[14] kvfrans.com A intuitive explanation of natural gradient descent. “IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures” arXiv preprint 1802.01561 (2018). To reduce the variance, TD3 updates the policy at a lower frequency than the Q-function. (Image source: Lillicrap, et al., 2015), [paper|code (Search “github d4pg” and you will see a few.)]. “Phasic Policy Gradient.” arXiv preprint arXiv:2009.04416 (2020). I listed ACTKR here mainly for the completeness of this post, but I would not dive into details, as it involves a lot of theoretical knowledge on natural gradient and optimization methods. Policy Gradient Theorem Now hopefully we have a clear setup. Note that the regularity conditions A.1 imply that V (s) and r V (s) are continuous functions of and sand the compactness of Sfurther implies that for any , jjr V (s)jj, jjr aQ (s;a)j a= In the first, the rows and columns of the Fisher are divided into groups, each of which corresponds to all the weights in a given layer, and this gives rise to a block-partitioning of the matrix. To resolve the inconsistency, a coordinator in A2C waits for all the parallel actors to finish their work before updating the global parameters and then in the next iteration parallel actors starts from the same policy. $$\bar{\rho}$$ impacts the fixed-point of the value function we converge to and $$\bar{c}$$ impacts the speed of convergence. $$E_\pi$$ and $$E_V$$ control the sample reuse (i.e. In order to scale up RL training to achieve a very high throughput, IMPALA (“Importance Weighted Actor-Learner Architecture”) framework decouples acting from learning on top of basic actor-critic setup and learns from all experience trajectories with V-trace off-policy correction. Fig 3. How-ever, almost all modern policy gradient algorithms deviate from the original theorem by dropping one of the two instances of the discount factor that appears in the theorem. Tons of policy gradient algorithms have been proposed during recent years and there is no way for me to exhaust them. A2C is a synchronous, deterministic version of A3C; that’s why it is named as “A2C” with the first “A” (“asynchronous”) removed. 本篇blog作为一个引子，介绍下Policy Gradient的基本思想。那么大家会发现，如何确定这个评价指标才是实现Policy Gradient方法的关键所在。所以，在下一篇文章中。我们将来分析一下这个评价指标的问题。 Therefore, to maximize $$f(\pi_T)$$, the dual problem is listed as below. It goes without being said that we also need to update the parameters ω of the critic. Experience replay (training data sampled from a replay memory buffer); Target network that is either frozen periodically or updated slower than the actively learned policy network; The critic and actor can share lower layer parameters of the network and two output heads for policy and value functions. One issue that these algorithms must ad- dress is how to estimate the action-value function Qˇ(s;a). The value function parameter is therefore updated in the direction of: The policy parameter $$\phi$$ is updated through policy gradient. $$\theta'$$: $$d\theta \leftarrow d\theta + \nabla_{\theta'} \log \pi_{\theta'}(a_i \vert s_i)(R - V_{w'}(s_i))$$; Update asynchronously $$\theta$$ using $$\mathrm{d}\theta$$, and $$w$$ using $$\mathrm{d}w$$. 2. This concludes the derivation of the Policy Gradient Theorem for entire trajectories. Fig. )\), the value of (state, action) pair when we follow a policy $$\pi$$; $$Q^\pi(s, a) = \mathbb{E}_{a\sim \pi} [G_t \vert S_t = s, A_t = a]$$. These have been taken out of the learning loop of real code. Imagine that the goal is to go from state s to x after k+1 steps while following policy $$\pi_\theta$$. “High-dimensional continuous control using generalized advantage estimation.” ICLR 2016. The deterministic policy gradient update becomes: (2) $$N$$-step returns: When calculating the TD error, D4PG computes $$N$$-step TD target rather than one-step to incorporate rewards in more future steps. The state transition function involves all states, action and observation spaces $$\mathcal{T}: \mathcal{S} \times \mathcal{A}_1 \times \dots \mathcal{A}_N \mapsto \mathcal{S}$$. The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve. Where $$\mathcal{D}$$ is the memory buffer for experience replay, containing multiple episode samples $$(\vec{o}, a_1, \dots, a_N, r_1, \dots, r_N, \vec{o}')$$ — given current observation $$\vec{o}$$, agents take action $$a_1, \dots, a_N$$ and get rewards $$r_1, \dots, r_N$$, leading to the new observation $$\vec{o}'$$. )\) infinitely, it is easy to find out that we can transition from the starting state s to any state after any number of steps in this unrolling process and by summing up all the visitation probabilities, we get $$\nabla_\theta V^\pi(s)$$! Policy Gradient Book¶. (1) Distributional Critic: The critic estimates the expected Q value as a random variable ~ a distribution $$Z_w$$ parameterized by $$w$$ and therefore $$Q_w(s, a) = \mathbb{E} Z_w(x, a)$$. In this way, the target network values are constrained to change slowly, different from the design in DQN that the target network stays frozen for some period of time. This article was originally published here. PPO has been tested on a set of benchmark tasks and proved to produce awesome results with much greater simplicity. Consider the case when we are doing off-policy RL, the policy $$\beta$$ used for collecting trajectories on rollout workers is different from the policy $$\pi$$ to optimize for. It makes a lot of sense to learn the value function in addition to the policy, since knowing the value function can assist the policy update, such as by reducing gradient variance in vanilla policy gradients, and that is exactly what the Actor-Critic method does. If we represent the total reward for a given trajectory τ as r(τ), we arrive at the following definition. We can first travel from s to a middle point s’ (any state can be a middle point, $$s' \in \mathcal{S}$$) after k steps and then go to the final state x during the last step. Say, there are N agents in total with a set of states $$\mathcal{S}$$. [22] David Knowles. Given that the environment is generally unknown, it is difficult to estimate the effect on the state distribution by a policy update. Deterministic policy gradient algorithms. This problem is aggravated by the scale of rewards. The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve. 9. “Addressing Function Approximation Error in Actor-Critic Methods.” arXiv preprint arXiv:1802.09477 (2018). Because $$Q^\pi$$ is a function of the target policy and thus a function of policy parameter $$\theta$$, we should take the derivative of $$\nabla_\theta Q^\pi(s, a)$$ as well according to the product rule. Let’s consider the following visitation sequence and label the probability of transitioning from state s to state x with policy $$\pi_\theta$$ after k step as $$\rho^\pi(s \to x, k)$$. It is certainly not in your (agent’s) control. [21] Tuomas Haarnoja, et al. In this way, we are able to update the visitation probability recursively: $$\rho^\pi(s \to x, k+1) = \sum_{s'} \rho^\pi(s \to s', k) \rho^\pi(s' \to x, 1)$$. Hopefully, with the prior knowledge on TD learning, Q-learning, importance sampling and TRPO, you will find the paper slightly easier to follow :). If we don’t have any prior information, we might set $$q_0$$ as a uniform distribution and set $$q_0(\theta)$$ to a constant. Usually the temperature $$\alpha$$ follows an annealing scheme so that the training process does more exploration at the beginning but more exploitation at a later stage. a Gaussian radial basis function, measures the similarity between particles. Sharing parameters between policy and value networks have pros and cons. 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