基于策略迭代和值迭代的POMDP算法

部分可观察Markov决策过程是通过引入信念状态空间将非Markov链问题转化为Markov链问题来求解,其描述真实世界的特性使它成为研究随机决策过程的重要分支.介绍了部分可观察Markov决策过程的基本原理和决策过程,提出一种基于策略迭代和值迭代的部分可观察Markov决策算法,该算法利用线性规划和动态规划的思想,解决当信念状态空间较大时出现的"维数灾"问题,得到Markov决策的逼近最优解.实验数据表明该算法是可行的和有效的.     

一种基于独立任务的POMDP问题的解决方法*

部分可观测马尔可夫决策过程(POMDP)是马尔可夫决策过程(MDP)的扩展。通常利用POMDPs来模拟在部分可观测的随机环境中决策的Agents。针对完整POMDP的求解方法扩展能力弱的问题,提出把一个多元的POMDP分解成一组受限制的POMDPs,然后分别独立地求解每个这样的模型,获得一个值函数并将这些受限制的POMDPs的值函数结合起来以便获得一个完整POMDP的策略。该方法主要阐述了识别与独立任务相关的状态变量的过程,以及如何构造一个被限制在一个单独任务上的模型。将该方法应用到两个不同规模的岩石采样问题中,实验结果表明,该方法能够获得很好的策略。     

Planning for multiple measurement channels in a continuous-state POMDP

Continuous-state partially observable Markov decision processes (POMDPs) are an intuitive choice of representation for many stochastic planning problems with a hidden state. We consider a continuous-state POMDPs with finite action and observation spaces, where the POMDP is parametrised by weighted sums of Gaussians, or Gaussian mixture models (GMMs). In particular, we study the problem of optimising the selection of measurement channel in such a framework. A new error bound for a point-based value iteration algorithm is derived, and a method for constructing a subset of belief states that attempts to reduce the error bound is implemented. In the experiments, applying continuous-state POMDPs for optimal selection of the measurement channel is demonstrated, and the performance of three GMM simplification methods is compared. Convergence of a point-based value iteration algorithm is investigated by considering various metrics for the obtained control policies.     

An online multi-agent co-operative learning algorithm in POMDPs

Solving partially observable Markov decision processes (POMDPs) is a complex task that is often intractable. This paper examines the problem of finding an optimal policy for POMDPs. While a lot of effort has been made to develop algorithms to solve POMDPs, the question of automatically finding good low-dimensional spaces in multi-agent co-operative learning domains has not been explored thoroughly. To identify this question, an online algorithm CMEAS is presented to improve the POMDP model. This algorithm is based on a look-ahead search to find the best action to execute at each cycle. Thus the overwhelming complexity of computing a policy for each possible situation is avoided. A series of simulations demonstrate this good strategy and performance of the proposed algorithm when multiple agents co-operate to find an optimal policy for POMDPs.     

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.     

基于信念重用的WSNs能量高效跟踪

针对无线传感器网络(WSNs)中目标跟踪性能与传感器能量消耗难以平衡问题,提出一种信念重用的WSNs能量高效跟踪算法。使用部分可观察马尔可夫决策过程(POMDPs)对动态不确定环境下的WSNs进行建模,将跟踪性能与能量消耗平衡优化问题转化为POMDPs最优值函数求解过程;采用最大报酬值启发式查找方法获得跟踪性能的逼近最优值;采用信念重用方法避免重复获取信念,有效降低传感器通信带来的能量消耗。实验结果表明:信念重用算法能够有效优化跟踪性能与能量消耗之间的平衡,达到以较低的能量消耗获得较高跟踪性能的目的。     

Partially Observable Markov Decision Processes With Reward Information: Basic Ideas and Models

In a partially observable Markov decision process (POMDP), if the reward can be observed at each step, then the observed reward history contains information on the unknown state. This information, in addition to the information contained in the observation history, can be used to update the state probability distribution. The policy thus obtained is called a reward-information policy (RI-policy); an optimal RI-policy performs no worse than any normal optimal policy depending only on the observation history. The above observation leads to four different problem-formulations for POMDPs depending on whether the reward function is known and whether the reward at each step is observable. This exploratory work may attract attention to these interesting problems     

基于采样的POMDP近似算法

部分可观察马尔科夫决策过程（POMDP）是一种描述机器人在动态不确定环境下行动选择的问题模型。对于具有稀疏转移矩阵的POMDP问题模型,该文提出了一种求解该问题模型的快速近似算法。该算法首先利用QMDP算法产生的策略进行信念空间采样,并通过点迭代算法快速生成POMDP值函数,从而产生近似的最优行动选择策略。在相同的POMDP试验模型上,执行该算法产生的策略得到的回报值与执行其他近似算法产生的策略得到的回报值相当,但该算法计算速度快,它产生的策略表示向量集合小于现有其他近似算法产生的集合。因此,它比这些近似算法更适应于大规模的稀疏状态转移矩阵POMDP模型求解计算。     

基于点的POMDPs在线值迭代算法

部分可观察马尔可夫决策过程(partially observable Markov decision processes,简称POMDPs)是动态不确定环境下序贯决策的理想模型,但是现有离线算法陷入信念状态“维数灾”和“历史灾”问题,而现有在线算法无法同时满足低误差与高实时性的要求,造成理想的POMDPs模型无法在实际工程中得到应用.对此,提出一种基于点的POMDPs在线值迭代算法(point-based online value iteration,简称PBOVI).该算法在给定的可达信念状态点上进行更新操作,避免对整个信念状态空间单纯体进行求解,加速问题求解;采用分支界限裁剪方法对信念状态与或树进行在线裁剪;提出信念状态结点重用思想,重用上一时刻已求解出的信念状态点,避免重复计算.实验结果表明,该算法具有较低误差率、较快收敛性,满足系统实时性的要求.     

Partially Observable Markov Decision Processes and Performance Sensitivity Analysis

The sensitivity-based optimization of Markov systems has become an increasingly important area. From the perspective of performance sensitivity analysis, policy-iteration algorithms and gradient estimation methods can be directly obtained for Markov decision processes (MDPs). In this correspondence, the sensitivity-based optimization is extended to average reward partially observable MDPs (POMDPs). We derive the performance-difference and performance-derivative formulas of POMDPs. On the basis of the performance-derivative formula, we present a new method to estimate the performance gradients. From the performance-difference formula, we obtain a sufficient optimality condition without the discounted reward formulation. We also propose a policy-iteration algorithm to obtain a nearly optimal finite-state-controller policy.      

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.     

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.     

Minimizing mean weighted tardiness in unrelated parallel machine scheduling with reinforcement learning

We address an unrelated parallel machine scheduling problem with R-learning, an average-reward reinforcement learning (RL) method. Different types of jobs dynamically arrive in independent Poisson processes. Thus the arrival time and the due date of each job are stochastic. We convert the scheduling problems into RL problems by constructing elaborate state features, actions, and the reward function. The state features and actions are defined fully utilizing prior domain knowledge. Minimizing the reward per decision time step is equivalent to minimizing the schedule objective, i.e. mean weighted tardiness. We apply an on-line R-learning algorithm with function approximation to solve the RL problems. Computational experiments demonstrate that R-learning learns an optimal or near-optimal policy in a dynamic environment from experience and outperforms four effective heuristic priority rules (i.e. WSPT, WMDD, ATC and WCOVERT) in all test problems.     

ADAPTIVE MODEL LEARNING BASED ON DYNA-Q LEARNING

Dyna-Q, a well-known model-based reinforcement learning (RL) method, interplays offline simulations and action executions to update Q functions. It creates a world model that predicts the feature values in the next state and the reward function of the domain directly from the data and uses the model to train Q functions to accelerate policy learning. In general, tabular methods are always used in Dyna-Q to establish the model, but a tabular model needs many more samples of experience to approximate the environment concisely. In this article, an adaptive model learning method based on tree structures is presented to enhance sampling efficiency in modeling the world model. The proposed method is to produce simulated experiences for indirect learning. Thus, the proposed agent has additional experience for updating the policy. The agent works backwards from collections of state transition and associated rewards, utilizing coarse coding to learn their definitions for the region of state space that tracks back to the precedent states. The proposed method estimates the reward and transition probabilities between states from past experience. Because the resultant tree is always concise and small, the agent can use value iteration to quickly estimate the Q-values of each action in the induced states and determine a policy. The effectiveness and generality of our method is further demonstrated in two numerical simulations. Two simulations, a mountain car and a mobile robot in a maze, are used to verify the proposed methods. The simulation result demonstrates that the training rate of our method can improve obviously.     

Potential-based reward shaping for finite horizon online POMDP planning

In this paper, we address the problem of suboptimal behavior during online partially observable Markov decision process (POMDP) planning caused by time constraints on planning. Taking inspiration from the related field of reinforcement learning (RL), our solution is to shape the agent’s reward function in order to lead the agent to large future rewards without having to spend as much time explicitly estimating cumulative future rewards, enabling the agent to save time to improve the breadth planning and build higher quality plans. Specifically, we extend potential-based reward shaping (PBRS) from RL to online POMDP planning. In our extension, information about belief states is added to the function optimized by the agent during planning. This information provides hints of where the agent might find high future rewards beyond its planning horizon, and thus achieve greater cumulative rewards. We develop novel potential functions measuring information useful to agent metareasoning in POMDPs (reflecting on agent knowledge and/or histories of experience with the environment), theoretically prove several important properties and benefits of using PBRS for online POMDP planning, and empirically demonstrate these results in a range of classic benchmark POMDP planning problems.     

马尔可夫决策过程两种抽象模式

抽象层次上马尔可夫决策过程的引入,使得人们可简洁地、陈述地表达复杂的马尔可夫决策过程,解决常规马尔可夫决策过程(MDPs)在实际中所遇到的大型状态空间的表达问题.介绍了结构型和概括型两种不同类型抽象马尔可夫决策过程基本概念以及在各种典型抽象MDPs中的最优策略的精确或近似算法,其中包括与常规MDPs根本不同的一个算法:把Bellman方程推广到抽象状态空间的方法,并且对它们的研究历史进行总结和对它们的发展做一些展望,使得人们对它们有一个透彻的、全面而又重点的理解.     

Reasoning and predicting POMDP planning complexity via covering numbers

Partially observable Markov decision processes (POMDPs) provide a rich mathematical framework for planning tasks in partially observable stochastic environments. The notion of the covering number, a metric of capturing the search space size of a POMDP planning problem, has been proposed as a complexity measure of approximate POMDP planning. Existing theoretical results are based on POMDPs with finite and discrete state spaces and measured in the l ₁-metric space. When considering heuristics, they are assumed to be always admissible. This paper extends the theoretical results on the covering numbers of different search spaces, including the newly defined space reachable under inadmissible heuristics, to the l _n-metric spaces. We provide a simple but scalable algorithm for estimating covering numbers. Experimentally, we provide estimated covering numbers of the search spaces reachable by following different policies on several benchmark problems, and analyze their abilities to predict the runtime of POMDP planning algorithms.     

Labeling Q-learning in hidden state environments

Recently,reinforcement learning (RL) methods have been used for learning problems in environments with embedded hidden states. However, conventional RL methods have been limited to handlingMarkov decision process problems. In order to overcome hidden states, several algorithms were proposed, but these need an extreme amount of memory of past sequences which represent historical state transitions. The aim of this work was to extend our previously proposed algorithm for hidden states in an environment, calledlabeling Q-learning (LQ-learning), which reinforces incompletely observed perception by labeling. In LQ-learning, the agent has a perception structure which consists of pairs of observations and labels. From these pairs, the agent can distinguish more exactly hidden states which look the same but are actually different each other. Labeling is carried out by labeling functions. Numerous labeling functions can be considered, but here we introduce some labeling functions based on the sequence of only the last and the current observations. This extended LQ-learning is applied to grid-world problems which have hidden states. The results of these simulations show the availability of LQ-learning. This work was presented in part at the Sixth International Symposium on Artificial Life and Robotics, Tokyo, January 15–17, 2001     

基于马氏决策过程模型的动态系统学习控制:研究前沿与展望

基于马氏决策过程(Markov decision process, MDP)的动态系统学习控制是近年来一个涉及机器学习、控制理论和运筹学等多个学科的交叉研究方向, 其主要目标是实现系统在模型复杂或者不确定等条件下基于数据驱动的多阶段优化控制. 本文对基于MDP的动态系统学习控制理论、算法与应用的发展前沿进行综述,重点讨论增强学习(Reinforcement learning, RL)与近似动态规划(Approximate dynamic programming, ADP)理论与方法的研究进展,其中包括时域差值学习理论、求解连续状态与行为空间MDP的值函数逼近方法、 直接策略搜索与近似策略迭代、自适应评价设计算法等,最后对相关研究领域的应用及发展趋势进行分析和探讨.     

Monte-Carlo tree search for Bayesian reinforcement learning

Bayesian model-based reinforcement learning can be formulated as a partially observable Markov decision process (POMDP) to provide a principled framework for optimally balancing exploitation and exploration. Then, a POMDP solver can be used to solve the problem. If the prior distribution over the environment’s dynamics is a product of Dirichlet distributions, the POMDP’s optimal value function can be represented using a set of multivariate polynomials. Unfortunately, the size of the polynomials grows exponentially with the problem horizon. In this paper, we examine the use of an online Monte-Carlo tree search (MCTS) algorithm for large POMDPs, to solve the Bayesian reinforcement learning problem online. We will show that such an algorithm successfully searches for a near-optimal policy. In addition, we examine the use of a parameter tying method to keep the model search space small, and propose the use of nested mixture of tied models to increase robustness of the method when our prior information does not allow us to specify the structure of tied models exactly. Experiments show that the proposed methods substantially improve scalability of current Bayesian reinforcement learning methods.