Evolutionary Development of Hierarchical Learning Structures

Hierarchical reinforcement learning (RL) algorithms can learn a policy faster than standard RL algorithms. However, the applicability of hierarchical RL algorithms is limited by the fact that the task decomposition has to be performed in advance by the human designer. We propose a Lamarckian evolutionary approach for automatic development of the learning structure in hierarchical RL. The proposed method combines the MAXQ hierarchical RL method and genetic programming (GP). In the MAXQ framework, a subtask can optimize the policy independently of its parent task's policy, which makes it possible to reuse learned policies of the subtasks. In the proposed method, the MAXQ method learns the policy based on the task hierarchies obtained by GP, while the GP explores the appropriate hierarchies using the result of the MAXQ method. To show the validity of the proposed method, we have performed simulation experiments for a foraging task in three different environmental settings. The results show strong interconnection between the obtained learning structures and the given task environments. The main conclusion of the experiments is that the GP can find a minimal strategy, i.e., a hierarchy that minimizes the number of primitive subtasks that can be executed for each type of situation. The experimental results for the most challenging environment also show that the policies of the subtasks can continue to improve, even after the structure of the hierarchy has been evolutionary stabilized, as an effect of Lamarckian mechanisms     

Continuous-action reinforcement learning with fast policy search and adaptive basis function selection

As an important approach to solving complex sequential decision problems, reinforcement learning (RL) has been widely studied in the community of artificial intelligence and machine learning. However, the generalization ability of RL is still an open problem and it is difficult for existing RL algorithms to solve Markov decision problems (MDPs) with both continuous state and action spaces. In this paper, a novel RL approach with fast policy search and adaptive basis function selection, which is called Continuous-action Approximate Policy Iteration (CAPI), is proposed for RL in MDPs with both continuous state and action spaces. In CAPI, based on the value functions estimated by temporal-difference learning, a fast policy search technique is suggested to search for optimal actions in continuous spaces, which is computationally efficient and easy to implement. To improve the generalization ability and learning efficiency of CAPI, two adaptive basis function selection methods are developed so that sparse approximation of value functions can be obtained efficiently both for linear function approximators and kernel machines. Simulation results on benchmark learning control tasks with continuous state and action spaces show that the proposed approach not only can converge to a near-optimal policy in a few iterations but also can obtain comparable or even better performance than Sarsa-learning, and previous approximate policy iteration methods such as LSPI and KLSPI.     

Hierarchical multi-agent reinforcement learning

In this paper, we investigate the use of hierarchical reinforcement learning (HRL) to speed up the acquisition of cooperative multi-agent tasks. We introduce a hierarchical multi-agent reinforcement learning (RL) framework, and propose a hierarchical multi-agent RL algorithm called Cooperative HRL. In this framework, agents are cooperative and homogeneous (use the same task decomposition). Learning is decentralized, with each agent learning three interrelated skills: how to perform each individual subtask, the order in which to carry them out, and how to coordinate with other agents. We define cooperative subtasks to be those subtasks in which coordination among agents significantly improves the performance of the overall task. Those levels of the hierarchy which include cooperative subtasks are called cooperation levels. A fundamental property of the proposed approach is that it allows agents to learn coordination faster by sharing information at the level of cooperative subtasks, rather than attempting to learn coordination at the level of primitive actions. We study the empirical performance of the Cooperative HRL algorithm using two testbeds: a simulated two-robot trash collection task, and a larger four-agent automated guided vehicle (AGV) scheduling problem. We compare the performance and speed of Cooperative HRL with other learning algorithms, as well as several well-known industrial AGV heuristics. We also address the issue of rational communication behavior among autonomous agents in this paper. The goal is for agents to learn both action and communication policies that together optimize the task given a communication cost. We extend the multi-agent HRL framework to include communication decisions and propose a cooperative multi-agent HRL algorithm called COM-Cooperative HRL. In this algorithm, we add a communication level to the hierarchical decomposition of the problem below each cooperation level. Before an agent makes a decision at a cooperative subtask, it decides if it is worthwhile to perform a communication action. A communication action has a certain cost and provides the agent with the actions selected by the other agents at a cooperation level. We demonstrate the efficiency of the COM-Cooperative HRL algorithm as well as the relation between the communication cost and the learned communication policy using a multi-agent taxi problem.     

The $n$th-Order Bias Optimality for Multichain Markov Decision Processes

In this paper, we propose a new approach to the theory of finite multichain Markov decision processes (MDPs) with different performance optimization criteria. We first propose the concept of nth-order bias; then, using the average reward and bias difference formulas derived in this paper, we develop an optimization theory for finite MDPs that covers a complete spectrum from average optimality, bias optimality, to all high-order bias optimality, in a unified way. The approach is simple, direct, natural, and intuitive; it depends neither on Laurent series expansion nor on discounted MDPs. We also propose one-phase policy iteration algorithms for bias and high-order bias optimal policies, which are more efficient than the two-phase algorithms in the literature. Furthermore, we derive high-order bias optimality equations. This research is a part of our effort in developing sensitivity-based learning and optimization theory.     

Kernel-based reinforcement learning in average-cost problems

Reinforcement learning (RL) is concerned with the identification of optimal controls in Markov decision processes (MDPs) where no explicit model of the transition probabilities is available. We propose a class of RL algorithms which always produces stable estimates of the value function. In detail, we use "local averaging" methods to construct an approximate dynamic programming (ADP) algorithm. Nearest-neighbor regression, grid-based approximations, and trees can all be used as the basis of this approximation. We provide a thorough theoretical analysis of this approach and we demonstrate that ADP converges to a unique approximation in continuous-state average-cost MDPs. In addition, we prove that our method is consistent in the sense that an optimal approximate strategy is identified asymptotically. With regard to a practical implementation, we suggest a reduction of ADP to standard dynamic programming in an artificial finite-state MDP.     

Markov decision Processes with fractional costs

Certain methods for constructing embedded Markov decision processes (MDPs) lead to performance measures that are the ratio of two long-run averages. For such MDPs with finite state and action spaces and under an ergodicity assumption, this note presents algorithms for computing optimal policies based on policy iterations, linear programming, value iterations and Q-learning.     

Transfer learning with Partially Constrained Models: Application to reinforcement learning of linked multicomponent robot system control

Transfer learning is a hierarchical approach to reinforcement learning of complex tasks modeled as Markov Decision Processes. The learning results on the source task are used as the starting point for the learning on the target task. In this paper we deal with a hierarchy of constrained systems, where the source task is an under-constrained system, hence called the Partially Constrained Model (PCM). Constraints in the framework of reinforcement learning are dealt with by state-action veto policies. We propose a theoretical background for the hierarchy of training refinements, showing that the effective action repertoires learnt on the PCM are maximal, and that the PCM-optimal policy gives maximal state value functions. We apply the approach to learn the control of Linked Multicomponent Robotic Systems using Reinforcement Learning. The paradigmatic example is the transportation of a hose. The system has strong physical constraints and a large state space. Learning experiments in the target task are realized over an accurate but computationally expensive simulation of the hose dynamics. The PCM is obtained simplifying the hose model. Learning results of the PCM Transfer Learning show an spectacular improvement over conventional Q-learning on the target task.     

Solving Controlled Markov Set-Chains With Discounting via Multipolicy Improvement

We consider Markov decision processes (MDPs) where the state transition probability distributions are not uniquely known, but are known to belong to some intervals-so called "controlled Markov set-chains"-with infinite-horizon discounted reward criteria. We present formal methods to improve multiple policies for solving such controlled Markov set-chains. Our multipolicy improvement methods follow the spirit of parallel rollout and policy switching for solving MDPs. In particular, these methods are useful for online control of Markov set-chains and for designing policy iteration (PI) type algorithms. We develop a PI-type algorithm and prove that it converges to an optimal policy     

Transfer in variable-reward hierarchical reinforcement learning

Transfer learning seeks to leverage previously learned tasks to achieve faster learning in a new task. In this paper, we consider transfer learning in the context of related but distinct Reinforcement Learning (RL) problems. In particular, our RL problems are derived from Semi-Markov Decision Processes (SMDPs) that share the same transition dynamics but have different reward functions that are linear in a set of reward features. We formally define the transfer learning problem in the context of RL as learning an efficient algorithm to solve any SMDP drawn from a fixed distribution after experiencing a finite number of them. Furthermore, we introduce an online algorithm to solve this problem, Variable-Reward Reinforcement Learning (VRRL), that compactly stores the optimal value functions for several SMDPs, and uses them to optimally initialize the value function for a new SMDP. We generalize our method to a hierarchical RL setting where the different SMDPs share the same task hierarchy. Our experimental results in a simplified real-time strategy domain show that significant transfer learning occurs in both flat and hierarchical settings. Transfer is especially effective in the hierarchical setting where the overall value functions are decomposed into subtask value functions which are more widely amenable to transfer across different SMDPs.     

分层强化学习中的并行自动分层方法研究

为加快分层强化学习中任务层次结构的自动生成速度,提出了一种基于多智能体系统的并行自动分层方法,该方法以Sutton提出的Option分层强化学习方法为理论框架,首先由多智能体合作对状态空间进行并行探测并集中聚类产生状态子空间,然后多智能体并行学习生成各子空间上内部策略,最终生成Option.以二维有障碍栅格空间内两点间最短路径规划为任务背景给出了算法并进行了仿真实验和分析,结果表明,并行自动分层方法生成任务层次结构的速度明显快于以往的串行自动分层方法.本文的方法适用于空间探测、路径规划、追逃等类问题领域.     

Convergence Results for Single-Step On-Policy Reinforcement-Learning Algorithms

An important application of reinforcement learning (RL) is to finite-state control problems and one of the most difficult problems in learning for control is balancing the exploration/exploitation tradeoff. Existing theoretical results for RL give very little guidance on reasonable ways to perform exploration. In this paper, we examine the convergence of single-step on-policy RL algorithms for control. On-policy algorithms cannot separate exploration from learning and therefore must confront the exploration problem directly. We prove convergence results for several related on-policy algorithms with both decaying exploration and persistent exploration. We also provide examples of exploration strategies that can be followed during learning that result in convergence to both optimal values and optimal policies.     

The linguistic attribute hierarchy and its optimisation for classification

A hierarchical approach to decomposing a high-dimensional model into series of low-dimensional sub-models can be an effective way to overcome the ‘curse of dimensionality’ problem. We investigate a hierarchy of linguistic decision trees (LDTs) for classification, and present linguistic interpretation of the hierarchy of LDTs. Due to the uncertain and non-linear relationship between input attributes and a goal, different hierarchies could have different performance for classification. We develop a GA with the linguistic ID3 in wrapper to optimize linguistic attribute hierarchy. The experimental results show that optimised linguistic attribute hierarchies perform better on the benchmark databases than a single LDT does, and they can greatly reduce the number of rules when the relationship between a goal variable and input attributes is highly uncertain and nonlinear. Comparing with well-known machine learning approaches, C4.5, Naive Bayes, and Neural Networks, the optimised linguistic attribute hierarchy achieves the highest accuracies for most tested databases. The trained hierarchy can be a real-time classifier if the optimization of hierarchies is performed offline.     

Structured prediction with reinforcement learning

We formalize the problem of Structured Prediction as a Reinforcement Learning task. We first define a Structured Prediction Markov Decision Process (SP-MDP), an instantiation of Markov Decision Processes for Structured Prediction and show that learning an optimal policy for this SP-MDP is equivalent to minimizing the empirical loss. This link between the supervised learning formulation of structured prediction and reinforcement learning (RL) allows us to use approximate RL methods for learning the policy. The proposed model makes weak assumptions both on the nature of the Structured Prediction problem and on the supervision process. It does not make any assumption on the decomposition of loss functions, on data encoding, or on the availability of optimal policies for training. It then allows us to cope with a large range of structured prediction problems. Besides, it scales well and can be used for solving both complex and large-scale real-world problems. We describe two series of experiments. The first one provides an analysis of RL on classical sequence prediction benchmarks and compares our approach with state-of-the-art SP algorithms. The second one introduces a tree transformation problem where most previous models fail. This is a complex instance of the general labeled tree mapping problem. We show that RL exploration is effective and leads to successful results on this challenging task. This is a clear confirmation that RL could be used for large size and complex structured prediction problems.     

Pneumatic artificial muscle-driven robot control using local update reinforcement learning

In this study, a new value function based Reinforcement learning (RL) algorithm, Local Update Dynamic Policy Programming (LUDPP), is proposed. It exploits the nature of smooth policy update using Kullback–Leibler divergence to update its value function locally and considerably reduces the computational complexity. We firstly investigated the learning performance of LUDPP and other algorithms without smooth policy update for tasks of pendulum swing up and n DOFs manipulator reaching in simulation. Only LUDPP could efficiently and stably learn good control policies in high dimensional systems with limited number of training samples. In real word application, we applied LUDPP to control Pneumatic Artificial Muscles (PAMs) driven robots without the knowledge of model which is challenging for traditional methods due to the high nonlinearities of PAM’s air pressure dynamics and mechanical structure. LUDPP successfully achieved one finger control of Shadow Dexterous Hand, a PAM-driven humanoid robot hand, with far lower computational resource compared with other conventional value function based RL algorithms.     

Kernel-based least squares policy iteration for reinforcement learning.

In this paper, we present a kernel-based least squares policy iteration (KLSPI) algorithm for reinforcement learning (RL) in large or continuous state spaces, which can be used to realize adaptive feedback control of uncertain dynamic systems. By using KLSPI, near-optimal control policies can be obtained without much a priori knowledge on dynamic models of control plants. In KLSPI, Mercer kernels are used in the policy evaluation of a policy iteration process, where a new kernel-based least squares temporal-difference algorithm called KLSTD-Q is proposed for efficient policy evaluation. To keep the sparsity and improve the generalization ability of KLSTD-Q solutions, a kernel sparsification procedure based on approximate linear dependency (ALD) is performed. Compared to the previous works on approximate RL methods, KLSPI makes two progresses to eliminate the main difficulties of existing results. One is the better convergence and (near) optimality guarantee by using the KLSTD-Q algorithm for policy evaluation with high precision. The other is the automatic feature selection using the ALD-based kernel sparsification. Therefore, the KLSPI algorithm provides a general RL method with generalization performance and convergence guarantee for large-scale Markov decision problems (MDPs). Experimental results on a typical RL task for a stochastic chain problem demonstrate that KLSPI can consistently achieve better learning efficiency and policy quality than the previous least squares policy iteration (LSPI) algorithm. Furthermore, the KLSPI method was also evaluated on two nonlinear feedback control problems, including a ship heading control problem and the swing up control of a double-link underactuated pendulum called acrobot. Simulation results illustrate that the proposed method can optimize controller performance using little a priori information of uncertain dynamic systems. It is also demonstrated that KLSPI can be applied to online learning control by incorporating an initial controller to ensure online performance.     

Key hierarchies for hierarchical access control in secure group communications

The problem of hierarchical access control in secure group communications has elicited much interest in the literatures. However, most of the researches to date on hierarchical access control pay more attention to the particular encryption techniques, but considered little about the features of key hierarchies. In hierarchical access control systems, keys are usually organized hierarchically. We analyze the user-based, resource-based and unified key hierarchies in this paper. The first two hierarchies are established from the access matrix. By unifying these two hierarchies, we get the unified key hierarchy. Furthermore, we introduce the explicit accessible set and the explicit dominating set to describe the key distributions for these hierarchies, and prove that the unified key hierarchy can be formed from the explicit dominating sets in the user-based key hierarchy or the explicit accessible sets in the resource-based key hierarchy. To evaluate the efficiency of the described key hierarchies, we combine these hierarchies with the existing key assignment models and analyze their storage and rekey overheads. These overheads can be derived from the access matrix, and the derivation procedure is described. The conclusions of this paper can help to establish a suitable key hierarchy so as to make the key assignment scheme more efficient in practical applications.     

一种基于自生成样本学习的奖赏塑形方法

强化学习通过从以往的决策反馈中学习,使Agent 做出正确的短期决策,以最大化其获得的累积奖赏值.以往研究发现,奖赏塑形方法通过提供简单、易学的奖赏替代函数(即奖赏塑性函数)来替换真实的环境奖赏,能够有效地提高强化学习性能.然而奖赏塑形函数通常是在领域知识或者最优策略示例的基础上建立的,均需要专家参与,代价高昂.研究是否可以在强化学习过程中自动地学习有效的奖赏塑形函数.通常,强化学习算法在学习过程中会采集大量样本.这些样本虽然有很多是失败的尝试,但对构造奖赏塑形函数可能提供有用信息.提出了针对奖赏塑形的新型最优策略不变条件,并在此基础上提出了RFPotential 方法,从自生成样本中学习奖赏塑形.在多个强化学习算法和问题上进行了实验,其结果表明,该方法可以加速强化学习过程.     

概率近似正确的强化学习算法解决连续状态空间控制问题

在线学习时长是强化学习算法的一个重要指标.传统在线强化学习算法如Q学习、状态–动作–奖励–状态–动作(state-action-reward-state-action,SARSA)等算法不能从理论分析角度给出定量的在线学习时长上界.本文引入概率近似正确(probably approximately correct,PAC)原理,为连续时间确定性系统设计基于数据的在线强化学习算法.这类算法有效记录在线数据,同时考虑强化学习算法对状态空间探索的需求,能够在有限在线学习时间内输出近似最优的控制.我们提出算法的两种实现方式,分别使用状态离散化和kd树(k-dimensional树)技术,存储数据和计算在线策略.最后我们将提出的两个算法应用在双连杆机械臂运动控制上,观察算法的效果并进行比较.     

Formal validation of automated policy refinement in the management of network security systems

Policy hierarchies and automated policy refinement are powerful approaches to simplify administration of security services in complex network environments. A crucial issue for the practical use of these approaches is to ensure the validity of the policy hierarchy, i.e. since the policy sets for the lower levels are automatically derived from the abstract policies (defined by the modeller), we must be sure that the derived policies uphold the high-level ones. This paper builds upon previous work on Model-based Management, particularly on the Diagram of Abstract Subsystems approach, and goes further to propose a formal validation approach for the policy hierarchies yielded by the automated policy refinement process. We establish general validation conditions for a multi-layered policy model, i.e. necessary and sufficient conditions that a policy hierarchy must satisfy so that the lower-level policy sets are valid refinements of the higher-level policies according to the criteria of consistency and completeness. Relying upon the validation conditions and upon axioms about the model representativeness, two theorems are proved to ensure compliance between the resulting system behaviour and the abstract policies that are modelled.     

A hierarchical reinforcement learning approach for optimal path tracking of wheeled mobile robots

Robust motion control is fundamental to autonomous mobile robots. In the past few years, reinforcement learning (RL) has attracted considerable attention in the feedback control of wheeled mobile robot. However, it is still difficult for RL to solve problems with large or continuous state spaces, which is common in robotics. To improve the generalization ability of RL, this paper presents a novel hierarchical RL approach for optimal path tracking of wheeled mobile robots. In the proposed approach, a graph Laplacian-based hierarchical approximate policy iteration (GHAPI) algorithm is developed, in which the basis functions are constructed automatically using the graph Laplacian operator. In GHAPI, the state space of an Markov decision process is divided into several subspaces and approximate policy iteration is carried out on each subspace. Then, a near-optimal path-tracking control strategy can be obtained by GHAPI combined with proportional-derivative (PD) control. The performance of the proposed approach is evaluated by using a P3-AT wheeled mobile robot. It is demonstrated that the GHAPI-based PD control can obtain better near-optimal control policies than previous approaches.