Anomaly detection is widely applied in a variety of domains, involving for instance, smart home systems, network traffic monitoring, IoT applications and sensor networks. In this paper, we study deep reinforcement learning based active sequential testing for anomaly detection. We assume that there is an unknown number of abnormal processes at a time and the agent can only check with one sensor in each sampling step. To maximize the confidence level of the decision and minimize the stopping time concurrently, we propose a deep actor-critic reinforcement learning framework that can dynamically select the sensor based on the posterior probabilities. We provide simulation results for both the training phase and testing phase, and compare the proposed framework with the Chernoff test in terms of claim delay and loss.
We consider the dynamic multichannel access problem, which can be formulated as a partially observable Markov decision process (POMDP). We first propose a model-free actor-critic deep reinforcement learning based framework to explore the sensing policy. To evaluate the performance of the proposed sensing policy and the framework's tolerance against uncertainty, we test the framework in scenarios with different channel switching patterns and consider different switching probabilities. Then, we consider a time-varying environment to identify the adaptive ability of the proposed framework. Additi…
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.
We consider the problem of detecting anomalies among a given set of processes using their noisy binary sensor measurements. The noiseless sensor measurement corresponding to a normal process is 0, and the measurement is 1 if the process is anomalous. The decision-making algorithm is assumed to have no knowledge of the number of anomalous processes. The algorithm is allowed to choose a subset of the sensors at each time instant until the confidence level on the decision exceeds the desired value. Our objective is to design a sequential sensor selection policy that dynamically determines which p…
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…
We describe a novel extension of soft actor-critics for hierarchical Deep Q-Networks (HDQN) architectures using mutual information metric. The proposed extension provides a suitable framework for encouraging explorations in such hierarchical networks. A natural utilization of this framework is an adversarial setting, where meta-controller and controller play minimax over the mutual information objective but cooperate on maximizing expected rewards.
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…
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…
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…
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…
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,…
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…
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 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 …
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".
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…
Princeton University（普林斯顿大学）；Georgia Institute of Technology（佐治亚理工学院）；University of Minnesota（明尼苏达大学）；Northwestern University（西北大学）
Despite the empirical success of the actor-critic algorithm, its theoretical understanding lags behind. In a broader context, actor-critic can be viewed as an online alternating update algorithm for bilevel optimization, whose convergence is known to be fragile. To understand the instability of actor-critic, we focus on its application to linear quadratic regulators, a simple yet fundamental setting of reinforcement learning. We establish a nonasymptotic convergence analysis of actor-critic in this setting. In particular, we prove that actor-critic finds a globally optimal pair of actor (polic…
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）
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…
In this paper we propose a hybrid architecture of actor-critic algorithms for reinforcement learning in parameterized action space, which consists of multiple parallel sub-actor networks to decompose the structured action space into simpler action spaces along with a critic network to guide the training of all sub-actor networks. While this paper is mainly focused on parameterized action space, the proposed architecture, which we call hybrid actor-critic, can be extended for more general action spaces which has a hierarchical structure. We present an instance of the hybrid actor-critic archite…
Actor-critic (AC) methods have exhibited great empirical success compared with other reinforcement learning algorithms, where the actor uses the policy gradient to improve the learning policy and the critic uses temporal difference learning to estimate the policy gradient. Under the two time-scale learning rate schedule, the asymptotic convergence of AC has been well studied in the literature. However, the non-asymptotic convergence and finite sample complexity of actor-critic methods are largely open. In this work, we provide a non-asymptotic analysis for two time-scale actor-critic methods u…
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.
Soft Actor-Critic is a state-of-the-art reinforcement learning algorithm for continuous action settings that is not applicable to discrete action settings. Many important settings involve discrete actions, however, and so here we derive an alternative version of the Soft Actor-Critic algorithm that is applicable to discrete action settings. We then show that, even without any hyperparameter tuning, it is competitive with the tuned model-free state-of-the-art on a selection of games from the Atari suite.
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…
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.
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…
Despite definite success in deep reinforcement learning problems, actor-critic algorithms are still confronted with sample inefficiency in complex environments, particularly in tasks where efficient exploration is a bottleneck. These methods consider a policy (the actor) and a value function (the critic) whose respective losses are built using different motivations and approaches. This paper introduces a third protagonist: the adversary. While the adversary mimics the actor by minimizing the KL-divergence between their respective action distributions, the actor, in addition to learning to solv…
We study the problem of off-policy critic evaluation in several variants of value-based off-policy actor-critic algorithms. Off-policy actor-critic algorithms require an off-policy critic evaluation step, to estimate the value of the new policy after every policy gradient update. Despite enormous success of off-policy policy gradients on control tasks, existing general methods suffer from high variance and instability, partly because the policy improvement depends on gradient of the estimated value function. In this work, we present a new way of off-policy policy evaluation in actor-critic, ba…
We reformulate the option framework as two parallel augmented MDPs. Under this novel formulation, all policy optimization algorithms can be used off the shelf to learn intra-option policies, option termination conditions, and a master policy over options. We apply an actor-critic algorithm on each augmented MDP, yielding the Double Actor-Critic (DAC) architecture. Furthermore, we show that, when state-value functions are used as critics, one critic can be expressed in terms of the other, and hence only one critic is necessary. We conduct an empirical study on challenging robot simulation tasks…
University of Alberta（阿尔伯塔大学）；Stanford University（斯坦福大学）；Google Brain（谷歌大脑）
Actor-critic (AC) methods are ubiquitous in reinforcement learning. Although it is understood that AC methods are closely related to policy gradient (PG), their precise connection has not been fully characterized previously. In this paper, we explain the gap between AC and PG methods by identifying the exact adjustment to the AC objective/gradient that recovers the true policy gradient of the cumulative reward objective (PG). Furthermore, by viewing the AC method as a two-player Stackelberg game between the actor and critic, we show that the Stackelberg policy gradient can be recovered as a sp…
Many policy gradient methods are variants of Actor-Critic (AC), where a value function (critic) is learned to facilitate updating the parameterized policy (actor). The update to the actor involves a log-likelihood update weighted by the action-values, with the addition of entropy regularization for soft variants. In this work, we explore an alternative update for the actor, based on an extension of the cross entropy method (CEM) to condition on inputs (states). The idea is to start with a broader policy and slowly concentrate around maximal actions, using a maximum likelihood update towards ac…
Berkeley Artificial Intelligence Research, University of California, Berkeley（加州大学伯克利分校伯克利人工智能研究中心）
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, …
Our effort is toward unifying GAN and DRL algorithms into a unifying AI model (AGI or general-purpose AI or artificial general intelligence which has general-purpose applications to: (A) offline learning (of stored data) like GAN in (un/semi-/fully-)SL setting such as big data analytics (mining) and visualization; (B) online learning (of real or simulated devices) like DRL in RL setting (with/out environment reward) such as (real or simulated) robotics and control; Our core proposal is adding an (generative/predictive) environment model to the actor-critic (model-free) architecture which resul…
The exploitation of extra state information has been an active research area in multi-agent reinforcement learning (MARL). QMIX represents the joint action-value using a non-negative function approximator and achieves the best performance, by far, on multi-agent benchmarks, StarCraft II micromanagement tasks. However, our experiments show that, in some cases, QMIX is incompatible with A2C, a training paradigm that promotes algorithm training efficiency. To obtain a reasonable trade-off between training efficiency and algorithm performance, we extend value-decomposition to actor-critics that ar…
We propose a new algorithm, Mean Actor-Critic (MAC), for discrete-action continuous-state reinforcement learning. MAC is a policy gradient algorithm that uses the agent's explicit representation of all action values to estimate the gradient of the policy, rather than using only the actions that were actually executed. We prove that this approach reduces variance in the policy gradient estimate relative to traditional actor-critic methods. We show empirical results on two control domains and on six Atari games, where MAC is competitive with state-of-the-art policy search algorithms.
Finite-Time Global Optimality Convergence in Deep Neural Actor-Critic Methods for Decentralized Multi-Agent Reinforcement Learning
The Ohio State University, Columbus, Ohio, USA（俄亥俄州立大学）；University of Wisconsin-Whitewater, Whitewater, Wisconsin, USA（威斯康星大学-威奇托分校）；University of Colorado Boulder, Boulder, Colorado, USA（科罗拉多大学博尔德分校）
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…
