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Title: Distributed Distributional Deterministic Policy Gradients

Paper content:
This work adopts the very successful distributional perspective on reinforcement learning and adapts it to the continuous control setting.
We combine this within a distributed framework for off-policy learning in order to develop what we call the Distributed Distributional Deep Deterministic Policy Gradient algorithm, D4PG.
We also combine this technique with a number of additional, simple improvements such as the use of N-step returns and prioritized experience replay.
Experimentally we examine the contribution of each of these individual components, and show how they interact, as well as their combined contributions.
Our results show that across a wide variety of simple control tasks, difficult manipulation tasks, and a set of hard obstacle-based locomotion tasks the D4PG algorithm achieves state of the art performance.
The ability to solve complex control tasks with high-dimensional input and action spaces is a key milestone in developing real-world artificial intelligence.
The use of reinforcement learning to solve these types of tasks has exploded following the work of the Deep Q Network (DQN) algorithm BID11 , capable of human-level performance on many Atari games.
Similarly, ground breaking achievements have been made in classical games such as Go .
However, these algorithms are restricted to problems with a finite number of discrete actions.In control tasks, commonly seen in the robotics domain, continuous action spaces are the norm.
For algorithms such as DQN the policy is only implicitly defined in terms of its value function, with actions selected by maximizing this function.
In the continuous control domain this would require either a costly optimization step or discretization of the action space.
While discretization is perhaps the most straightforward solution, this can prove a particularly poor approximation in highdimensional settings or those that require finer grained control.
Instead, a more principled approach is to parameterize the policy explicitly and directly optimize the long term value of following this policy.In this work we consider a number of modifications to the Deep Deterministic Policy Gradient (DDPG) algorithm BID9 .
This algorithm has several properties that make it ideal for the enhancements we consider, which is at its core an off-policy actor-critic method.
In particular, the policy gradient used to update the actor network depends only on a learned critic.
This means that any improvements to the critic learning procedure will directly improve the quality of the actor updates.
In this work we utilize a distributional BID0 version of the critic update which provides a better, more stable learning signal.
Such distributions model the randomness due to intrinsic factors, among these is the inherent uncertainty imposed by function approximation in a continuous environment.
We will see that using this distributional update directly results in better gradients and hence improves the performance of the learning algorithm.Due to the fact that DDPG is capable of learning off-policy it is also possible to modify the way in which experience is gathered.
In this work we utilize this fact to run many actors in parallel, all feeding into a single replay table.
This allows us to seamlessly distribute the task of gathering Authors contributed equally.
The Deterministic Policy Gradient (DPG) algorithm BID19 upon which this work is based starts from a different set of ideas, namely the policy gradient theorem of BID22 .
The deterministic policy gradient theorem builds upon this earlier approach, but replaces the stochastic policy with one that includes no randomness.
This approach is particularly important because it had previously been believed that the deterministic policy gradient did not exist in a model-free setting.
The form of this gradient is also interesting in that it does not require one to integrate over the action space, and hence may require less samples to learn.
DPG was later built upon by BID9 who extended this algorithm and made use of a deep neural network as the function approximator, primarily as a mechanism for extending these results to work with vision-based inputs.
Further, this entire endeavor lends itself very readily to an off-policy actorcritic architecture such that the actor's gradients depend only on derivatives through the learned critic.
This means that by improving estimation of the critic one is directly able to improve the actor gradients.
Most interestingly, there have also been recent attempts to distribute updates for the DDPG algorithm, (e.g. BID15 and more generally in this work we build on work of BID5 for implementing distributed actors.Recently, BID0 showed that the distribution over returns, whose expectation is the value function, obeys a distributional Bellman equation.
Although the idea of estimating a distribution over returns has been revisited before BID21 BID13 , Bellemare et al. demonstrated that this estimation alone was enough to achieve state-of-the-art results on the Atari 2600 benchmarks.
Crucially, this technique achieves these gains by directly improving updates for the critic.
In this work we introduced the D4PG, or Distributed Distributional DDPG, algorithm.
Our main contributions include the inclusion of a distributional updates to the DDPG algorithm, combined with the use of multiple distributed workers all writing into the same replay table.
We also consider a number of other, smaller changes to the algorithm.
All of these simple modifications contribute to the overall performance of the D4PG algorithm; the biggest performance gain of these simple changes is arguably the use of N -step returns.
Interestingly we found that the use of priority was less crucial to the overall D4PG algorithm especially on harder problems.
While the use of prioritization was definitely able to increase the performance of the D3PG algorithm, we found that it can also lead to unstable updates.
This was most apparent in the manipulation tasks.Finally, as our results can attest, the D4PG algorithm is capable of state-of-the-art performance on a number of very difficult continuous control problems.

assistant: text: We develop an agent that we call the Distributional Deterministic Deep Policy Gradient algorithm, which achieves state of the art performance on a number of challenging continuous control problems.