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.     

Technical Update: Least-Squares Temporal Difference Learning

TD./ is a popular family of algorithms for approximate policy evaluation in large MDPs. TD./ works by incrementally updating the value function after each observed transition. It has two major drawbacks: it may make inefficient use of data, and it requires the user to manually tune a stepsize schedule for good performance. For the case of linear value function approximations and = 0, the Least-Squares TD (LSTD) algorithm of Bradtke and Barto (1996, Machine learning, 22:1–3, 33–57) eliminates all stepsize parameters and improves data efficiency.This paper updates Bradtke and Barto's work in three significant ways. First, it presents a simpler derivation of the LSTD algorithm. Second, it generalizes from = 0 to arbitrary values of ; at the extreme of = 1, the resulting new algorithm is shown to be a practical, incremental formulation of supervised linear regression. Third, it presents a novel and intuitive interpretation of LSTD as a model-based reinforcement learning technique.     

Reinforcement Learning in Continuous Time and Space: Interference and Not Ill Conditioning Is the Main Problem When Using Distributed Function Approximators

Many interesting problems in reinforcement learning (RL) are continuous and/or high dimensional, and in this instance, RL techniques require the use of function approximators for learning value functions and policies. Often, local linear models have been preferred over distributed nonlinear models for function approximation in RL. We suggest that one reason for the difficulties encountered when using distributed architectures in RL is the problem of negative interference, whereby learning of new data disrupts previously learned mappings. The continuous temporal difference (TD) learning algorithm TD(lambda) was used to learn a value function in a limited-torque pendulum swing-up task using a multilayer perceptron (MLP) network. Three different approaches were examined for learning in the MLP networks; 1) simple gradient descent; 2) vario-eta; and 3) a pseudopattern rehearsal strategy that attempts to reduce the effects of interference. Our results show that MLP networks can be used for value function approximation in this task but require long training times. We also found that vario-eta destabilized learning and resulted in a failure of the learning process to converge. Finally, we showed that the pseudopattern rehearsal strategy drastically improved the speed of learning. The results indicate that interference is a greater problem than ill conditioning for this task.     

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.     

Reducing reinforcement learning to KWIK online regression

One of the key problems in reinforcement learning (RL) is balancing exploration and exploitation. Another is learning and acting in large Markov decision processes (MDPs) where compact function approximation has to be used. This paper introduces REKWIRE, a provably efficient, model-free algorithm for finite-horizon RL problems with value function approximation (VFA) that addresses the exploration-exploitation tradeoff in a principled way. The crucial element of this algorithm is a reduction of RL to online regression in the recently proposed KWIK learning model. We show that, if the KWIK online regression problem can be solved efficiently, then the sample complexity of exploration of REKWIRE is polynomial. Therefore, the reduction suggests a new and sound direction to tackle general RL problems. The efficiency of our algorithm is verified on a set of proof-of-concept experiments where popular, ad hoc exploration approaches fail.     

Continuous state/action reinforcement learning: A growing self-organizing map approach

This paper proposes an algorithm to deal with continuous state/action space in the reinforcement learning (RL) problem. Extensive studies have been done to solve the continuous state RL problems, but more research should be carried out for RL problems with continuous action spaces. Due to non-stationary, very large size, and continuous nature of RL problems, the proposed algorithm uses two growing self-organizing maps (GSOM) to elegantly approximate the state/action space through addition and deletion of neurons. It has been demonstrated that GSOM has a better performance in topology preservation, quantization error reduction, and non-stationary distribution approximation than the standard SOM. The novel algorithm proposed in this paper attempts to simultaneously find the best representation for the state space, accurate estimation of Q-values, and appropriate representation for highly rewarded regions in the action space. Experimental results on delayed reward, non-stationary, and large-scale problems demonstrate very satisfactory performance of the proposed algorithm.     

一种优先级扫描的Dyna结构优化算法

不确定环境的时序决策问题是强化学习研究的主要内容之一,agent的目标是最大化其与环境交互过程中获得的累计奖赏值.直接学习方法寻找最优策略的算法收敛效率较差,而采用Dyna结构将学习与规划并行集成,可提高算法的收敛效率.为了进一步提高传统Dyna结构的收敛速度和收敛精度,提出了Dyna-PS算法,并在理论上证明了其收敛性.该算法在Dyna结构规划部分使用优先级扫描算法的思想,对优先级函数值高的状态优先更新,剔除了传统值迭代、策略迭代过程中不相关和无更新意义的状态更新,提升了规划的收敛效率,从而进一步提升了Dyna结构算法的性能.将此算法应用于一系列经典规划问题,实验结果表明,Dyna-PS算法有更快的收敛速度和更高的收敛精度,且对于状态空间的增长具有较强的鲁棒性.     

Least Squares Policy Evaluation Algorithms with Linear Function Approximation

We consider policy evaluation algorithms within the context of infinite-horizon dynamic programming problems with discounted cost. We focus on discrete-time dynamic systems with a large number of states, and we discuss two methods, which use simulation, temporal differences, and linear cost function approximation. The first method is a new gradient-like algorithm involving least-squares subproblems and a diminishing stepsize, which is based on the -policy iteration method of Bertsekas and Ioffe. The second method is the LSTD() algorithm recently proposed by Boyan, which for =0 coincides with the linear least-squares temporal-difference algorithm of Bradtke and Barto. At present, there is only a convergence result by Bradtke and Barto for the LSTD(0) algorithm. Here, we strengthen this result by showing the convergence of LSTD(), with probability 1, for every [0, 1].     

Natural Actor-Critic

In this paper, we suggest a novel reinforcement learning architecture, the Natural Actor-Critic. The actor updates are achieved using stochastic policy gradients employing Amari's natural gradient approach, while the critic obtains both the natural policy gradient and additional parameters of a value function simultaneously by linear regression. We show that actor improvements with natural policy gradients are particularly appealing as these are independent of coordinate frame of the chosen policy representation, and can be estimated more efficiently than regular policy gradients. The critic makes use of a special basis function parameterization motivated by the policy-gradient compatible function approximation. We show that several well-known reinforcement learning methods such as the original Actor-Critic and Bradtke's Linear Quadratic Q-Learning are in fact Natural Actor-Critic algorithms. Empirical evaluations illustrate the effectiveness of our techniques in comparison to previous methods, and also demonstrate their applicability for learning control on an anthropomorphic robot arm.     

一种用于连续动作空间的最小二乘行动者-评论家方法

解决具有连续动作空间的问题是当前强化学习领域的一个研究热点和难点.在处理这类问题时,传统的强化学习算法通常利用先验信息对连续动作空间进行离散化处理,然后再求解最优策略.然而,在很多实际应用中,由于缺乏用于离散化处理的先验信息,算法效果会变差甚至算法失效.针对这类问题,提出了一种最小二乘行动者-评论家方法(least square actor-critic algorithm, LSAC),使用函数逼近器近似表示值函数及策略,利用最小二乘法在线动态求解近似值函数参数及近似策略参数,以近似值函数作为评论家指导近似策略参数的求解.将LSAC算法用于解决经典的具有连续动作空间的小车平衡杆问题和mountain car问题,并与Cacla(continuous actor-critic learning automaton)算法和eNAC(episodic natural actor-critic)算法进行比较.结果表明,LSAC算法能有效地解决连续动作空间问题,并具有较优的执行性能.     

Ensemble Algorithms in Reinforcement Learning

This paper describes several ensemble methods that combine multiple different reinforcement learning (RL) algorithms in a single agent. The aim is to enhance learning speed and final performance by combining the chosen actions or action probabilities of different RL algorithms. We designed and implemented four different ensemble methods combining the following five different RL algorithms: $Q$ -learning, Sarsa, actor–critic (AC), $QV$-learning, and AC learning automaton. The intuitively designed ensemble methods, namely, majority voting (MV), rank voting, Boltzmann multiplication (BM), and Boltzmann addition, combine the policies derived from the value functions of the different RL algorithms, in contrast to previous work where ensemble methods have been used in RL for representing and learning a single value function. We show experiments on five maze problems of varying complexity; the first problem is simple, but the other four maze tasks are of a dynamic or partially observable nature. The results indicate that the BM and MV ensembles significantly outperform the single RL algorithms.      

一种高斯过程的带参近似策略迭代算法

在大规模状态空间或者连续状态空间中,将函数近似与强化学习相结合是当前机器学习领域的一个研究热点;同时,在学习过程中如何平衡探索和利用的问题更是强化学习领域的一个研究难点.针对大规模状态空间或者连续状态空间、确定环境问题中的探索和利用的平衡问题,提出了一种基于高斯过程的近似策略迭代算法.该算法利用高斯过程对带参值函数进行建模,结合生成模型,根据贝叶斯推理,求解值函数的后验分布.在学习过程中,根据值函数的概率分布,求解动作的信息价值增益,结合值函数的期望值,选择相应的动作.在一定程度上,该算法可以解决探索和利用的平衡问题,加快算法收敛.将该算法用于经典的Mountain Car 问题,实验结果表明,该算法收敛速度较快,收敛精度较好.     

一种近似模型表示的启发式Dyna优化算法

针对基于查询表的Dyna优化算法在大规模状态空间中收敛速度慢、环境模型难以表征以及对变化环境的学习滞后性等问题,提出一种新的基于近似模型表示的启发式Dyna优化算法(a heuristic Dyna optimization algorithm using approximate model representation, HDyna-AMR),其利用线性函数近似逼近Q值函数,采用梯度下降方法求解最优值函数.HDyna-AMR算法可以分为学习阶段和规划阶段.在学习阶段,利用agent与环境的交互样本近似表示环境模型并记录特征出现频率;在规划阶段,基于近似环境模型进行值函数的规划学习,并根据模型逼近过程中记录的特征出现频率设定额外奖赏.从理论的角度证明了HDyna-AMR的收敛性.将算法用于扩展的Boyan chain问题和Mountain car问题.实验结果表明,HDyna-AMR在离散状态空间和连续状态空间问题中能学习到最优策略,同时与Dyna-LAPS(Dyna-style planning with linear approximation and prioritized sweeping)和Sarsa(λ)相比,HDyna-AMR具有收敛速度快以及对变化环境的近似模型修正及时的优点.     

Reinforcement Learning Soccer Teams with Incomplete World Models

We use reinforcement learning (RL) to compute strategies for multiagent soccer teams. RL may profit significantly from world models (WMs) estimating state transition probabilities and rewards. In high-dimensional, continuous input spaces, however, learning accurate WMs is intractable. Here we show that incomplete WMs can help to quickly find good action selection policies. Our approach is based on a novel combination of CMACs and prioritized sweeping-like algorithms. Variants thereof outperform both Q()-learning with CMACs and the evolutionary method Probabilistic Incremental Program Evolution (PIPE) which performed best in previous comparisons.     

A robust Markov game controller for nonlinear systems

This paper proposes a reinforcement learning (RL)-based game-theoretic formulation for designing robust controllers for nonlinear systems affected by bounded external disturbances and parametric uncertainties. Based on the theory of Markov games, we consider a differential game in which a ‘disturbing’ agent tries to make worst possible disturbance while a ‘control’ agent tries to make best control input. The problem is formulated as finding a min–max solution of a value function. We propose an online procedure for learning optimal value function and for calculating a robust control policy. Proposed game-theoretic paradigm has been tested on the control task of a highly nonlinear two-link robot system. We compare the performance of proposed Markov game controller with a standard RL-based robust controller, and an H_∞ theory-based robust game controller. For the robot control task, the proposed controller achieved superior robustness to changes in payload mass and external disturbances, over other control schemes. Results also validate the effectiveness of neural networks in extending the Markov game framework to problems with continuous state–action spaces.     

基于Dyna框架的非参数化近似策略迭代增强学习

为解决当前近似策略迭代增强学习算法逼近器不能完全自动构建的问题,提出一种基于Dyna框架的非参数化近似策略迭代（NPAPI-Dyna）增强学习算法。引入采样缓存和采样变化率设计二级随机采样过程采集样本,基于轮廓指标、采用K均值聚类算法实现trial-and-error过程生成核心状态基函数,采用以样本完全覆盖为目标的估计方法生成Q值函数逼近器,采用贪心策略设计动作选择器,利用对状态基函数的访问频次描述环境拓扑特征并构建环境估计模型;而后基于Dyna框架的模型辨识思想,将学习和规划过程有机结合,进一步加快了增强学习速度。一级倒立摆平衡控制的仿真实验中,当增强学习误差率为0.01时,算法学习成功率为100%,学习成功的最小尝试次数仅为2,平均尝试次数仅为7.73,角度平均绝对偏差为3.0538°,角度平均振荡范围为2.759°;当增强学习误差率为0.1时进行100次独立仿真运算,相比Online-LSPI和BLSPI算法平均需要150次以上尝试才能学习得到控制策略,而NPAPI-Dyna基本可在50次尝试内学习成功。实验分析表明,NPAPI-Dyna能够完全自动地构建、调整增强学习结构,学习结果精度较高,同时较快收敛。     

Sparse online kernelized actor-critic Learning in reproducing kernel Hilbert space

In this paper, we develop a novel non-parametric online actor-critic reinforcement learning (RL) algorithm to solve optimal regulation problems for a class of continuous-time affine nonlinear dynamical systems. To deal with the value function approximation (VFA) with inherent nonlinear and unknown structure, a reproducing kernel Hilbert space (RKHS)-based kernelized method is designed through online sparsification, where the dictionary size is fixed and consists of updated elements. In addition, the linear independence check condition, i.e., an online criteria, is designed to determine whether the online data should be inserted into the dictionary. The RHKS-based kernelized VFA has a variable structure in accordance with the online data collection, which is different from classical parametric VFA methods with a fixed structure. Furthermore, we develop a sparse online kernelized actor-critic learning RL method to learn the unknown optimal value function and the optimal control policy in an adaptive fashion. The convergence of the presented kernelized actor-critic learning method to the optimum is provided. The boundedness of the closed-loop signals during the online learning phase can be guaranteed. Finally, a simulation example is conducted to demonstrate the effectiveness of the presented kernelized actor-critic learning algorithm.

     

基于CMAC的非参数化近似策略迭代增强学习

为解决在线近似策略迭代增强学习计算复杂度高、收敛速度慢的问题，引入CMAC结构作为值函数逼近器，提出一种基于CMAC的非参数化近似策略迭代增强学习（NPAPI-CMAC）算法。算法通过构建样本采集过程确定CMAC泛化参数，利用初始划分和拓展划分确定CMAC状态划分方式，利用量化编码结构构建样本数集合定义增强学习率，实现了增强学习结构和参数的完全自动构建。此外，该算法利用delta规则和最近邻思想在学习过程中自适应调整增强学习参数，利用贪心策略对动作投票器得到的结果进行选择。一级倒立摆平衡控制的仿真实验结果验证了算法的有效性、鲁棒性和快速收敛能力。     

基于优先采样模型的离线强化学习

离线强化学习通过减小分布偏移实现了习得策略向行为策略的逼近, 但离线经验缓存的数据分布往往会直接影响习得策略的质量. 通过优化采样模型来改善强化学习智能体的训练效果, 提出两种离线优先采样模型: 基于时序差分误差的采样模型和基于鞅的采样模型. 基于时序差分误差的采样模型可以使智能体更多地学习值估计不准确的经验数据, 通过估计更准确的值函数来应对可能出现的分布外状态. 基于鞅的采样模型可以使智能体更多地学习对策略优化有利的正样本, 减少负样本对值函数迭代的影响. 进一步, 将所提离线优先采样模型分别与批约束深度Q学习(Batch-constrained deep Q-learning, BCQ)相结合, 提出基于时序差分误差的优先BCQ和基于鞅的优先BCQ. D4RL和Torcs数据集上的实验结果表明: 所提离线优先采样模型可以有针对性地选择有利于值函数估计或策略优化的经验数据, 获得更高的回报.     

Characterizing reinforcement learning methods through parameterized learning problems

The field of reinforcement learning (RL) has been energized in the past few decades by elegant theoretical results indicating under what conditions, and how quickly, certain algorithms are guaranteed to converge to optimal policies. However, in practical problems, these conditions are seldom met. When we cannot achieve optimality, the performance of RL algorithms must be measured empirically. Consequently, in order to meaningfully differentiate learning methods, it becomes necessary to characterize their performance on different problems, taking into account factors such as state estimation, exploration, function approximation, and constraints on computation and memory. To this end, we propose parameterized learning problems, in which such factors can be controlled systematically and their effects on learning methods characterized through targeted studies. Apart from providing very precise control of the parameters that affect learning, our parameterized learning problems enable benchmarking against optimal behavior; their relatively small sizes facilitate extensive experimentation. Based on a survey of existing RL applications, in this article, we focus our attention on two predominant, ??first order?? factors: partial observability and function approximation. We design an appropriate parameterized learning problem, through which we compare two qualitatively distinct classes of algorithms: on-line value function-based methods and policy search methods. Empirical comparisons among various methods within each of these classes project Sarsa(??) and Q-learning(??) as winners among the former, and CMA-ES as the winner in the latter. Comparing Sarsa(??) and CMA-ES further on relevant problem instances, our study highlights regions of the problem space favoring their contrasting approaches. Short run-times for our experiments allow for an extensive search procedure that provides additional insights on relationships between method-specific parameters??such as eligibility traces, initial weights, and population sizes??and problem instances.