Questions. To sample, we use the random.choices function, let’s see how this is implemented. The new features in this Prioritised Experience Replay example is the calculation of error. 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). Why do we want to use Deep Q-Network here? Standard versions of experience replay in deep Q learning consist of storing experience-tuples of the agent as it interacts with it's environment. This can be solved using the Prioritized Experience Replay. This is actually okay as the priorities are still updated for the next batches sampling so this difference won’t be seen after many sampling iterations. Other games from the Atari collection might need several orders of magnitude more experiences to be considered solved. prioritized_replay_alpha – (float)alpha parameter for prioritized replay buffer. Another aspect of Prioritised Experience Replay is a concept called Importance Sampling (IS). We can’t fail to notice that Lunar Lander is a fairly simple environment to solve, with about 400 experiences needed. 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. It is possible that implementing two dueling Q-networks would enable the prioritized experience replay to unleash its full potential. In this article, we will use the OpenAI environment called Lunar Lander to train an agent to play as well as a human! There is more to IS, but, in this case, it is about applying weights to the TD error to try to correct the aforementioned bias. For Prioritized Experience Replay, we do need to associate every experience with additional information, its priority, probability and weight. Questions. Bingo! 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 $-\beta$. The right hand part of the equation is what the Double Q network is actually predicting at the present time: $Q(s_{t}, a_{t}; \theta_t)$. First that we were able to implement the prioritized experience replay for deep Q-network with almost no additional computation complexity. When we are performing some Q based learning, we are trying to minimise the TD error by changing the model parameters $\theta$. The container that we choose is a dictionary. Prioritized Experience Replay is a type of experience replay in reinforcement learning where … Of course not! The publication advises us to compute a sampling probability which is proportional to the loss obtained after the forward pass of the neural network. The next function uses the get_per_error function just reviewed, updates the priority values for these samples in the memory, and also trains the primary network: As can be observed, first a batch of samples are extracted from the memory. In this article, we want to implement a variant of the DQN named Prioritized Experience Replay (see publication link). So we now get 4 variables to associate. By looking at the equation, you can observe that the higher the probability of the sampling, the lower this weight value will be. One of the possible improvements already acknowledged in the original research2 lays in the way experience is used. Finally, these frame / state arrays, associated rewards and terminal states, and the IS weights are returned from the method. | Before training of the network is actually started (i.e. Next we initialise the Memory class and declare a number of other ancillary functions (which have already been discussed here). 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. 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. 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. 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. Notice the $\alpha$ factor – this is a way of scaling the prioritisation based on the TD error up or down. 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. The environment will then provide a reward for attaining this new state, which can be positive or negative (penalty). However, by drawing experience tuples based on the prioritisation discussed above, we are skewing or biasing this expected value calculation. 2.2 Prioritized Experience Replay The main part of prioritized experience replay is the index used to reflect the importance of each transition. The current_batch variable represents which batch is currently used to feed the neural network and is here reset to 0. 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 ・・・ … Should we always keep track of the order of the values in the container? Further reading. 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. This example will be demonstrated in the Space Invaders Atari OpenAI environment. 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. After this appending, the $P(i) = \frac{p_i^\alpha}{\sum_k p_k^\alpha}$ value is calculated. 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. What can we conclude in this experiment? Notice that the “raw” priority is not passed to the SumTree update, but rather the “raw” priority is first passed to the adjust_priority method. Our dictionary being of size 10e5, that’s far from being negligible. On the next line of the code, the following values are appended to the is_weights list: $\left( N \cdot P(i) \right)$. 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. Summary. One of the possible improvements already acknowledged in the original research2 lays in the way experience is used. A good 7 November, 2016. Next, the states and next_states arrays are initialised – in this case, these arrays will consist of 4 stacked frames of images for each training sample. 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 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. The priority is updated according to the loss obtained after the forward pass of the neural network. Of course, we use the trained agent from the prioritized memory replay implementation, it took more time but it’s still trained well enough! Finally, the primary network is trained on the batch of states and target Q values. Next, the available_samples value is incremented, but only if it is less than the size of the memory, otherwise it is clipped at the size of the memory. Last but not least, let’s observe a trained agent play the game! Next, let’s dissect the probably most computationally expensive step, the random sampling. During the training of the deep Q network, batches of prior experience are extracted from this memory. 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. Alternatively, if $\alpha = 1$ then “full prioritisation” occurs i.e. We need something that can, given two known states close enough to our current state, predict what would be the best action to take in our current state. You guessed it, the solution is some form of interpolation. In this introduction, I'll be using a Dueling Q network architecture, and referring to a previous post on the SumTree algorithm. 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. 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. 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. These weights can “slow down” the learning of certain experience samples with respect to others. This might seem easy to do, basically just comparing the newly updated values with the max at each step. Following this, a custom Huber loss function is declared, this will be used later in the code. Coding the Deep Learning Revolution eBook, Python TensorFlow Tutorial – Build a Neural Network, Bayes Theorem, maximum likelihood estimation and TensorFlow Probability, Policy Gradient Reinforcement Learning in TensorFlow 2, Prioritised Experience Replay in Deep Q Learning. Time to test out our implementation! 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. Let’s dig into the details of the implementation. We are now able to sample experiences with probability weights efficiently. This is understandable given the fact that the container of 10e5 elements becomes full at about this stage. Here is an expression of the weights which will be applied to the loss values during training: $$w_i = \left( \frac{1}{N} \cdot \frac{1}{P(i)} \right)^\beta$$. 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