Model-based reinforcement learning (MBRL) approaches rely on discrete-time state transition models whereas physical systems and the vast majority of control tasks operate in continuous-time. To avoid time-discretization approximation of the underlying process, we propose a continuous-time MBRL framework based on a novel actor-critic method. Our approach also infers the unknown state evolution differentials with Bayesian neural ordinary differential equations (ODE) to account for epistemic uncertainty. We implement and test our method on a new ODE-RL suite that explicitly solves continuous-time control systems. Our experiments illustrate that the model is robust against irregular and noisy data, is sample-efficient, and can solve control problems which pose challenges to discrete-time MBRL methods.
Continuous reinforcement learning such as DDPG and A3C are widely used in robot control and autonomous driving. However, both methods have theoretical weaknesses. While DDPG cannot control noises in the control process, A3C does not satisfy the continuity conditions under the Gaussian policy. To address these concerns, we propose a new continues reinforcement learning method based on stochastic differential equations and we call it Incremental Reinforcement Learning (IRL). This method not only guarantees the continuity of actions within any time interval, but controls the variance of actions i…
Inverse Reinforcement Learning (IRL) is the problem of finding a reward function which describes observed/known expert behavior. The IRL setting is remarkably useful for automated control, in situations where the reward function is difficult to specify manually or as a means to extract agent preference. In this work, we provide a new IRL algorithm for the continuous state space setting with unknown transition dynamics by modeling the system using a basis of orthonormal functions. Moreover, we provide a proof of correctness and formal guarantees on the sample and time complexity of our algorith…
We adapt the ideas underlying the success of Deep Q-Learning to the continuous action domain. We present an actor-critic, model-free algorithm based on the deterministic policy gradient that can operate over continuous action spaces. Using the same learning algorithm, network architecture and hyper-parameters, our algorithm robustly solves more than 20 simulated physics tasks, including classic problems such as cartpole swing-up, dexterous manipulation, legged locomotion and car driving. Our algorithm is able to find policies whose performance is competitive with those found by a planning algo…
Deep reinforcement learning enables algorithms to learn complex behavior, deal with continuous action spaces and find good strategies in environments with high dimensional state spaces. With deep reinforcement learning being an active area of research and many concurrent inventions, we decided to focus on a relatively simple robotic task to evaluate a set of ideas that might help to solve recent reinforcement learning problems. We test a newly created combination of two commonly used reinforcement learning methods, whether it is able to learn more effectively than a baseline. We also compare d…
We present two elegant solutions for modeling continuous-time dynamics, in a novel model-based reinforcement learning (RL) framework for semi-Markov decision processes (SMDPs), using neural ordinary differential equations (ODEs). Our models accurately characterize continuous-time dynamics and enable us to develop high-performing policies using a small amount of data. We also develop a model-based approach for optimizing time schedules to reduce interaction rates with the environment while maintaining the near-optimal performance, which is not possible for model-free methods. We experimentally …
Amazon Web Services（亚马逊云科技）；University of Pennsylvania（宾夕法尼亚大学）
Reliant on too many experiments to learn good actions, current Reinforcement Learning (RL) algorithms have limited applicability in real-world settings, which can be too expensive to allow exploration. We propose an algorithm for batch RL, where effective policies are learned using only a fixed offline dataset instead of online interactions with the environment. The limited data in batch RL produces inherent uncertainty in value estimates of states/actions that were insufficiently represented in the training data. This leads to particularly severe extrapolation when our candidate policies dive…
We derive sublinear regret bounds for undiscounted reinforcement learning in continuous state space. The proposed algorithm combines state aggregation with the use of upper confidence bounds for implementing optimism in the face of uncertainty. Beside the existence of an optimal policy which satisfies the Poisson equation, the only assumptions made are Holder continuity of rewards and transition probabilities.
Amazon Web Services（亚马逊云科技）；University of Pennsylvania（宾夕法尼亚大学）
This paper prescribes a suite of techniques for off-policy Reinforcement Learning (RL) that simplify the training process and reduce the sample complexity. First, we show that simple Deterministic Policy Gradient works remarkably well as long as the overestimation bias is controlled. This is contrast to existing literature which creates sophisticated off-policy techniques. Second, we pinpoint training instabilities, typical of off-policy algorithms, to the greedy policy update step; existing solutions such as delayed policy updates do not mitigate this issue. Third, we show that ideas in the p…
Many real-world control problems involve both discrete decision variables - such as the choice of control modes, gear switching or digital outputs - as well as continuous decision variables - such as velocity setpoints, control gains or analogue outputs. However, when defining the corresponding optimal control or reinforcement learning problem, it is commonly approximated with fully continuous or fully discrete action spaces. These simplifications aim at tailoring the problem to a particular algorithm or solver which may only support one type of action space. Alternatively, expert heuristics a…
A policy is said to be robust if it maximizes the reward while considering a bad, or even adversarial, model. In this work we formalize two new criteria of robustness to action uncertainty. Specifically, we consider two scenarios in which the agent attempts to perform an action $a$, and (i) with probability $α$, an alternative adversarial action $\bar a$ is taken, or (ii) an adversary adds a perturbation to the selected action in the case of continuous action space. We show that our criteria are related to common forms of uncertainty in robotics domains, such as the occurrence of abrupt forces…
University of Freiburg（弗莱堡大学）；German Cancer Research Center (DKFZ)（德国癌症研究中心（DKFZ））；Bosch Center for Artificial Intelligence（博世人工智能中心）
Current Deep Reinforcement Learning algorithms still heavily rely on handcrafted neural network architectures. We propose a novel approach to automatically find strong topologies for continuous control tasks while only adding a minor overhead in terms of interactions in the environment. To achieve this, we combine Neuroevolution techniques with off-policy training and propose a novel architecture mutation operator. Experiments on five continuous control benchmarks show that the proposed Actor-Critic Neuroevolution algorithm often outperforms the strong Actor-Critic baseline and is capable of a…
McGill University（麦吉尔大学）；Facebook AI Research（Facebook人工智能研究院）
The risks and perils of overfitting in machine learning are well known. However most of the treatment of this, including diagnostic tools and remedies, was developed for the supervised learning case. In this work, we aim to offer new perspectives on the characterization and prevention of overfitting in deep Reinforcement Learning (RL) methods, with a particular focus on continuous domains. We examine several aspects, such as how to define and diagnose overfitting in MDPs, and how to reduce risks by injecting sufficient training diversity. This work complements recent findings on the brittlenes…
Action delays degrade the performance of reinforcement learning in many real-world systems. This paper proposes a formal definition of delay-aware Markov Decision Process and proves it can be transformed into standard MDP with augmented states using the Markov reward process. We develop a delay-aware model-based reinforcement learning framework that can incorporate the multi-step delay into the learned system models without learning effort. Experiments with the Gym and MuJoCo platforms show that the proposed delay-aware model-based algorithm is more efficient in training and transferable betwe…
Imperial College London（帝国理工学院）；MRC Clinical Science Center（英国医学研究委员会临床科学中心）
Nonlinear optimal control problems are often solved with numerical methods that require knowledge of system's dynamics which may be difficult to infer, and that carry a large computational cost associated with iterative calculations. We present a novel neurobiologically inspired hierarchical learning framework, Reinforcement Learning Optimal Control, which operates on two levels of abstraction and utilises a reduced number of controllers to solve nonlinear systems with unknown dynamics in continuous state and action spaces. Our approach is inspired by research at two levels of abstraction: fir…
Tencent AI Lab（腾讯人工智能实验室）；Princeton University（普林斯顿大学）；Northwestern University（西北大学）
Most existing deep reinforcement learning (DRL) frameworks consider either discrete action space or continuous action space solely. Motivated by applications in computer games, we consider the scenario with discrete-continuous hybrid action space. To handle hybrid action space, previous works either approximate the hybrid space by discretization, or relax it into a continuous set. In this paper, we propose a parametrized deep Q-network (P- DQN) framework for the hybrid action space without approximation or relaxation. Our algorithm combines the spirits of both DQN (dealing with discrete action…
Department of Informatics Universit\"at Hamburg Germany
Deep reinforcement learning has recently gained a focus on problems where policy or value functions are independent of goals. Evidence exists that the sampling of goals has a strong effect on the learning performance, but there is a lack of general mechanisms that focus on optimizing the goal sampling process. In this work, we present a simple and general goal masking method that also allows us to estimate a goal's difficulty level and thus realize a curriculum learning approach for deep RL. Our results indicate that focusing on goals with a medium difficulty level is appropriate for deep dete…
This manuscript surveys reinforcement learning from the perspective of optimization and control with a focus on continuous control applications. It surveys the general formulation, terminology, and typical experimental implementations of reinforcement learning and reviews competing solution paradigms. In order to compare the relative merits of various techniques, this survey presents a case study of the Linear Quadratic Regulator (LQR) with unknown dynamics, perhaps the simplest and best-studied problem in optimal control. The manuscript describes how merging techniques from learning theory an…
Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）
In this article, we sketch an algorithm that extends the Q-learning algorithms to the continuous action space domain. Our method is based on the discretization of the action space. Despite the commonly used discretization methods, our method does not increase the discretized problem dimensionality exponentially. We will show that our proposed method is linear in complexity when the discretization is employed. The variant of the Q-learning algorithm presented in this work, labeled as Finite Step Q-Learning (FSQ), can be deployed to both shallow and deep neural network architectures.
This paper proposes GProp, a deep reinforcement learning algorithm for continuous policies with compatible function approximation. The algorithm is based on two innovations. Firstly, we present a temporal-difference based method for learning the gradient of the value-function. Secondly, we present the deviator-actor-critic (DAC) model, which comprises three neural networks that estimate the value function, its gradient, and determine the actor's policy respectively. We evaluate GProp on two challenging tasks: a contextual bandit problem constructed from nonparametric regression datasets that i…
Reinforcement learning (RL) has demonstrated its ability to solve high dimensional tasks by leveraging non-linear function approximators. However, these successes are mostly achieved by 'black-box' policies in simulated domains. When deploying RL to the real world, several concerns regarding the use of a 'black-box' policy might be raised. In order to make the learned policies more transparent, we propose in this paper a policy iteration scheme that retains a complex function approximator for its internal value predictions but constrains the policy to have a concise, hierarchical, and human-re…
Exploration in environments with continuous control and sparse rewards remains a key challenge in reinforcement learning (RL). Recently, surprise has been used as an intrinsic reward that encourages systematic and efficient exploration. We introduce a new definition of surprise and its RL implementation named Variational Assorted Surprise Exploration (VASE). VASE uses a Bayesian neural network as a model of the environment dynamics and is trained using variational inference, alternately updating the accuracy of the agent's model and policy. Our experiments show that in continuous control spars…
EDF R&D（法国电力公司研发部）；FIME（FIME实验室）；University of California, Berkeley（加州大学伯克利分校）；University of Oxford（牛津大学）
We study finite-time horizon continuous-time linear-quadratic reinforcement learning problems in an episodic setting, where both the state and control coefficients are unknown to the controller. We first propose a least-squares algorithm based on continuous-time observations and controls, and establish a logarithmic regret bound of order $O((\ln M)(\ln\ln M))$, with $M$ being the number of learning episodes. The analysis consists of two parts: perturbation analysis, which exploits the regularity and robustness of the associated Riccati differential equation; and parameter estimation error, whi…
Reinforcement Learning and the Evolutionary Strategy are two major approaches in addressing complicated control problems. Both are strong contenders and have their own devotee communities. Both groups have been very active in developing new advances in their own domain and devising, in recent years, leading-edge techniques to address complex continuous control tasks. Here, in the context of Deep Reinforcement Learning, we formulate a parallelized version of the Proximal Policy Optimization method and a Deep Deterministic Policy Gradient method. Moreover, we conduct a thorough comparison betwee…
INRIA Lille – Nord Europe（里尔-北欧法国国家信息与自动化研究所）；Renault Group（雷诺集团）；Microsoft Research（微软研究院）；Orange Labs（奥兰治实验室）；Google Research（谷歌研究院）
A Budgeted Markov Decision Process (BMDP) is an extension of a Markov Decision Process to critical applications requiring safety constraints. It relies on a notion of risk implemented in the shape of a cost signal constrained to lie below an - adjustable - threshold. So far, BMDPs could only be solved in the case of finite state spaces with known dynamics. This work extends the state-of-the-art to continuous spaces environments and unknown dynamics. We show that the solution to a BMDP is a fixed point of a novel Budgeted Bellman Optimality operator. This observation allows us to introduce natu…
In recent years significant progress has been made in dealing with challenging problems using reinforcement learning.Despite its great success, reinforcement learning still faces challenge in continuous control tasks. Conventional methods always compute the derivatives of the optimal goal with a costly computation resources, and are inefficient, unstable and lack of robust-ness when dealing with such tasks. Alternatively, derivative-based methods treat the optimization process as a blackbox and show robustness and stability in learning continuous control tasks, but not data efficient in learni…
Maluuba, A Microsoft Company（Maluuba，微软旗下公司）；McGill University（麦吉尔大学）
Policy gradient methods in reinforcement learning have become increasingly prevalent for state-of-the-art performance in continuous control tasks. Novel methods typically benchmark against a few key algorithms such as deep deterministic policy gradients and trust region policy optimization. As such, it is important to present and use consistent baselines experiments. However, this can be difficult due to general variance in the algorithms, hyper-parameter tuning, and environment stochasticity. We investigate and discuss: the significance of hyper-parameters in policy gradients for continuous c…
Many real-world physical control systems are required to satisfy constraints upon deployment. Furthermore, real-world systems are often subject to effects such as non-stationarity, wear-and-tear, uncalibrated sensors and so on. Such effects effectively perturb the system dynamics and can cause a policy trained successfully in one domain to perform poorly when deployed to a perturbed version of the same domain. This can affect a policy's ability to maximize future rewards as well as the extent to which it satisfies constraints. We refer to this as constrained model misspecification. We present …
Nanjing University（南京大学）；East China Normal University（华东师范大学）
This paper addresses policy learning in non-stationary environments and games with continuous actions. Rather than the classical reward maximization mechanism, inspired by the ideas of follow-the-regularized-leader (FTRL) and mirror descent (MD) update, we propose a no-regret style reinforcement learning algorithm PORL for continuous action tasks. We prove that PORL has a last-iterate convergence guarantee, which is important for adversarial and cooperative games. Empirical studies show that, in stationary environments such as MuJoCo locomotion controlling tasks, PORL performs equally well as,…
In the coming years, the satellite broadband market will experience significant increases in the service demand, especially for the mobility sector, where demand is burstier. Many of the next generation of satellites will be equipped with numerous degrees of freedom in power and bandwidth allocation capabilities, making manual resource allocation impractical and inefficient. Therefore, it is desirable to automate the operation of these highly flexible satellites. This paper presents a novel power allocation approach based on Deep Reinforcement Learning (DRL) that represents the problem as cont…
We provide a framework for incorporating robustness -- to perturbations in the transition dynamics which we refer to as model misspecification -- into continuous control Reinforcement Learning (RL) algorithms. We specifically focus on incorporating robustness into a state-of-the-art continuous control RL algorithm called Maximum a-posteriori Policy Optimization (MPO). We achieve this by learning a policy that optimizes for a worst case expected return objective and derive a corresponding robust entropy-regularized Bellman contraction operator. In addition, we introduce a less conservative, sof…
We present Simion Zoo, a Reinforcement Learning (RL) workbench that provides a complete set of tools to design, run, and analyze the results,both statistically and visually, of RL control applications. The main features that set apart Simion Zoo from similar software packages are its easy-to-use GUI, its support for distributed execution including deployment over graphics processing units (GPUs) , and the possibility to explore concurrently the RL metaparameter space, which is key to successful RL experimentation.
McGill University（麦吉尔大学）；Mila – Quebec AI Institute（米拉-魁北克人工智能研究所）；Google Brain（谷歌大脑）
Continuous-time reinforcement learning offers an appealing formalism for describing control problems in which the passage of time is not naturally divided into discrete increments. Here we consider the problem of predicting the distribution of returns obtained by an agent interacting in a continuous-time, stochastic environment. Accurate return predictions have proven useful for determining optimal policies for risk-sensitive control, learning state representations, multiagent coordination, and more. We begin by establishing the distributional analogue of the Hamilton-Jacobi-Bellman (HJB) equa…
McGill University（麦吉尔大学）；Mila；Deakin University（迪肯大学）；Université Laval（拉瓦尔大学）；Facebook AI Research；MSR Montreal（蒙特利尔微软研究院）；Université de Montréal（蒙特利尔大学）
Continuous control tasks in reinforcement learning are important because they provide an important framework for learning in high-dimensional state spaces with deceptive rewards, where the agent can easily become trapped into suboptimal solutions. One way to avoid local optima is to use a population of agents to ensure coverage of the policy space, yet learning a population with the "best" coverage is still an open problem. In this work, we present a novel approach to population-based RL in continuous control that leverages properties of normalizing flows to perform attractive and repulsive op…
Indian Institute of Technology (BHU)（印度理工学院（贝拿勒斯印度教大学））；Indian Institute of Technology, Hyderabad（印度理工学院海得拉巴分校）
We consider the finite horizon continuous reinforcement learning problem. Our contribution is three-fold. First,we give a tractable algorithm based on optimistic value iteration for the problem. Next,we give a lower bound on regret of order $Ω(T^{2/3})$ for any algorithm discretizes the state space, improving the previous regret bound of $Ω(T^{1/2})$ of Ortner and Ryabko \cite{contrl} for the same problem. Next,under the assumption that the rewards and transitions are Hölder Continuous we show that the upper bound on the discretization error is $const.Ln^{-α}T$. Finally,we give some simple exp…
Reinforcement learning (RL) is empirically successful in complex nonlinear Markov decision processes (MDPs) with continuous state spaces. By contrast, the majority of theoretical RL literature requires the MDP to satisfy some form of linear structure, in order to guarantee sample efficient RL. Such efforts typically assume the transition dynamics or value function of the MDP are described by linear functions of the state features. To resolve this discrepancy between theory and practice, we introduce the Effective Planning Window (EPW) condition, a structural condition on MDPs that makes no lin…
Tianjin University（天津大学）；Fuxi AI Lab in Netease（网易伏羲人工智能实验室）
Deep Reinforcement Learning (DRL) has been applied to address a variety of cooperative multi-agent problems with either discrete action spaces or continuous action spaces. However, to the best of our knowledge, no previous work has ever succeeded in applying DRL to multi-agent problems with discrete-continuous hybrid (or parameterized) action spaces which is very common in practice. Our work fills this gap by proposing two novel algorithms: Deep Multi-Agent Parameterized Q-Networks (Deep MAPQN) and Deep Multi-Agent Hierarchical Hybrid Q-Networks (Deep MAHHQN). We follow the centralized trainin…
This paper explores the potential of event cameras to enable continuous time reinforcement learning. We formalise this problem where a continuous stream of unsynchronised observations is used to produce a corresponding stream of output actions for the environment. This lack of synchronisation enables greatly enhanced reactivity. We present a method to train on event streams derived from standard RL environments, thereby solving the proposed continuous time RL problem. The CERiL algorithm uses specialised network layers which operate directly on an event stream, rather than aggregating events i…
We present DrQ-v2, a model-free reinforcement learning (RL) algorithm for visual continuous control. DrQ-v2 builds on DrQ, an off-policy actor-critic approach that uses data augmentation to learn directly from pixels. We introduce several improvements that yield state-of-the-art results on the DeepMind Control Suite. Notably, DrQ-v2 is able to solve complex humanoid locomotion tasks directly from pixel observations, previously unattained by model-free RL. DrQ-v2 is conceptually simple, easy to implement, and provides significantly better computational footprint compared to prior work, with the…
Syracuse University（雪城大学）；DiDi AI Labs, Didi Chuxing（滴滴出行人工智能实验室）
While Deep Reinforcement Learning (DRL) has emerged as a promising approach to many complex tasks, it remains challenging to train a single DRL agent that is capable of undertaking multiple different continuous control tasks. In this paper, we present a Knowledge Transfer based Multi-task Deep Reinforcement Learning framework (KTM-DRL) for continuous control, which enables a single DRL agent to achieve expert-level performance in multiple different tasks by learning from task-specific teachers. In KTM-DRL, the multi-task agent first leverages an offline knowledge transfer algorithm designed pa…
Reinforcement learning algorithms rely on exploration to discover new behaviors, which is typically achieved by following a stochastic policy. In continuous control tasks, policies with a Gaussian distribution have been widely adopted. Gaussian exploration however does not result in smooth trajectories that generally correspond to safe and rewarding behaviors in practical tasks. In addition, Gaussian policies do not result in an effective exploration of an environment and become increasingly inefficient as the action rate increases. This contributes to a low sample efficiency often observed in…
Continuous Time Continuous Space Homeostatic Reinforcement Learning (CTCS-HRRL) : Towards Biological Self-Autonomous Agent
Ecole Normale Superieure（巴黎高等师范学院）；BITS Pilani K. K. Birla Goa Campus（比拉理工学院K. K. Birla果阿校区）；Ecole Normale Supérieure Paris-Saclay（巴黎-萨克雷高等师范学院）；Université Paris-Saclay（巴黎-萨克雷大学）
University of California, Berkeley（加州大学伯克利分校）；Ghent University（根特大学）；OpenAI
Recently, researchers have made significant progress combining the advances in deep learning for learning feature representations with reinforcement learning. Some notable examples include training agents to play Atari games based on raw pixel data and to acquire advanced manipulation skills using raw sensory inputs. However, it has been difficult to quantify progress in the domain of continuous control due to the lack of a commonly adopted benchmark. In this work, we present a benchmark suite of continuous control tasks, including classic tasks like cart-pole swing-up, tasks with very high st…
Reinforcement Learning with Continuous Actions Under Unmeasured Confounding
Department of Statistics, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校统计学系）；Department of Human Development and Family Studies, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校人类发展与家庭研究系）；Department of Statistics, University of California Irvine（加州大学尔湾分校统计学系）；Department of Decision Sciences, The George Washington University（乔治华盛顿大学决策科学系）；School of Management & Center for Data Science, Zhejiang University（浙江大学管理学院及数据科学中心）
