Next, the experience buffer is initialized with zeros. The first part of the code can be observed below: First, the reader can see that various constants are declared. To have a sense of what we want to accomplish, let’s watch an untrained agent play the game. Note that in practice these weights $w_i$ in each training batch are rescaled so that they range between 0 and 1. The graph below shows the progress of the rewards over ~1000 episodes of training in the Open AI Space Invader environment, using Prioritised Experience Replay: Prioritised Experience Replay training results. Please note that this code will heavily utilise code from one of my previous tutorials on Dueling Q learning in Atari environments and common code components will not be explained in detail in this post. 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. This concludes my post introducing the important Prioritised Experience Replay concept. It seems that our implementation can provide similar results which is rather satisfying. When we are performing some Q based learning, we are trying to minimise the TD error by changing the model parameters $\theta$. Now how do we distribute the weights for each experience? However, by drawing experience tuples based on the prioritisation discussed above, we are skewing or biasing this expected value calculation. Our architecture substantially improves the state of … 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. Note that a third argument is passed to the Keras train_on_batch function – the importance sampling weights. So to look at a real comparison we can limit ourselves to the first 300 experiences which see little difference between the two implementations! Eco-driving is a complex control problem where the driver’s actions are guided over a period of time or distance so as to achieve a certain goal such as optimizing fuel consumption. Notice the $\alpha$ factor – this is a way of scaling the prioritisation based on the TD error up or down. It has been shown to improve sample efﬁciency and stability by storing a ﬁxed number of the most recently collected transitions for training. The update method of the Memory class in turn calls the SumTree update function which is outside this class. Prioritized Experience Replay is a type of experience replay in reinforcement learning where … For Prioritized Experience Replay, we do need to associate every experience with additional information, its priority, probability and weight. Why do we want to use Deep Q-Network here? In the uniform sampling DQN, we randomly sample through the experiences with a linear distribution, which means we only need one container to store the experiences without any need for additional computation. When treating all samples the same, we are not using the fact that we can learn more from some transitions than from others. By looking at the equation, you can observe that the higher the probability of the sampling, the lower this weight value will be. It determines how much prioritization is used, with alpha=0 corresponding to the uniform case. 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. In practice, that’s a different story… The algorithm does not even converge anymore! Then we apply a ReLu function to assign the difference to be 0 if negative, else do nothing. During learning, we applyQ-learningupdates,onsamples (orminibatches)ofexperience ... observedhippocampalreplay29,andrelatestothenotionof‘prioritized Neural networks give us the possibility to predict the best action to take given known states (and their optimal actions) with a non-linear model. If we use this method, all replay memory in Experience are legal and can be sampled as we like. The architecture relies on prioritized experience replay to focus only on the most significant data generated by the actors. 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). 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. 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. We studied a couple of variants, devised implementations that scale to large replay memories, and found that prioritized replay speeds up learning by a factor 2 and leads to a new state-of-the-art of performance on the Atari benchmark. The variable N refers to the number of experience tuples already stored in your memory (and will top-out at the size of your memory buffer once it's full). What can we conclude in this experiment? The most obvious answer is the difference between the predicted Q value, and what the Q value should be in that state and for that action. 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. Since the two experiments are similar, we can safely directly compare the training duration. 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. Instead, we can prioritize transitions and sample according to priority. For more details, as stated previously, see my SumTree post. Now what if we delete the maximum, how do we find the second highest value? So we now get 4 variables to associate. However, we don't have an exact function for the TD error based on all the possible states, actions and rewards in an environment. This framework is called a Markov Decision Process. Next, a custom Keras model is created which instantiates a Dueling Q architecture – again, refer to my previous post for more details on this. On the next line of the code, the following values are appended to the is_weights list: $\left( N \cdot P(i) \right)$. Prioritized Experience Replay Experience replay (Lin, 1992) has long been used in reinforce- ment learning to improve data efﬁciency. Experience replay is the fundamental data generating mech- anism in off-policy deep reinforcement learning (Lin,1992). In this introduction, I'll be using a Dueling Q network architecture, and referring to a previous post on the SumTree algorithm. Also recall that the $\alpha$ value has already been applied to all samples as the “raw” priorities are added to the SumTree. The next major difference results from the need to feed a priority value into memory along with the experience tuple during each episode step. 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. In order to sample experiences according to the prioritisation values, we need some way of organising our memory buffer so that this sampling is efficient. That’s where neural network comes onto the stage. Here is an expression of the weights which will be applied to the loss values during training: $$w_i = \left( \frac{1}{N} \cdot \frac{1}{P(i)} \right)^\beta$$. In a sense, we wish to use this experience multiple times to train the neural network as an example of what is working and what direction we should take to improve the weights of the network. For each memory index, the error is passed to the Memory update method. So we keep track of the max, then compare every deleted entry with it. So we are fine with sorting the container once in a while. 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. Now it's time to implement Prioritized Experience Replay (PER) which was introduced in 2015 by Tom Schaul. 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. Should we always keep track of the order of the values in the container? If $\alpha = 0$ then all of the $p_i^{\alpha}$ terms go to 1 and every experience has the same chance of being selected, regardless of the TD error. For that purpose, we tried to following adaptation: we look at the signed difference between the neural networks actual output and the expected value. That concludes the theory component of Prioritised Experience Replay and now we can move onto what the code looks like. However, this criterion is easy to think of but hard to put in practice. Now it’s time to implement Prioritized Experience Replay (PER) which was introduced in 2015 by Tom Schaul. The Asynchronous Advantage Actor Critic Network. Further reading. Few reasons that could explain what went wrong here: As a matter of fact, we tried tweaking the algorithm so as to prioritize the positive experiences only. These weights can “slow down” the learning of certain experience samples with respect to others. episodes < DELAY_TRAINING), the reward is substituted for the priority in the memory. DRQN. 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 ・・・ … Because we need to find the data back after processing them in the neural network, a dictionary is a good fit since the complexity of its accessor is of magnitude o(1) as we don’t need to browse the whole container. 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. Looking at the graph, it seems that until 300 episodes, both algorithms require about the same time to process but diverge later. 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. Our architecture substantially improves the state of the art on the Arcade Learning Environment, achieving better final performance in a … One feasible way of sampling is to create a cumulative sum of all the prioritisation values, and then sample from a uniform distribution of interval (0, max(cumulative_prioritisation)). When treating all samples the same, we are not using the fact that we can learn more from some transitions than from others. We want to take in priority experience where there is a big difference between our prediction and the TD target, since it … Second, that this implementation seems not improving the agent’s learning efficiency for this environment. Summary. We plot the obtained graph shown as below: No, this is not a mistake, the uniform sampling is outperforming the prioritized sampling! Another aspect of Prioritised Experience Replay is a concept called Importance Sampling (IS). It allows agents to get the most “bang for their buck,” squeezing out as much information as possible from past experiences. Following this, a custom Huber loss function is declared, this will be used later in the code. Now, the IS weights are calculated according to the following: $$w_i = \left( N \cdot P(i) \right)^{-\beta}$$. In this article, we want to implement a variant of the DQN named Prioritized Experience Replay (see publication link). This sampling is performed by selecting a uniform random number between 0 and the base node value of the SumTree. For example, a robot arm for which the environment state is a list of joint positions and velocities. Great, we are now sure that our approach is valid. The curr_write_idx variable designates the current position in the buffer to place new experience tuples. every sample is randomly selected proportional to its TD error (plus the constant). Let’s take a look at the PER algorithm to understand how to include our sampling in the bigger picture. After this declaration, the SumTree data structures and functions are developed. 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. 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}. 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. DARQN. The priority is updated according to the loss obtained after the forward pass of the neural network. So what could we do next? This is a version of experience replay which more frequently calls on those experiences of the agent where there is more learning value. Deep learning. It is important that you initialize this buffer at the beginning of the training, as you will be able to instantly determine whether your machine has enough memory to handle the size of this buffer. This sample value is then retrieved from the SumTree data structure according to the stored priorities. 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 Therefore, what we are really trying to minimise the expected value of the TD error, based on these samples. Experience replay is an essential part of off-policy learning. Our dictionary being of size 10e5, that’s far from being negligible. 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. It is only towards the end of the training that this bias needs to be corrected, so the $\beta$ value being closer to 1 decreases the weights for high priority / probability samples and therefore corrects the bias more. What is Deep Q-Network (DQN) and why do we use it? The SumTree is initialised with the number of leaf nodes equal to the size of the buffer, and with a value of 0. This promotes some exploration in addition to the PER process. 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”. In this post, I'm going to introduce an important concept called Prioritised Experience Replay (PER). The tests done with the implementation showed that a sampling size of 2000 (compared to a container of size 10e5) showed the best results. Prioritized experience replay. Now comes another question, how do prioritizing some experiences may help us to obtain better or faster results in this scenario? We will try to focus here on the implementation with a regular container, as it seems more challenging to optimize so as to reduce complexity, providing with a good coding exercise! We run two tests, one with the prioritized experience replay implementation, another one with the uniform sampling DQN. This is fine for small-medium sized datasets, however for very large datasets such as the memory buffer in deep Q learning (which can be millions of entries long), this is an inefficient way of selecting prioritised samples. | Powered by WordPress. 7 November, 2016. 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. We are now able to sample experiences with probability weights efficiently. Finally, the primary network is trained on the batch of states and target Q values. Try this agent on other environments to see if the prioritized experience replay can lead to improve results given this implementation. Both the target Q values and the Huber error / $\delta_i$ are returned from this function. In practice, we can simply find the maximum each time the maximum value gets deleted. 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. Once the buffer has been filled for the first time, this variable will be equal to the size variable. It is natural to select how much an agent can learn from the transition as the criterion, given the current state. For more explanation on training in an Atari environment with stacked frames – see this post. This can be solved using the Prioritized Experience Replay. We can’t fail to notice that Lunar Lander is a fairly simple environment to solve, with about 400 experiences needed. 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. 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. If you continue to use this site we will assume that you are happy with it. As we can see, our implementation does increase the overall computation time to solve the environment from 2426s to 3161s, which corresponds to approximately a 34% increase. What should the measure be to “rank” the sampling used in Prioritised Experience Replay? Of course, these results depend on the hyper-parameters chosen for the prioritized experience replay implementation, namely how many batches do you want to sample at once and how frequently do you want to update the parameters alpha and beta (which need to update every single probability in the buffer). 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. To sample, we use the random.choices function, let’s see how this is implemented. Prioritized Experience Replay. This is equivalent to say that we want to keep the experiences which led to an important difference between the expected reward and the reward that we actually got, or in other terms, we want to keep the experiences that made the neural network learn a lot. The following variable declarations (frame_idx, action_idx, reward_idx and terminal_idx) specify what tuple indices relate to each of the variable types stored in the buffer. In this article, we will use the OpenAI environment called Lunar Lander to train an agent to play as well as a human! This would mean o(n) complexity at each step. Worse than that, we need to be able to update these variables. Standard versions of experience replay in deep Q learning consist of storing experience-tuples of the agent as it interacts with it's environment. 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 first step is a while loop which iterates until num_samples have been sampled. The next method in the Memory class appends a new experience tuple to the buffer and also updates the priority value in the SumTree: Here you can observe that both the experience tuple (state, action, reward, terminal) and the priority of this experience are passed to this method. The experience tuple is written to the buffer at curr_write_idx and the priority is sent to the update method of the class. If it’s positive, we actually got a better reward than what we expected! The concept is quite simple: when we sample experiences to feed the Neural Network, we assume that some experiences are more valuable than others. 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). The new features in this Prioritised Experience Replay example is the calculation of error. Actually two dictionaries, one for the experiences themselves and one for the associated data, this is fine since we need to remember the index anyway. When linear interpolation simply consists in “drawing a line between two states”, we need to be able to predict with a higher degree of complexity. Questions. Next we initialise the Memory class and declare a number of other ancillary functions (which have already been discussed here). It is not certain that lunar lander will benefit of prioritizing experiences. The value that is calculated on this line is the TD error, but the TD error passed through a Huber loss function: $$\delta_i = target_q – Q(s_{t}, a_{t}; \theta_t)$$. The code following is the main training / episode loop: This training loop has been explained in detail here, so please refer to that post for a detailed explanation. 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. Often, to reduce the variance of $\delta_i$, the Huber loss function is used on this TD error. 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. So compared to the uniform DQN we now have 3 values to associate with the experiences. This is understandable given the fact that the container of 10e5 elements becomes full at about this stage. The priority is updated according to the loss obtained after the forward pass of the neural network. In terms of implementation, it means that after randomly sampling our experiences, we still need to remember from where we took these experiences. Prioritized experience replay. For Prioritized Experience Replay, we do need to associate every experience with additional information, its priority, probability and weight. The higher these two values get, the faster the algorithm would compute, but that would probably have a non-negligible impact on the training. DQN posed several implementation problems, related to the training part of the neural network. Well here, all the priorities are the same so it does happen every time once the container is full. Alternatively, if $\alpha = 1$ then “full prioritisation” occurs i.e. Prioritized replay further liberate s agents from considering transitions with the same frequency that they are experienced. 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. Finally, the IS $\beta$ and the PER $\alpha$ values are initialised with values previously discussed above, and the minimum priority value to add to each experience tuple is defined as some small float value. After this appending, the $P(i) = \frac{p_i^\alpha}{\sum_k p_k^\alpha}$ value is calculated. However, this approach simply replays transitions at the same frequency that they were originally experienced, regardless of their significance. The container that we choose is a dictionary. In other terms, you would learn to touch the ground properly but would have no idea how to go get close to the ground! Other games from the Atari collection might need several orders of magnitude more experiences to be considered solved. In future posts, I'll deal with other types of reinforcement learning algorithms. The paper introduces two more hyper-parameters alpha and beta, which control how much we want to prioritize: at the end of the training, we want to sample uniformly to avoid overfitting due to some experiences being constantly prioritized. Of course, we use the trained agent from the prioritized memory replay implementation, it took more time but it’s still trained well enough! One of the possible improvements already acknowledged in the original research2 lays in the way experience is used. The reader can go back to that post if they wish to review the intricacies of Dueling Q learning and using it in the Atari environment. 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. We also add a small for loop to initialize the dictionaries indexes. 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. The states of this environment are described by 8 variables: x, y coordinates and velocities, rotation and angular velocity of the lander, and two boolean variables to state whether the legs of the lander are in contact with the ground. This is calculated by calling the get_per_error function that was explained previously, and this error is passed to the memory append method. The right hand part of the equation is what the Double Q network is actually predicting at the present time: $Q(s_{t}, a_{t}; \theta_t)$. Instead, what we have are samples from the environment in the form of these experience tuples (states, actions, rewards). Questions. The higher the value, the more often this sample should be chosen. By admin The alternative to this method of sampling is the SumTree data structure and algorithms. In the replay buffer, so as to not just delete purely the experiences with a negative difference, we assign them with average priority. Alright, now that we got the concept, it’s time to implement on a real case scenario. 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. In that case, the difference between the expected result (negative reward) and the actual output (positive reward) would be significant, leading to a much higher probability for this experience to be sampled. Note that $Q(s_{t}, a_{t}; \theta_t)$ is extracted from the primary network (with weights of $\theta_t$). Summary. However, another experience sample may result in a poor estimation of the actual Q value at this state – this signifies that there is something valuable to learn about the experience and the algorithm should be encouraged to sample it. Following this, the IS weights are then normalised so that they span between 0 and 1, which acts to stabilise learning. Because the value within the bracket is always < 1, a $\beta$ of < 1 will actually increase the weight values towards 1 and reduce the effect of these weight values. So, in our previous tutorial we implemented Double Dueling DQN Network model, and we saw that this way our agent improved slightly. The environment will then provide a reward for attaining this new state, which can be positive or negative (penalty). 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. This paper introduced prioritized replay, a method that can make learning from experience replay more efficient. Because experience samples with a high priority / probability will be sampled more frequently under PER, this weight value ensures that the learning is slowed for these samples. If you don't initialize but dynamically append to a list, you run the risk of exceeding the memory of your machine half way through your training – which can be frustrating during long training runs! Make learning your daily ritual. Following the accumulation of the samples, the IS weights are then converted from a list to a numpy array, then each value is raised element-wise to the power of $-\beta$. -  Designed by Thrive Themes Functions are developed result in simply prioritizing a bit of unpacking, for it is natural to how. Add a small for loop to initialize the dictionaries indexes potential usage in combination with dual! The constant ) based on these samples penalized if the prioritized experience via. They range between 0 and 1 tries to leverage this fact by the. You are happy with it 's environment 2020 by Adventures in Machine learning the results for.! With sorting the container of 10e5 elements becomes full at about this.. 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