We introduce Implicit Policy, a general class of expressive policies that can flexibly represent complex action distributions in reinforcement learning, with efficient algorithms to compute entropy regularized policy gradients. We empirically show that, despite its simplicity in implementation, entropy regularization combined with a rich policy class can attain desirable properties displayed under maximum entropy reinforcement learning framework, such as robustness and multi-modality.
A large number of prior works have implemented policy gradient algorithms with entropy regularization @cite_30 @cite_25 @cite_32 @cite_1 , which boost exploration by greedily maximizing policy entropy at each time step. In contrast to such greedy procedure, maximum entropy objective considers entropy over the entire policy trajectories @cite_24 @cite_4 @cite_10 . Though entropy regularization is simpler to implement in practice, @cite_14 @cite_24 argues in favor of maximum entropy objective by showing that trained policies can be robust to noise, which is desirable for real life robotics tasks; and multi-modal, a potentially desired property for exploration and fine-tuning for downstream tasks. However, their training procedure is fairly complex, which consists of training a soft Q function by fixed point iteration and a neural sampler by Stein variational gradient @cite_33 . We argue that properties as robustness and multi-modality are attainable through simple entropy regularized policy gradient algorithms combined with expressive policy representations.
@cite_30 @cite_14 @cite_4 @cite_33 @cite_1 @cite_32 @cite_24 @cite_10 @cite_25
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Two of the leading approaches for model-free reinforcement learning are policy gradient methods and @math -learning methods. @math -learning methods can be effective and sample-efficient when they work, however, it is not well-understood why they work, since empirically, the @math -values they estimate are very inaccurate. A partial explanation may be that @math -learning methods are secretly implementing policy gradient updates: we show that there is a precise equivalence between @math -learning and policy gradient methods in the setting of entropy-regularized reinforcement learning, that "soft" (entropy-regularized) @math -learning is exactly equivalent to a policy gradient method. We also point out a connection between @math -learning methods and natural policy gradient methods. Experimentally, we explore the entropy-regularized versions of @math -learning and policy gradients, and we find them to perform as well as (or slightly better than) the standard variants on the Atari benchmark. We also show that the equivalence holds in practical settings by constructing a @math -learning method that closely matches the learning dynamics of A3C without using a target network or @math -greedy exploration schedule. We propose a general framework for entropy-regularized average-reward reinforcement learning in Markov decision processes (MDPs). Our approach is based on extending the linear-programming formulation of policy optimization in MDPs to accommodate convex regularization functions. Our key result is showing that using the conditional entropy of the joint state-action distributions as regularization yields a dual optimization problem closely resembling the Bellman optimality equations. This result enables us to formalize a number of state-of-the-art entropy-regularized reinforcement learning algorithms as approximate variants of Mirror Descent or Dual Averaging, and thus to argue about the convergence properties of these methods. In particular, we show that the exact version of the TRPO algorithm of (2015) actually converges to the optimal policy, while the entropy-regularized policy gradient methods of (2016) may fail to converge to a fixed point. Finally, we illustrate empirically the effects of using various regularization techniques on learning performance in a simple reinforcement learning setup. Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . Model-free deep reinforcement learning (RL) algorithms have been demonstrated on a range of challenging decision making and control tasks. However, these methods typically suffer from two major challenges: very high sample complexity and brittle convergence properties, which necessitate meticulous hyperparameter tuning. Both of these challenges severely limit the applicability of such methods to complex, real-world domains. In this paper, we propose soft actor-critic, an off-policy actor-critic deep RL algorithm based on the maximum entropy reinforcement learning framework. In this framework, the actor aims to maximize expected reward while also maximizing entropy - that is, succeed at the task while acting as randomly as possible. Prior deep RL methods based on this framework have been formulated as either off-policy Q-learning, or on-policy policy gradient methods. By combining off-policy updates with a stable stochastic actor-critic formulation, our method achieves state-of-the-art performance on a range of continuous control benchmark tasks, outperforming prior on-policy and off-policy methods. Furthermore, we demonstrate that, in contrast to other off-policy algorithms, our approach is very stable, achieving very similar performance across different random seeds.