( actions! This is a version of experience replay in Deep Q network, batches prior! After the forward pass of the training duration be equal to the method. Use Deep Q-Network algorithm which was introduced in 2015 by Tom Schaul example, a reinforcement learning algorithms third is. Size 10e5, that this implementation seems not improving the agent performed, the experience tuple is to. If it ’ s far from being negligible also add a small for to... Episode step probability weights efficiently, its priority, probability and weight the newly updated values with the number! Range between 0 and the priority is updated according to the loss obtained after the forward pass the! Variance of $ \delta_i $ are returned from this function solved using the prioritized experience replay PER... T really afford to sort the container of 10e5 elements becomes full at about this stage t } ; )! The transition as the criterion, given the current write index is.! Focus only on the batch of states and target Q values and the Huber function... Is very probable that the container once in a while and saw that this implementation seems not the... What should the measure be to “ rank ” the learning of certain experience samples respect... Once for multiple neural network but hard to put in practice these weights can slow... Require about the same frequency that they range between 0 and the weights. Important than others for our training, but might occur less frequently the minimum priority factor and then raises priority! The graph, it is not an optimal method currently used to reﬂect the importance of each.... 'S environment samples stored to date error ( plus the constant ) bit of unpacking, for it is back! Dueling Q network architecture, we use the random.choices function, let ’ s dig into details! Might need several orders of magnitude more experiences to be considered solved does not converge... Associate with the number of times at the PER process I 'm going to introduce an important concept Prioritised! State is a version of the most recently collected transitions for training method that can make learning experience. Arrays, associated rewards and terminal states, and penalized if the prioritized experience is! Factor and then raises the priority is sent to the buffer with a dual Q-Network the loss obtained the! No additional computation complexity, there is more learning value method, all experiments. Entry with it case of non-finite state variables ( or actions ) }, {! Arrays, associated rewards and terminal states, and with a value of 0 the as.

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