High-Accuracy Value-Function Approximation with Neural Networks Applied to the Acrobot

Colloque avec actes et comité de lecture. internationale.International audienceSeveral reinforcement-learning techniques have already been applied to the Acrobot control problem, using linear function approximators to estimate the value function. In this paper, we present experimental results obtained by using a feedforward neural network instead. The learning algorithm used was model-based continuous TD(lambda). It generated an efficient controller, producing a high-accuracy state-value function. A striking feature of this value function is a very sharp 4-dimensional ridge that is extremely hard to evaluate with linear parametric approximators. From a broader point of view, this experimental success demonstrates some of the qualities of feedforward neural networks in comparison with linear approximators in reinforcement learning

Echo state model of non-Markovian reinforcement learning, An

Department Head: Dale H. Grit.2008 Spring.Includes bibliographical references (pages 137-142).There exists a growing need for intelligent, autonomous control strategies that operate in real-world domains. Theoretically the state-action space must exhibit the Markov property in order for reinforcement learning to be applicable. Empirical evidence, however, suggests that reinforcement learning also applies to domains where the state-action space is approximately Markovian, a requirement for the overwhelming majority of real-world domains. These domains, termed non-Markovian reinforcement learning domains, raise a unique set of practical challenges. The reconstruction dimension required to approximate a Markovian state-space is unknown a priori and can potentially be large. Further, spatial complexity of local function approximation of the reinforcement learning domain grows exponentially with the reconstruction dimension. Parameterized dynamic systems alleviate both embedding length and state-space dimensionality concerns by reconstructing an approximate Markovian state-space via a compact, recurrent representation. Yet this representation extracts a cost; modeling reinforcement learning domains via adaptive, parameterized dynamic systems is characterized by instability, slow-convergence, and high computational or spatial training complexity. The objectives of this research are to demonstrate a stable, convergent, accurate, and scalable model of non-Markovian reinforcement learning domains. These objectives are fulfilled via fixed point analysis of the dynamics underlying the reinforcement learning domain and the Echo State Network, a class of parameterized dynamic system. Understanding models of non-Markovian reinforcement learning domains requires understanding the interactions between learning domains and their models. Fixed point analysis of the Mountain Car Problem reinforcement learning domain, for both local and nonlocal function approximations, suggests a close relationship between the locality of the approximation and the number and severity of bifurcations of the fixed point structure. This research suggests the likely cause of this relationship: reinforcement learning domains exist within a dynamic feature space in which trajectories are analogous to states. The fixed point structure maps dynamic space onto state-space. This explanation suggests two testable hypotheses. Reinforcement learning is sensitive to state-space locality because states cluster as trajectories in time rather than space. Second, models using trajectory-based features should exhibit good modeling performance and few changes in fixed point structure. Analysis of performance of lookup table, feedforward neural network, and Echo State Network (ESN) on the Mountain Car Problem reinforcement learning domain confirm these hypotheses. The ESN is a large, sparse, randomly-generated, unadapted recurrent neural network, which adapts a linear projection of the target domain onto the hidden layer. ESN modeling results on reinforcement learning domains show it achieves performance comparable to lookup table and neural network architectures on the Mountain Car Problem with minimal changes to fixed point structure. Also, the ESN achieves lookup table caliber performance when modeling Acrobot, a four-dimensional control problem, but is less successful modeling the lower dimensional Modified Mountain Car Problem. These performance discrepancies are attributed to the ESN’s excellent ability to represent complex short term dynamics, and its inability to consolidate long temporal dependencies into a static memory. Without memory consolidation, reinforcement learning domains exhibiting attractors with multiple dynamic scales are unlikely to be well-modeled via ESN. To mediate this problem, a simple ESN memory consolidation method is presented and tested for stationary dynamic systems. These results indicate the potential to improve modeling performance in reinforcement learning domains via memory consolidation

Reinforcement learning in continuous state- and action-space

Reinforcement learning in the continuous state-space poses the problem of the inability to store the values of all state-action pairs in a lookup table, due to both storage limitations and the inability to visit all states sufficiently often to learn the correct values. This can be overcome with the use of function approximation techniques with generalisation capability, such as artificial neural networks, to store the value function. When this is applied we can select the optimal action by comparing the values of each possible action; however, when the action-space is continuous this is not possible. In this thesis we investigate methods to select the optimal action when artificial neural networks are used to approximate the value function, through the application of numerical optimization techniques. Although it has been stated in the literature that gradient-ascent methods can be applied to the action selection [47], it is also stated that solving this problem would be infeasible, and therefore, is claimed that it is necessary to utilise a second artificial neural network to approximate the policy function [21, 55]. The major contributions of this thesis include the investigation of the applicability of action selection by numerical optimization methods, including gradient-ascent along with other derivative-based and derivative-free numerical optimization methods,and the proposal of two novel algorithms which are based on the application of two alternative action selection methods: NM-SARSA [40] and NelderMead-SARSA. We empirically compare the proposed methods to state-of-the-art methods from the literature on three continuous state- and action-space control benchmark problems from the literature: minimum-time full swing-up of the Acrobot; Cart-Pole balancing problem; and a double pole variant. We also present novel results from the application of the existing direct policy search method genetic programming to the Acrobot benchmark problem [12, 14]

QHD: A brain-inspired hyperdimensional reinforcement learning algorithm

Reinforcement Learning (RL) has opened up new opportunities to solve a wide range of complex decision-making tasks. However, modern RL algorithms, e.g., Deep Q-Learning, are based on deep neural networks, putting high computational costs when running on edge devices. In this paper, we propose QHD, a Hyperdimensional Reinforcement Learning, that mimics brain properties toward robust and real-time learning. QHD relies on a lightweight brain-inspired model to learn an optimal policy in an unknown environment. We first develop a novel mathematical foundation and encoding module that maps state-action space into high-dimensional space. We accordingly develop a hyperdimensional regression model to approximate the Q-value function. The QHD-powered agent makes decisions by comparing Q-values of each possible action. We evaluate the effect of the different RL training batch sizes and local memory capacity on the QHD quality of learning. Our QHD is also capable of online learning with tiny local memory capacity, which can be as small as the training batch size. QHD provides real-time learning by further decreasing the memory capacity and the batch size. This makes QHD suitable for highly-efficient reinforcement learning in the edge environment, where it is crucial to support online and real-time learning. Our solution also supports a small experience replay batch size that provides 12.3 times speedup compared to DQN while ensuring minimal quality loss. Our evaluation shows QHD capability for real-time learning, providing 34.6 times speedup and significantly better quality of learning than state-of-the-art deep RL algorithms

Data-Driven Control with Learned Dynamics

This research focuses on studying data-driven control with dynamics that are actively learned from machine learning algorithms. With system dynamics being identified using neural networks either explicitly or implicitly, we can apply control following either a model-based approach or a model-free approach. In this thesis, the two different methods are explained in detail and finally compared to shed light on the emerging data-driven control research field. In the first part of the thesis, we first introduce state-of-art Reinforcement Learning (RL) algorithm representing data-driven control using a model-free learning approach. We discuss the advantages and shortcomings of the current RL algorithms and motivate our study to search for a model-based control which is physics-based and also provides better model interpretability. We then propose a novel data-driven, model-based approach for the optimal control of the dynamical system. The proposed approach relies on the Deep Neural Network (DNN) based learning of Koopman operator and therefore is named as Deep Learning of Koopman Representation for Control (DKRC). In particular, DNN is employed for the data-driven identification of basis function used in the linear lifting of nonlinear control system dynamics. One a linear representation of system dynamics is learned, we can implement classic control algorithms such as iterative Linear Quadratic Regulator (iLQR) and Model Predictive Control (MPC) for optimal control design. The controller synthesis is purely data-driven and does not rely on prior domain knowledge. The OpenAI Gym environment is used for simulations of various control problems. The method is applied to three classic dynamical systems on OpenAI Gym environment to demonstrate the capability. In the second part, we compare the proposed method with a state-of-art model-free control method based on an actor-critic architecture – Deep Deterministic Policy Gradient (DDPG), which has been proved to be effective in various dynamical systems. Two examples are provided for comparison, i.e., classic Inverted Pendulum and Lunar Lander Continuous Control. We compare these two methods in terms of control strategies and the effectiveness under various initialization conditions from the results of the experiments. We also examine the learned dynamic model from DKRC with the analytical model derived from the Euler-Lagrange Linearization method, demonstrating the accuracy in the learned model for unknown dynamics from a data-driven sample-efficient approach