Deterministic policy gradient algorithms are foundational for actor-critic methods in controlling continuous systems, yet they often encounter inaccuracies due to their dependence on the derivative of the critic's value estimates with respect to input actions. This reliance requires precise action-value gradient computations, a task that proves challenging under function approximation. We introduce an actor-critic algorithm that bypasses the need for such precision by employing a zeroth-order approximation of the action-value gradient through two-point stochastic gradient estimation within the action space. This approach provably and effectively addresses compatibility issues inherent in deterministic policy gradient schemes. Empirical results further demonstrate that our algorithm not only matches but frequently exceeds the performance of current state-of-the-art methods by a substantial extent.
This technical report is devoted to explaining how the actor loss of soft actor critic is obtained, as well as the associated gradient estimate. It gives the necessary mathematical background to derive all the presented equations, from the theoretical actor loss to the one implemented in practice. This necessitates a comparison of the reparameterization trick used in soft actor critic with the nabla log trick, which leads to open questions regarding the most efficient method to use.
University of Washington（华盛顿大学）；University of California, Santa Cruz（加利福尼亚大学圣克鲁兹分校）
The hierarchical interaction between the actor and critic in actor-critic based reinforcement learning algorithms naturally lends itself to a game-theoretic interpretation. We adopt this viewpoint and model the actor and critic interaction as a two-player general-sum game with a leader-follower structure known as a Stackelberg game. Given this abstraction, we propose a meta-framework for Stackelberg actor-critic algorithms where the leader player follows the total derivative of its objective instead of the usual individual gradient. From a theoretical standpoint, we develop a policy gradient t…
Quasi-Newton Compatible Actor-Critic for Deterministic Policies
Max Planck Institute for Software Systems（马克斯·普朗克软件系统研究所）；University of Birmingham（伯明翰大学）；Norwegian University of Science and Technology（挪威科学技术大学）；TU Dortmund（德累斯顿技术大学）
Georgia Institute of Technology（佐治亚理工学院）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Google AI（谷歌人工智能）
This paper proposes a new actor-critic-style algorithm called Dual Actor-Critic or Dual-AC. It is derived in a principled way from the Lagrangian dual form of the Bellman optimality equation, which can be viewed as a two-player game between the actor and a critic-like function, which is named as dual critic. Compared to its actor-critic relatives, Dual-AC has the desired property that the actor and dual critic are updated cooperatively to optimize the same objective function, providing a more transparent way for learning the critic that is directly related to the objective function of the acto…
Indian Institute of Science（印度科学学院）；Indian Institute of Technology Dharwad（印度理工学院达拉瓦德分校）
Learning optimal behavior from existing data is one of the most important problems in Reinforcement Learning (RL). This is known as "off-policy control" in RL where an agent's objective is to compute an optimal policy based on the data obtained from the given policy (known as the behavior policy). As the optimal policy can be very different from the behavior policy, learning optimal behavior is very hard in the "off-policy" setting compared to the "on-policy" setting where new data from the policy updates will be utilized in learning. This work proposes an off-policy natural actor-critic algor…
Tsinghua Shenzhen International Graduate School, Tsinghua University（清华大学深圳国际研究生院，清华大学）；Tsinghua University（清华大学）
How to obtain good value estimation is one of the key problems in Reinforcement Learning (RL). Current value estimation methods, such as DDPG and TD3, suffer from unnecessary over- or underestimation bias. In this paper, we explore the potential of double actors, which has been neglected for a long time, for better value function estimation in continuous setting. First, we uncover and demonstrate the bias alleviation property of double actors by building double actors upon single critic and double critics to handle overestimation bias in DDPG and underestimation bias in TD3 respectively. Next,…
Refined Analysis of Entropy-Regularized Actor-Critic
CMAP, CNRS, École Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France（法国巴黎政治学院CMAP、国家科学研究中心、巴黎政治学院、巴黎理工学院、法国Palaiseau）；Université Paris-Saclay, CNRS, LMO, 91405, Orsay, France. Now at Google DeepMind.（巴黎萨克雷大学、国家科学研究中心、LMO、法国Orsay、现就职于DeepMind）；Mohamed bin Zayed University of Artificial Intelligence, UAE（阿联酋Mohamed bin Zayed人工智能大学）
We introduce an Actor-Critic Ensemble(ACE) method for improving the performance of Deep Deterministic Policy Gradient(DDPG) algorithm. At inference time, our method uses a critic ensemble to select the best action from proposals of multiple actors running in parallel. By having a larger candidate set, our method can avoid actions that have fatal consequences, while staying deterministic. Using ACE, we have won the 2nd place in NIPS'17 Learning to Run competition, under the name of "Megvii-hzwer".
Actor-Critic Pretraining for Proximal Policy Optimization
Institute for Control Engineering of Machine Tools and Manufacturing Units ISW, University of Stuttgart（斯图加特大学机床与制造装置控制工程研究所ISW）；Materials Testing Institute MPA, University of Stuttgart（斯图加特大学材料测试研究所MPA）
This paper presents an actor-critic deep reinforcement learning agent with experience replay that is stable, sample efficient, and performs remarkably well on challenging environments, including the discrete 57-game Atari domain and several continuous control problems. To achieve this, the paper introduces several innovations, including truncated importance sampling with bias correction, stochastic dueling network architectures, and a new trust region policy optimization method.
Xiamen University（厦门大学）；University of Technology Sydney（悉尼科技大学）；Yuan Ze University（元智大学）；Northumbria University（诺森比亚大学）；Aberystwyth University（阿伯里斯特威斯大学）
On error of value function inevitably causes an overestimation phenomenon and has a negative impact on the convergence of the algorithms. To mitigate the negative effects of the approximation error, we propose Error Controlled Actor-critic which ensures confining the approximation error in value function. We present an analysis of how the approximation error can hinder the optimization process of actor-critic methods.Then, we derive an upper boundary of the approximation error of Q function approximator and find that the error can be lowered by restricting on the KL-divergence between every tw…
Boston University（波士顿大学）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）
Actors and critics in actor-critic reinforcement learning algorithms are functionally separate, yet they often use the same network architectures. This case study explores the performance impact of network sizes when considering actor and critic architectures independently. By relaxing the assumption of architectural symmetry, it is often possible for smaller actors to achieve comparable policy performance to their symmetric counterparts. Our experiments show up to 99% reduction in the number of network weights with an average reduction of 77% over multiple actor-critic algorithms on 9 indepen…
Microsoft Research（微软研究院）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Google Research（谷歌研究院）
We propose Adversarially Trained Actor Critic (ATAC), a new model-free algorithm for offline reinforcement learning (RL) under insufficient data coverage, based on the concept of relative pessimism. ATAC is designed as a two-player Stackelberg game: A policy actor competes against an adversarially trained value critic, who finds data-consistent scenarios where the actor is inferior to the data-collection behavior policy. We prove that, when the actor attains no regret in the two-player game, running ATAC produces a policy that provably 1) outperforms the behavior policy over a wide range of hy…
Existing imitation learning methods mainly focus on making an agent effectively mimic a demonstrated behavior, but do not address the potential contradiction between the behavior style and the objective of a task. There is a general lack of efficient methods that allow an agent to partially imitate a demonstrated behavior to varying degrees, while completing the main objective of a task. In this paper we propose a method called Regularized Soft Actor-Critic which formulates the main task and the imitation task under the Constrained Markov Decision Process framework (CMDP). The main task is def…
INRIA（法国国家信息与自动化研究所）；ENSTA-ParisTech（巴黎高科国立高等先进技术学校）；University of Alberta（阿尔伯塔大学）
This paper presents the first actor-critic algorithm for off-policy reinforcement learning. Our algorithm is online and incremental, and its per-time-step complexity scales linearly with the number of learned weights. Previous work on actor-critic algorithms is limited to the on-policy setting and does not take advantage of the recent advances in off-policy gradient temporal-difference learning. Off-policy techniques, such as Greedy-GQ, enable a target policy to be learned while following and obtaining data from another (behavior) policy. For many problems, however, actor-critic methods are mo…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；NVIDIA（英伟达）
We introduce a hybrid CPU/GPU version of the Asynchronous Advantage Actor-Critic (A3C) algorithm, currently the state-of-the-art method in reinforcement learning for various gaming tasks. We analyze its computational traits and concentrate on aspects critical to leveraging the GPU's computational power. We introduce a system of queues and a dynamic scheduling strategy, potentially helpful for other asynchronous algorithms as well. Our hybrid CPU/GPU version of A3C, based on TensorFlow, achieves a significant speed up compared to a CPU implementation; we make it publicly available to other rese…
In this paper, we propose actor-director-critic, a new framework for deep reinforcement learning. Compared with the actor-critic framework, the director role is added, and action classification and action evaluation are applied simultaneously to improve the decision-making performance of the agent. Firstly, the actions of the agent are divided into high quality actions and low quality actions according to the rewards returned from the environment. Then, the director network is trained to have the ability to discriminate high and low quality actions and guide the actor network to reduce the rep…
In this paper, we devise a distributional framework on actor-critic as a solution to distributional instability, action type restriction, and conflation between samples and statistics. We propose a new method that minimizes the Cramér distance with the multi-step Bellman target distribution generated from a novel Sample-Replacement algorithm denoted SR($λ$), which learns the correct value distribution under multiple Bellman operations. Parameterizing a value distribution with Gaussian Mixture Model further improves the efficiency and the performance of the method, which we name GMAC. We empiri…
Inst. for Comp. and Math. Engineering（计算与数学工程研究所）；Departments of Statistics and EECS（统计系与电子工程和计算机科学系）
Actor-critic methods are widely used in offline reinforcement learning practice, but are not so well-understood theoretically. We propose a new offline actor-critic algorithm that naturally incorporates the pessimism principle, leading to several key advantages compared to the state of the art. The algorithm can operate when the Bellman evaluation operator is closed with respect to the action value function of the actor's policies; this is a more general setting than the low-rank MDP model. Despite the added generality, the procedure is computationally tractable as it involves the solution of …
Actor-critic style two-time-scale algorithms are one of the most popular methods in reinforcement learning, and have seen great empirical success. However, their performance is not completely understood theoretically. In this paper, we characterize the \emph{global} convergence of an online natural actor-critic algorithm in the tabular setting using a single trajectory of samples. Our analysis applies to very general settings, as we only assume ergodicity of the underlying Markov decision process. In order to ensure enough exploration, we employ an $ε$-greedy sampling of the trajectory. For a …
In this work, we consider policy-based methods for solving the reinforcement learning problem, and establish the sample complexity guarantees. A policy-based algorithm typically consists of an actor and a critic. We consider using various policy update rules for the actor, including the celebrated natural policy gradient. In contrast to the gradient ascent approach taken in the literature, we view natural policy gradient as an approximate way of implementing policy iteration, and show that natural policy gradient (without any regularization) enjoys geometric convergence when using increasing s…
Actor learning and critic learning are two components of the outstanding and mostly used Deep Deterministic Policy Gradient (DDPG) reinforcement learning method. Since actor and critic learning plays a significant role in the overall robot's learning, the performance of the DDPG approach is relatively sensitive and unstable as a result. We propose a multi-actor-critic DDPG for reliable actor-critic learning to further enhance the performance and stability of DDPG. This multi-actor-critic DDPG is then integrated with Hindsight Experience Replay (HER) to form our new deep learning framework call…
Technische Universität Darmstadt（达姆施塔特工业大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Actor-critic methods can achieve incredible performance on difficult reinforcement learning problems, but they are also prone to instability. This is partly due to the interaction between the actor and critic during learning, e.g., an inaccurate step taken by one of them might adversely affect the other and destabilize the learning. To avoid such issues, we propose to regularize the learning objective of the actor by penalizing the temporal difference (TD) error of the critic. This improves stability by avoiding large steps in the actor update whenever the critic is highly inaccurate. The resu…
University of Oxford（牛津大学）；Microsoft Research Montreal（微软研究院蒙特利尔分院）
We investigate the discounting mismatch in actor-critic algorithm implementations from a representation learning perspective. Theoretically, actor-critic algorithms usually have discounting for both actor and critic, i.e., there is a $γ^t$ term in the actor update for the transition observed at time $t$ in a trajectory and the critic is a discounted value function. Practitioners, however, usually ignore the discounting ($γ^t$) for the actor while using a discounted critic. We investigate this mismatch in two scenarios. In the first scenario, we consider optimizing an undiscounted objective $(γ…
Carnegie Mellon University（卡内基梅隆大学）；MIT Media Lab（麻省理工学院媒体实验室）；Adobe（奥多比公司）
The two-time scale nature of SAC, which is an actor-critic algorithm, is characterised by the fact that the critic estimate has not converged for the actor at any given time, but since the critic learns faster than the actor, it ensures eventual consistency between the two. Various strategies have been introduced in literature to learn better gradient estimates to help achieve better convergence. Since gradient estimates depend upon the critic, we posit that improving the critic can provide a better gradient estimate for the actor at each time. Utilizing this, we propose Soft Actor Retrospecti…
University of Oxford（牛津大学）；Auburn University（奥本大学）；Huawei Technologies（华为技术有限公司）
We present the first provably convergent two-timescale off-policy actor-critic algorithm (COF-PAC) with function approximation. Key to COF-PAC is the introduction of a new critic, the emphasis critic, which is trained via Gradient Emphasis Learning (GEM), a novel combination of the key ideas of Gradient Temporal Difference Learning and Emphatic Temporal Difference Learning. With the help of the emphasis critic and the canonical value function critic, we show convergence for COF-PAC, where the critics are linear and the actor can be nonlinear.
Nara Institute of Science and Technology（奈良先端科学技术大学院大学）
The oscillating performance of off-policy learning and persisting errors in the actor-critic (AC) setting call for algorithms that can conservatively learn to suit the stability-critical applications better. In this paper, we propose a novel off-policy AC algorithm cautious actor-critic (CAC). The name cautious comes from the doubly conservative nature that we exploit the classic policy interpolation from conservative policy iteration for the actor and the entropy-regularization of conservative value iteration for the critic. Our key observation is the entropy-regularized critic facilitates an…
After presenting Actor Critic Methods (ACM), we show ACM are control variate estimators. Using the projection theorem, we prove that the Q and Advantage Actor Critic (A2C) methods are optimal in the sense of the $L^2$ norm for the control variate estimators spanned by functions conditioned by the current state and action. This straightforward application of Pythagoras theorem provides a theoretical justification of the strong performance of QAC and AAC most often referred to as A2C methods in deep policy gradient methods. This enables us to derive a new formulation for Advantage Actor Critic m…
We propose a single time-scale actor-critic algorithm to solve the linear quadratic regulator (LQR) problem. A least squares temporal difference (LSTD) method is applied to the critic and a natural policy gradient method is used for the actor. We give a proof of convergence with sample complexity $\mathcal{O}(\varepsilon^{-1} \log(\varepsilon^{-1})^2)$. The method in the proof is applicable to general single time-scale bilevel optimization problem. We also numerically validate our theoretical results on the convergence.
Actor-Critic based approaches were among the first to address reinforcement learning in a general setting. Recently, these algorithms have gained renewed interest due to their generality, good convergence properties, and possible biological relevance. In this paper, we introduce an online temporal difference based actor-critic algorithm which is proved to converge to a neighborhood of a local maximum of the average reward. Linear function approximation is used by the critic in order estimate the value function, and the temporal difference signal, which is passed from the critic to the actor. T…
In this paper, we present a probability one convergence proof, under suitable conditions, of a certain class of actor-critic algorithms for finding approximate solutions to entropy-regularized MDPs using the machinery of stochastic approximation. To obtain this overall result, we prove the convergence of policy evaluation with general regularizers when using linear approximation architectures and show convergence of entropy-regularized policy improvement.
The University of Edinburgh（爱丁堡大学）；National University of Defense Technology（国防科技大学）；Samsung AI Centre, Cambridge（三星人工智能中心（剑桥））
Off-Policy Actor-Critic (Off-PAC) methods have proven successful in a variety of continuous control tasks. Normally, the critic's action-value function is updated using temporal-difference, and the critic in turn provides a loss for the actor that trains it to take actions with higher expected return. In this paper, we introduce a novel and flexible meta-critic that observes the learning process and meta-learns an additional loss for the actor that accelerates and improves actor-critic learning. Compared to the vanilla critic, the meta-critic network is explicitly trained to accelerate the lea…
LTCI（通信与信息处理实验室）；Télécom Paris（巴黎电信学院）；Institut Polytechnique de Paris（巴黎理工学院）
Actor-critic methods integrating target networks have exhibited a stupendous empirical success in deep reinforcement learning. However, a theoretical understanding of the use of target networks in actor-critic methods is largely missing in the literature. In this paper, we reduce this gap between theory and practice by proposing the first theoretical analysis of an online target-based actor-critic algorithm with linear function approximation in the discounted reward setting. Our algorithm uses three different timescales: one for the actor and two for the critic. Instead of using the standard s…
North Carolina State University（北卡罗来纳州立大学）；University of Alberta（阿尔伯塔大学）；University of New Mexico（新墨西哥大学）；University of Michigan（密歇根大学）
We develop an off-policy actor-critic algorithm for learning an optimal policy from a training set composed of data from multiple individuals. This algorithm is developed with a view towards its use in mobile health.
Institute for Systems Research, University of Maryland（马里兰大学系统研究所）；Astrome Technologies Pvt Ltd（Astrome科技私人有限公司）；Indian Institute of Science（印度科学学院）
We propose a novel actor-critic algorithm with guaranteed convergence to an optimal policy for a discounted reward Markov decision process. The actor incorporates a descent direction that is motivated by the solution of a certain non-linear optimization problem. We also discuss an extension to incorporate function approximation and demonstrate the practicality of our algorithms on a network routing application.
We study the global convergence and global optimality of actor-critic, one of the most popular families of reinforcement learning algorithms. While most existing works on actor-critic employ bi-level or two-timescale updates, we focus on the more practical single-timescale setting, where the actor and critic are updated simultaneously. Specifically, in each iteration, the critic update is obtained by applying the Bellman evaluation operator only once while the actor is updated in the policy gradient direction computed using the critic. Moreover, we consider two function approximation settings …
