On the other hand, estimating the gradient by finite horizon like traditional value gradient methods [39, 25, 14] may cause large bias of the gradient. However, when rollout workers and optimizers are running in parallel asynchronously, the behavior policy can get stale.

The major obstacle to making A3C off policy is how to control the stability of the off-policy estimator. Deterministic policy; we can also label this as \(\pi(s)\), but using a different letter gives better distinction so that we can easily tell when the policy is stochastic or deterministic without further explanation. The target policy network is found the same way as the target Q-function: by polyak averaging the policy parameters over the course of training. The \(n\)-step V-trace target is defined as: where the red part \(\delta_i V\) is a temporal difference for \(V\). One sentence summary is probably: “we first consider all combinations of parameters that result in a new network a constant KL divergence away from the old network. theoretical guarantee, we propose a class of the deterministic value gradient However, it suffers from the model bias which results in performance loss. We have two interesting findings: (1) The set of states visited by the policy is finite. If the constraint is invalidated, \(h(\pi_T) < 0\), we can achieve \(L(\pi_T, \alpha_T) \to -\infty\) by taking \(\alpha_T \to \infty\).

Actor-critic methods consist of two models, which may optionally share parameters: Let’s see how it works in a simple action-value actor-critic algorithm. Recall that DQN (Deep Q-Network) stabilizes the learning of Q-function by experience replay and the frozen target network. Lillicrap et al.

Based on this As the model is not given, we choose to predict the reward function and the transition function. This update guarantees that \(Q^{\pi_\text{new}}(s_t, a_t) \geq Q^{\pi_\text{old}}(s_t, a_t)\), please check the proof on this lemma in the Appendix B.2 in the original paper. Proof.

)\) for representing a deterministic policy instead of \(\pi(.)\). ∙

First, let’s denote the probability ratio between old and new policies as: Then, the objective function of TRPO (on policy) becomes: Without a limitation on the distance between \(\theta_\text{old}\) and \(\theta\), to maximize \(J^\text{TRPO} (\theta)\) would lead to instability with extremely large parameter updates and big policy ratios.

Retrace Q-value estimation method modifies \(\Delta Q\) to have importance weights truncated by no more than a constant \(c\): ACER uses \(Q^\text{ret}\) as the target to train the critic by minimizing the L2 error term: \((Q^\text{ret}(s, a) - Q(s, a))^2\).

value-policy gradient (DVPG) algorithm. Off-policy gives us better exploration and helps us use data samples more efficiently. When using the SVGD method to estimate the target posterior distribution \(q(\theta)\), it relies on a set of particle \(\{\theta_i\}_{i=1}^n\) (independently trained policy agents) and each is updated: where \(\epsilon\) is a learning rate and \(\phi^{*}\) is the unit ball of a RKHS (reproducing kernel Hilbert space) \(\mathcal{H}\) of \(\theta\)-shaped value vectors that maximally decreases the KL divergence between the particles and the target distribution. The policy network stays the same until the value error is small enough after several updates.

10/30/2015 ∙ by Nicolas Heess, et al. DDPG (Lillicrap, et al., 2015), short for Deep Deterministic Policy Gradient, is a model-free off-policy actor-critic algorithm, combining DPG with DQN.

(3) Target Policy Smoothing: Given a concern with deterministic policies that they can overfit to narrow peaks in the value function, TD3 introduced a smoothing regularization strategy on the value function: adding a small amount of clipped random noises to the selected action and averaging over mini-batches. Because the policy \(\pi_t\) at time t has no effect on the policy at the earlier time step, \(\pi_{t-1}\), we can maximize the return at different steps backward in time — this is essentially DP. Then we go back to unroll the recursive representation of \(\nabla_\theta V^\pi(s)\)! 16 / 16. It relates to how we compute the max over actions in .

In the DDPG setting, given two deterministic actors \((\mu_{\theta_1}, \mu_{\theta_2})\) with two corresponding critics \((Q_{w_1}, Q_{w_2})\), the Double Q-learning Bellman targets look like: However, due to the slow changing policy, these two networks could be too similar to make independent decisions.


(This also immediately gives us the action which maximizes the Q-value.) For any policy μθ and MDP with deterministic state transitions, if assumptions A.1 and A.2 hold, the value gradients exist, and. By repeating this process, we can learn the optimal temperature parameter in every step by minimizing the same objective function: The final algorithm is same as SAC except for learning \(\alpha\) explicitly with respect to the objective \(J(\alpha)\) (see Fig.

Finally, we conduct extensive experiments on standard benchmarks comparing with DDPG, DDPG with model-based rollouts, the stochastic value gradient algorithm, SVG(1) and state-of-the-art stochastic policy gradient methods.

method, a pi module, and a q module. In this way, we can directly obtain a 1-step estimator of the value gradients, Entropy maximization of the policy helps encourage exploration. “Asynchronous methods for deep reinforcement learning.” ICML. Asynchronous Advantage Actor-Critic (Mnih et al., 2016), short for A3C, is a classic policy gradient method with a special focus on parallel training.

To overcome these challenges, we use model-based approaches to predict the reward and transition function.

The problem can be formalized in the multi-agent version of MDP, also known as Markov games. continuous control benchmarks. Let’s consider an example of on-policy actor-critic algorithm to showcase the procedure. [Updated on 2019-09-12: add a new policy gradient method SVPG.] precisely PPO, to have separate training phases for policy and value functions. This is justified in the proof here (Degris, White & Sutton, 2012). 8. In other four environments, DVPG outperforms other algorithms in terms of both sample efficiency and the performance.

)\) and simplify the gradient computation \(\nabla_\theta J(\theta)\) a lot. The ACER paper is pretty dense with many equations. the action a and then take the gradient of the deterministic policy function \(\mu\) w.r.t. When \(\alpha \rightarrow 0\), \(\theta\) is updated only according to the expected return \(J(\theta)\). (Deterministic Value Gradient Theorem) Thus the new TD target is: (3) Multiple Distributed Parallel Actors: D4PG utilizes \(K\) independent actors, gathering experience in parallel and feeding data into the same replay buffer. If interested, check these papers/posts, before reading the ACKTR paper: Here is a high level summary from the K-FAC paper: “This approximation is built in two stages. )\) as a baseline. This may take some tuning to get right. We evaluate the effect of the weight of bootstrapping on DVPG with different values from 0.1 to 0.9, where the number of rollout steps is set to be 4. Deterministic Policy Gradient (DPG) Theorem [29], , proves the existence of the deterministic policy gradient for MDP that satisfies the regular condition, which requires the probability density of the next state. It is possible to learn with deterministic policy rather than stochastic one. Previous works consider and the future state value function \(V^\pi(s')\) can be repeated unrolled by following the same equation.

We then propose a temporal difference method to ensemble deterministic value gradients and deterministic policy gradients, to trade off between the bias due to the model error and the variance of the model-free policy gradients, called the DVPG algorithm.

In A3C each agent talks to the global parameters independently, so it is possible sometimes the thread-specific agents would be playing with policies of different versions and therefore the aggregated update would not be optimal. 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.

DDPG can only be used for environments with continuous action spaces. Join one of the world's largest A.I. Sample reward \(r_t \sim R(s, a)\) and next state \(s' \sim P(s' \vert s, a)\); Then sample the next action \(a' \sim \pi_\theta(a' \vert s')\); Update the policy parameters: \(\theta \leftarrow \theta + \alpha_\theta Q_w(s, a) \nabla_\theta \ln \pi_\theta(a \vert s)\); Compute the correction (TD error) for action-value at time t: Update \(a \leftarrow a'\) and \(s \leftarrow s'\).

Multiple actors generate experience in parallel, while the learner optimizes both policy and value function parameters using all the generated experience.

The architecture of A3C versus A2C. Meanwhile, multiple actors, one for each agent, are exploring and upgrading the policy parameters \(\theta_i\) on their own. analytical gradients by the learned model trade off between the variance of the
However, to the best of our knowledge, existing works of deterministic value gradient methods merely focus on finite horizon, which are too myopic and can lead to large bias. The behavior policy for collecting samples is a known policy (predefined just like a hyperparameter), labelled as \(\beta(a \vert s)\). 10. The value gradient methods estimate the gradient of value function recursively [5]: In fact, there are two kinds of approaches for estimating the gradient of the value function over the state, i.e., infinite and finite.

Based on this ensembled deterministic value-policy gradients, we propose the deterministic value-policy gradient algorithm, shown in Algorithm 2 444The only difference between the DVG(k) algorithm and the DVPG algorithm is the update rule of the policy.. We design a series of experiments to evaluate DVG and DVPG.

1. We choose to rollout k−1 steps to get rewards, then replace ∇skVμθ(sk) by ∇skQw(sk,μθ(sk)) in Eq.

We first prove that under proper condition, the deterministic value gradient does exist. ∙ ACKTR (actor-critic using Kronecker-factored trust region) (Yuhuai Wu, et al., 2017) proposed to use Kronecker-factored approximation curvature (K-FAC) to do the gradient update for both the critic and actor. “Distributed Distributional Deterministic Policy Gradients.” ICLR 2018 poster.

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