We consider the problem of Reinforcement Learning for nonlinear stochastic dynamical systems. We show that in the RL setting, there is an inherent ``Curse of Variance" in addition to Bellman's infamous ``Curse of Dimensionality", in particular, we show that the variance in the solution grows factorial-exponentially in the order of the approximation. A fundamental consequence is that this precludes the search for anything other than ``local" feedback solutions in RL, in order to control the explosive variance growth, and thus, ensure accuracy. We further show that the deterministic optimal control has a perturbation structure, in that the higher order terms do not affect the calculation of lower order terms, which can be utilized in RL to get accurate local solutions.
Reinforcement learning (RL) is always the preferred embodiment to construct the control strategy of complex tasks, like asymmetric assembly tasks. However, the convergence speed of reinforcement learning severely restricts its practical application. In this paper, the convergence is first accelerated by combining RL and compliance control. Then a completely innovative progressive extension of action dimension (PEAD) mechanism is proposed to optimize the convergence of RL algorithms. The PEAD method is verified in DDPG and PPO. The results demonstrate the PEAD method will enhance the data-effic…
University of Essex（埃塞克斯大学）；Harbin Institute of Technology（哈尔滨工业大学）；Delft University of Technology（代尔夫特理工大学）
In this paper, we consider the state estimation problem for nonlinear stochastic discrete-time systems. We combine Lyapunov's method in control theory and deep reinforcement learning to design the state estimator. We theoretically prove the convergence of the bounded estimate error solely using the data simulated from the model. An actor-critic reinforcement learning algorithm is proposed to learn the state estimator approximated by a deep neural network. The convergence of the algorithm is analysed. The proposed Lyapunov-based reinforcement learning state estimator is compared with a number o…
Ludwig Maximilian University of Munich（慕尼黑大学）；University of Colorado Boulder（科罗拉多大学博尔德分校）；Newcastle University（纽卡斯尔大学）
A novel reinforcement learning scheme to synthesize policies for continuous-space Markov decision processes (MDPs) is proposed. This scheme enables one to apply model-free, off-the-shelf reinforcement learning algorithms for finite MDPs to compute optimal strategies for the corresponding continuous-space MDPs without explicitly constructing the finite-state abstraction. The proposed approach is based on abstracting the system with a finite MDP (without constructing it explicitly) with unknown transition probabilities, synthesizing strategies over the abstract MDP, and then mapping the results …
Florida Institute for Human and Machine Cognition (IHMC)（佛罗里达人机认知研究所（IHMC））
Despite advancements in deep reinforcement learning algorithms, developing an effective exploration strategy is still an open problem. Most existing exploration strategies either are based on simple heuristics, or require the model of the environment, or train additional deep neural networks to generate imagination-augmented paths. In this paper, a revolutionary algorithm, called Policy Augmentation, is introduced. Policy Augmentation is based on a newly developed inductive matrix completion method. The proposed algorithm augments the values of unexplored state-action pairs, helping the agent …
C-STEP: Continuous Space-Time Empowerment for Physics-informed Safe Reinforcement Learning of Mobile Agents
Faculty of Technology, Bielefeld University, Germany（比勒菲尔德大学技术学院，德国）；Department of Electrical Engineering and Information Technology, Paderborn University, Germany（帕德博恩大学电气工程与信息科技系，德国）
School of Computing, Newcastle University（纽卡斯尔大学计算机学院）
This paper studies satisfaction of temporal properties on unknown stochastic processes that have continuous state spaces. We show how reinforcement learning (RL) can be applied for computing policies that are finite-memory and deterministic using only the paths of the stochastic process. We address properties expressed in linear temporal logic (LTL) and use their automaton representation to give a path-dependent reward function maximised via the RL algorithm. We develop the required assumptions and theories for the convergence of the learned policy to the optimal policy in the continuous state…
In this paper, we propose a generic framework for devising an adaptive approximation scheme for value function approximation in reinforcement learning, which introduces multiscale approximation. The two basic ingredients are multiresolution analysis as well as tree approximation. Starting from simple refinable functions, multiresolution analysis enables us to construct a wavelet system from which the basis functions are selected adaptively, resulting in a tree structure. Furthermore, we present the convergence rate of our multiscale approximation which does not depend on the regularity of basi…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
A common technique in reinforcement learning is to evaluate the value function from Monte Carlo simulations of a given policy, and use the estimated value function to obtain a new policy which is greedy with respect to the estimated value function. A well-known longstanding open problem in this context is to prove the convergence of such a scheme when the value function of a policy is estimated from data collected from a single sample path obtained from implementing the policy (see page 99 of [Sutton and Barto, 2018], page 8 of [Tsitsiklis, 2002]). We present a solution to the open problem by …
A basic simulation-based reinforcement learning algorithm is the Monte Carlo Exploring States (MCES) method, also known as optimistic policy iteration, in which the value function is approximated by simulated returns and a greedy policy is selected at each iteration. The convergence of this algorithm in the general setting has been an open question. In this paper, we investigate the convergence of this algorithm for the case with undiscounted costs, also known as the stochastic shortest path problem. The results complement existing partial results on this topic and thereby helps further settle…
In recent years, Reinforcement Learning (RL) has been applied to real-world problems with increasing success. Such applications often require to put constraints on the agent's behavior. Existing algorithms for constrained RL (CRL) rely on gradient descent-ascent, but this approach comes with a caveat. While these algorithms are guaranteed to converge on average, they do not guarantee last-iterate convergence, i.e., the current policy of the agent may never converge to the optimal solution. In practice, it is often observed that the policy alternates between satisfying the constraints and maxim…
Continuous World Coverage Path Planning for Fixed-Wing UAVs using Deep Reinforcement Learning
TUM School of Engineering and Design, Technical University of Munich（慕尼黑技术大学工程与设计学院）；Dept. of Electrical Engineering and Computer Sciences, University of California, Berkeley（加州大学伯克利分校电气工程与计算机科学系）
Many sequential decision-making problems need optimization of different objectives which possibly conflict with each other. The conventional way to deal with a multi-task problem is to establish a scalar objective function based on a linear combination of different objectives. However, for the case of having conflicting objectives with different scales, this method needs a trial-and-error approach to properly find proper weights for the combination. As such, in most cases, this approach cannot guarantee an optimal Pareto solution. In this paper, we develop a single-agent scale-independent mult…
University of Alberta（阿尔伯塔大学）；Harbin Institute of Technology（哈尔滨工业大学）；Huawei Technologies Ltd.（华为技术有限公司）
Anderson mixing has been heuristically applied to reinforcement learning (RL) algorithms for accelerating convergence and improving the sampling efficiency of deep RL. Despite its heuristic improvement of convergence, a rigorous mathematical justification for the benefits of Anderson mixing in RL has not yet been put forward. In this paper, we provide deeper insights into a class of acceleration schemes built on Anderson mixing that improve the convergence of deep RL algorithms. Our main results establish a connection between Anderson mixing and quasi-Newton methods and prove that Anderson mix…
Specialized Deep Residual Policy Safe Reinforcement Learning-Based Controller for Complex and Continuous State-Action Spaces
Software Competence Center Hagenberg, Data Science, Austria（哈根伯格软件中心数据科学部（奥地利））；Technological University Dublin, Computer Science, Dublin, Ireland（都柏林理工大学计算机科学系（爱尔兰都柏林））；ADAPT Research Centre, Dublin, Ireland（ADAPT研究中心（爱尔兰都柏林））
When designing algorithms for finite-time-horizon episodic reinforcement learning problems, a common approach is to introduce a fictitious discount factor and use stationary policies for approximations. Empirically, it has been shown that the fictitious discount factor helps reduce variance, and stationary policies serve to save the per-iteration computational cost. Theoretically, however, there is no existing work on convergence analysis for algorithms with this fictitious discount recipe. This paper takes the first step towards analyzing these algorithms. It focuses on two vanilla policy gra…
Technische Universität München（慕尼黑工业大学）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）
In this work, we study the system of interacting non-cooperative two Q-learning agents, where one agent has the privilege of observing the other's actions. We show that this information asymmetry can lead to a stable outcome of population learning, which generally does not occur in an environment of general independent learners. The resulting post-learning policies are almost optimal in the underlying game sense, i.e., they form a Nash equilibrium. Furthermore, we propose in this work a Q-learning algorithm, requiring predictive observation of two subsequent opponent's actions, yielding an opt…
Due to the increasing popularity of electric vehicles (EVs) and the technological advancement of EV electronics, the vehicle-to-grid (V2G) technique and large-scale scheduling algorithms have been developed to achieve a high level of renewable energy and power grid stability. This paper proposes a deep reinforcement learning (DRL) method for the continuous charging/discharging coordination strategy in aggregating large-scale EVs in V2G mode with renewable energy sources (RES). The DRL coordination strategy can efficiently optimize the electric vehicle aggregator's (EVA's) real-time charging/di…
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…
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…
Massachusetts Institute of Technology（麻省理工学院）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
We consider Model-Agnostic Meta-Learning (MAML) methods for Reinforcement Learning (RL) problems, where the goal is to find a policy using data from several tasks represented by Markov Decision Processes (MDPs) that can be updated by one step of stochastic policy gradient for the realized MDP. In particular, using stochastic gradients in MAML update steps is crucial for RL problems since computation of exact gradients requires access to a large number of possible trajectories. For this formulation, we propose a variant of the MAML method, named Stochastic Gradient Meta-Reinforcement Learning (…
Linear-Quadratic Mean-Field Reinforcement Learning: Convergence of Policy Gradient Methods
Program in Applied and Computational Mathematics, Princeton（普林斯顿大学应用与计算数学项目）；Shanghai Frontiers Science Center of Artificial Intelligence and Deep Learning（上海人工智能与深度学习前沿科学中心）；NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai（纽约大学-华东师范大学纽约大学上海数学科学研究所）；NYU Shanghai（上海纽约大学）；Walmart Global Tech（沃尔玛全球科技）
In this paper, we study the global convergence of model-based and model-free policy gradient descent and natural policy gradient descent algorithms for linear quadratic deep structured teams. In such systems, agents are partitioned into a few sub-populations wherein the agents in each sub-population are coupled in the dynamics and cost function through a set of linear regressions of the states and actions of all agents. Every agent observes its local state and the linear regressions of states, called deep states. For a sufficiently small risk factor and/or sufficiently large population, we pro…
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…
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 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.
In this paper, as a study of reinforcement learning, we converge the Q function to unbounded rewards such as Gaussian distribution. From the central limit theorem, in some real-world applications it is natural to assume that rewards follow a Gaussian distribution , but existing proofs cannot guarantee convergence of the Q-function. Furthermore, in the distribution-type reinforcement learning and Bayesian reinforcement learning that have become popular in recent years, it is better to allow the reward to have a Gaussian distribution. Therefore, in this paper, we prove the convergence of the Q-f…
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,…
Modern meta-reinforcement learning (Meta-RL) methods are mainly developed based on model-agnostic meta-learning, which performs policy gradient steps across tasks to maximize policy performance. However, the gradient conflict problem is still poorly understood in Meta-RL, which may lead to performance degradation when encountering distinct tasks. To tackle this challenge, this paper proposes a novel personalized Meta-RL (pMeta-RL) algorithm, which aggregates task-specific personalized policies to update a meta-policy used for all tasks, while maintaining personalized policies to maximize the a…
Tsinghua University（清华大学）；Carnegie Mellon University（卡内基梅隆大学）；Duke University（杜克大学）；California Institute of Technology（加州理工学院）
We study a multi-agent reinforcement learning (MARL) problem where the agents interact over a given network. The goal of the agents is to cooperatively maximize the average of their entropy-regularized long-term rewards. To overcome the curse of dimensionality and to reduce communication, we propose a Localized Policy Iteration (LPI) algorithm that provably learns a near-globally-optimal policy using only local information. In particular, we show that, despite restricting each agent's attention to only its $κ$-hop neighborhood, the agents are able to learn a policy with an optimality gap that …
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…
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…
Reinforcement Learning for Exponential Utility: Algorithms and Convergence in Discounted MDPs
Computer Science and Automation, Indian Institute of Science, Bengaluru（印度科学研究院计算机科学与自动化部门，班加罗尔）；Computer Science and Engineering, Indian Institute of Technology Madras, Chennai（印度理工学院马德拉斯分校计算机科学与工程系，钦奈）；Tata Consultancy Services Limited, Hyderabad（海得拉巴市塔塔咨询公司）
