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.

     

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.     

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.     

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.     

Heuristically Accelerated Reinforcement Learning by Means of Case-Based Reasoning and Transfer Learning

Reinforcement Learning (RL) is a well-known technique for learning the solutions of control problems from the interactions of an agent in its domain. However, RL is known to be inefficient in problems of the real-world where the state space and the set of actions grow up fast. Recently, heuristics, case-based reasoning (CBR) and transfer learning have been used as tools to accelerate the RL process. This paper investigates a class of algorithms called Transfer Learning Heuristically Accelerated Reinforcement Learning (TLHARL) that uses CBR as heuristics within a transfer learning setting to accelerate RL. The main contributions of this work are the proposal of a new TLHARL algorithm based on the traditional RL algorithm Q(λ) and the application of TLHARL on two distinct real-robot domains: a robot soccer with small-scale robots and the humanoid-robot stability learning. Experimental results show that our proposed method led to a significant improvement of the learning rate in both domains.     

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.     

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.     

Efficient reinforcement learning in continuous state and action spaces with Dyna and policy approximation

Dyna is an effective reinforcement learning (RL) approach that combines value function evaluation with model learning. However, existing works on Dyna mostly discuss only its efficiency in RL problems with discrete action spaces. This paper proposes a novel Dyna variant, called Dyna-LSTD-PA, aiming to handle problems with continuous action spaces. Dyna-LSTD-PA stands for Dyna based on least-squares temporal difference (LSTD) and policy approximation. Dyna-LSTD-PA consists of two simultaneous, interacting processes. The learning process determines the probability distribution over action spaces using the Gaussian distribution; estimates the underlying value function, policy, and model by linear representation; and updates their parameter vectors online by LSTD(λ). The planning process updates the parameter vector of the value function again by using offline LSTD(λ). Dyna-LSTD-PA also uses the Sherman–Morrison formula to improve the efficiency of LSTD(λ), and weights the parameter vector of the value function to bring the two processes together. Theoretically, the global error bound is derived by considering approximation, estimation, and model errors. Experimentally, Dyna-LSTD-PA outperforms two representative methods in terms of convergence rate, success rate, and stability performance on four benchmark RL problems.     

Adaptive-resolution reinforcement learning with polynomial exploration in deterministic domains

We propose a model-based learning algorithm, the Adaptive-resolution Reinforcement Learning (ARL) algorithm, that aims to solve the online, continuous state space reinforcement learning problem in a deterministic domain. Our goal is to combine adaptive-resolution approximation schemes with efficient exploration in order to obtain polynomial learning rates. The proposed algorithm uses an adaptive approximation of the optimal value function using kernel-based averaging, going from coarse to fine kernel-based representation of the state space, which enables us to use finer resolution in the “important” areas of the state space, and coarser resolution elsewhere. We consider an online learning approach, in which we discover these important areas online, using an uncertainty intervals exploration technique. In addition, we introduce an incremental variant of the ARL (IARL), which is a more practical version of the original algorithm with reduced computational complexity at each stage. Polynomial learning rates in terms of mistake bound (in a PAC framework) are established for these algorithms, under appropriate continuity assumptions.     

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.     

Greedy feature replacement for online value function approximation

Reinforcement learning （RL） in real-world problems requires function approximations that depend on selecting the appropriate feature representations. Representational expansion techniques can make linear approximators represent value functions more effectively; however, most of these techniques function well only for low dimensional problems. In this paper, we present the greedy feature replacement （GFR）, a novel online expansion technique, for value-based RL algorithms that use binary features. Given a simple initial representation, the feature representation is expanded incrementally. New feature dependencies are added automatically to the current representation and conjunctive features are used to replace current features greedily. The virtual temporal difference （TD） error is recorded for each conjunctive feature to judge whether the replacement can improve the approximation. Correctness guarantees and computational complexity analysis are provided for GFR. Experimental results in two domains show that GFR achieves much faster learning and has the capability to handle large-scale problems.     

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.     

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.     

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.     

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.     

Bayes-adaptive hierarchical MDPs

Reinforcement learning (RL) is an area of machine learning that is concerned with how an agent learns to make decisions sequentially in order to optimize a particular performance measure. For achieving such a goal, the agent has to choose either 1) exploiting previously known knowledge that might end up at local optimality or 2) exploring to gather new knowledge that expects to improve the current performance. Among other RL algorithms, Bayesian model-based RL (BRL) is well-known to be able to trade-off between exploitation and exploration optimally via belief planning, i.e. partially observable Markov decision process (POMDP). However, solving that POMDP often suffers from curse of dimensionality and curse of history. In this paper, we make two major contributions which are: 1) an integration framework of temporal abstraction into BRL that eventually results in a hierarchical POMDP formulation, which can be solved online using a hierarchical sample-based planning solver; 2) a subgoal discovery method for hierarchical BRL that automatically discovers useful macro actions to accelerate learning. In the experiment section, we demonstrate that the proposed approach can scale up to much larger problems. On the other hand, the agent is able to discover useful subgoals for speeding up Bayesian reinforcement learning.     

Multiagent reinforcement learning applied to a chase problem in a continuous world

Reinforcement learning (RL) is one of the methods of solving problems defined in multiagent systems. In the real world, the state is continuous, and agents take continuous actions. Since conventional RL schemes are often defined to deal with discrete worlds, there are difficulties such as the representation of an RL evaluation function. In this article, we intend to extend an RL algorithm so that it is applicable to continuous world problems. This extension is done by a combination of an RL algorithm and a function approximator. We employ Q-learning as the RL algorithm, and a neural network model called the normalized Gaussian network as the function approximator. The extended RL method is applied to a chase problem in a continuous world. The experimental result shows that our RL scheme was successful. This work was presented in part at the Fifth International Symposium on Artificial Life and Robotics, Oita, Japan, January 26–28, 2000     

一种基于动态参数调整的强化学习动作选择机制

强化学习是一种重要的无监督机器学习技术,它能够利用不确定的环境下的奖赏发现最优的行为序列,实现动态环境下的在线学习,被广泛地应用到Agent系统当中。应用强化学习算法的难点之一就是如何平衡强化学习当中探索和利用之间的关系,即如何进行动作选择。结合Q学习在ε-greedy策略基础上引入计数器,从而使动作选择时的参数ε能够分阶段进行调整,从而更好地平衡探索和利用间的关系。通过对方格世界的实验仿真,证明了方法的有效性。     

Hoeffding bound based evolutionary algorithm for symbolic regression

In symbolic regression area, it is difficult for evolutionary algorithms to construct a regression model when the number of sample points is very large. Much time will be spent in calculating the fitness of the individuals and in selecting the best individuals within the population. Hoeffding bound is a probability bound for sums of independent random variables. As a statistical result, it can be used to exactly decide how many samples are necessary for choosing i individuals from a population in evolutionary algorithms without calculating the fitness completely. This paper presents a Hoeffding bound based evolutionary algorithm (HEA) for regression or approximation problems when the number of the given learning samples is very large. In HEA, the original fitness function is used in every k generations to update the approximate fitness obtained by Hoeffding bound. The parameter 1?δ is the probability of correctly selecting i best individuals from population P, which can be tuned to avoid an unstable evolution process caused by a large discrepancy between the approximate model and the original fitness function. The major advantage of the proposed HEA algorithm is that it can guarantee that the solution discovered has performance matching what would be discovered with a traditional genetic programming (GP) selection operator with a determinate probability and the running time can be reduced largely. We examine the performance of the proposed algorithm with several regression problems and the results indicate that with the similar accuracy, the HEA algorithm can find the solution more efficiently than tradition EA. It is very useful for regression problems with large number of training samples.     

Backward Q-learning: The combination of Sarsa algorithm and Q-learning

Reinforcement learning (RL) has been applied to many fields and applications, but there are still some dilemmas between exploration and exploitation strategy for action selection policy. The well-known areas of reinforcement learning are the Q-learning and the Sarsa algorithms, but they possess different characteristics. Generally speaking, the Sarsa algorithm has faster convergence characteristics, while the Q-learning algorithm has a better final performance. However, Sarsa algorithm is easily stuck in the local minimum and Q-learning needs longer time to learn. Most literatures investigated the action selection policy. Instead of studying an action selection strategy, this paper focuses on how to combine Q-learning with the Sarsa algorithm, and presents a new method, called backward Q-learning, which can be implemented in the Sarsa algorithm and Q-learning. The backward Q-learning algorithm directly tunes the Q-values, and then the Q-values will indirectly affect the action selection policy. Therefore, the proposed RL algorithms can enhance learning speed and improve final performance. Finally, three experimental results including cliff walk, mountain car, and cart–pole balancing control system are utilized to verify the feasibility and effectiveness of the proposed scheme. All the simulations illustrate that the backward Q-learning based RL algorithm outperforms the well-known Q-learning and the Sarsa algorithm.