text: 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.
  @cite_1: Policy gradient is an efficient technique for improving a policy in a reinforcement learning setting. However, vanilla online variants are on-policy only and not able to take advantage of off-policy data. In this paper we describe a new technique that combines policy gradient with off-policy Q-learning, drawing experience from a replay buffer. This is motivated by making a connection between the fixed points of the regularized policy gradient algorithm and the Q-values. This connection allows us to estimate the Q-values from the action preferences of the policy, to which we apply Q-learning updates. We refer to the new technique as 'PGQL', for policy gradient and Q-learning. We also establish an equivalency between action-value fitting techniques and actor-critic algorithms, showing that regularized policy gradient techniques can be interpreted as advantage function learning algorithms. We conclude with some numerical examples that demonstrate improved data efficiency and stability of PGQL. In particular, we tested PGQL on the full suite of Atari games and achieved performance exceeding that of both asynchronous advantage actor-critic (A3C) and Q-learning.
  @cite_29: A softmax operator applied to a set of values acts somewhat like the maximization function and somewhat like an average. In sequential decision making, softmax is often used in settings where it is necessary to maximize utility but also to hedge against problems that arise from putting all of one's weight behind a single maximum utility decision. The Boltzmann softmax operator is the most commonly used softmax operator in this setting, but we show that this operator is prone to misbehavior. In this work, we study a differentiable softmax operator that, among other properties, is a non-expansion ensuring a convergent behavior in learning and planning. We introduce a variant of SARSA algorithm that, by utilizing the new operator, computes a Boltzmann policy with a state-dependent temperature parameter. We show that the algorithm is convergent and that it performs favorably in practice.
  @cite_4: We establish a new connection between value and policy based reinforcement learning (RL) based on a relationship between softmax temporal value consistency and policy optimality under entropy regularization. Specifically, we show that softmax consistent action values correspond to optimal entropy regularized policy probabilities along any action sequence, regardless of provenance. From this observation, we develop a new RL algorithm, Path Consistency Learning (PCL), that minimizes a notion of soft consistency error along multi-step action sequences extracted from both on- and off-policy traces. We examine the behavior of PCL in different scenarios and show that PCL can be interpreted as generalizing both actor-critic and Q-learning algorithms. We subsequently deepen the relationship by showing how a single model can be used to represent both a policy and the corresponding softmax state values, eliminating the need for a separate critic. The experimental evaluation demonstrates that PCL significantly outperforms strong actor-critic and Q-learning baselines across several benchmarks.
  @cite_7: 
summary: Prior works have studied the property of maximum entropy objective @cite_4 @cite_7 , entropy regularization @cite_1 and their connections with variants of operators @cite_29 . It is commonly believed that entropy regularization greedily maximizes local policy entropy and does not account for how a policy update impacts future states. In Section 4, we show that entropy regularized policy gradient update maximizes a lower bound of maximum entropy objective, given constraints on the differences between consecutive policy iterates. This partially justifies why simple entropy regularization combined with expressive policy classes can achieve competitive empirical performance in practice.