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Title: V-MPO: On-Policy Maximum a Posteriori Policy Optimization for Discrete and Continuous Control

Paper content:
Some of the most successful applications of deep reinforcement learning to challenging domains in discrete and continuous control have used policy gradient methods in the on-policy setting.
However, policy gradients can suffer from large variance that may limit performance, and in practice require carefully tuned entropy regularization to prevent policy collapse.
As an alternative to policy gradient algorithms, we introduce V-MPO, an on-policy adaptation of Maximum a Posteriori Policy Optimization (MPO) that performs policy iteration based on a learned state-value function.
We show that V-MPO surpasses previously reported scores for both the Atari-57 and DMLab-30 benchmark suites in the multi-task setting, and does so reliably without importance weighting, entropy regularization, or population-based tuning of hyperparameters.
On individual DMLab and Atari levels, the proposed algorithm can achieve scores that are substantially higher than has previously been reported.
V-MPO is also applicable to problems with high-dimensional, continuous action spaces, which we demonstrate in the context of learning to control simulated humanoids with 22 degrees of freedom from full state observations and 56 degrees of freedom from pixel observations, as well as example OpenAI Gym tasks where V-MPO achieves substantially higher asymptotic scores than previously reported.
Deep reinforcement learning (RL) with neural network function approximators has achieved superhuman performance in several challenging domains (Mnih et al., 2015; .
Some of the most successful recent applications of deep RL to difficult environments such as Dota 2 (OpenAI, 2018a), Capture the Flag , Starcraft II (Vinyals et al., 2019) , and dexterous object manipulation (OpenAI, 2018b) have used policy gradient-based methods such as Proximal Policy Optimization (PPO) (Schulman et al., 2017) and the Importance-Weighted Actor-Learner Architecture (IMPALA) , both in the approximately on-policy setting.
Policy gradients, however, can suffer from large variance that may limit performance, especially for high-dimensional action spaces (Wu et al., 2018) .
In practice, moreover, policy gradient methods typically employ carefully tuned entropy regularization in order to prevent policy collapse.
As an alternative to policy gradient-based algorithms, in this work we introduce an approximate policy iteration algorithm that adapts Maximum a Posteriori Policy Optimization (MPO) (Abdolmaleki et al., 2018a; b) to the on-policy setting.
The modified algorithm, V-MPO, relies on a learned state-value function V (s) instead of the state-action value function used in MPO.
Like MPO, rather than directly updating the parameters in the direction of the policy gradient, V-MPO first constructs a target distribution for the policy update subject to a sample-based KL constraint, then calculates the gradient that partially moves the parameters toward that target, again subject to a KL constraint.
As we are particularly interested in scalable RL algorithms that can be applied to multi-task settings where a single agent must perform a wide variety of tasks, we show for the case of discrete actions that the proposed algorithm surpasses previously reported performance in the multi-task setting for both the Atari-57 (Bellemare et al., 2012) and DMLab-30 (Beattie et al., 2016) benchmark suites, and does so reliably without population-based tuning of hyperparameters (Jaderberg et al., 2017a) .
For a few individual levels in DMLab and Atari we also show that V-MPO can achieve scores that are substantially higher than has previously been reported in the single-task setting, especially in the challenging Ms. Pacman.
V-MPO is also applicable to problems with high-dimensional, continuous action spaces.
We demonstrate this in the context of learning to control both a 22-dimensional simulated humanoid from full state observations-where V-MPO reliably achieves higher asymptotic performance than previous algorithms-and a 56-dimensional simulated humanoid from pixel observations (Tassa et al., 2018; Merel et al., 2019) .
In addition, for several OpenAI Gym tasks (Brockman et al., 2016) we show that V-MPO achieves higher asymptotic performance than has previously been reported.
In this work we have introduced a scalable on-policy deep reinforcement learning algorithm, V-MPO, that is applicable to both discrete and continuous control domains.
For the results presented in this work neither importance weighting nor entropy regularization was used; moreover, since the size of neural network parameter updates is limited by KL constraints, we were also able to use the same learning rate for all experiments.
This suggests that a scalable, performant RL algorithm may not require some of the tricks that have been developed over the past several years.
Interestingly, both the original MPO algorithm for replay-based off-policy learning (Abdolmaleki et al., 2018a; b) and V-MPO for on-policy learning are derived from similar principles, providing evidence for the benefits of this approach as an alternative to popular policy gradient-based methods.

assistant: text: A state-value function-based version of MPO that achieves good results in a wide range of tasks in discrete and continuous control.