Many motor skills in humanoid robotics can be learned using parametrized motor primitives as done in imitation learning. However, most interesting motor learning problems are high-dimensional reinforcement learning problems often beyond the reach of current methods. In this paper, we extend previous work on policy learning from the immediate reward case to episodic reinforcement learning. We show that this results in a general, common framework also connected to policy gradient methods and yielding a novel algorithm for policy learning that is particularly well-suited for dynamic motor primitives. The resulting algorithm is an EM-inspired algorithm applicable to complex motor learning tasks. We compare this algorithm to several well-known parametrized policy search methods and show that it outperforms them. We apply it in the context of motor learning and show that it can learn a complex Ball-in-a-Cup task using a real Barrett WAM TM robot arm. 1

Computational learning theory studies mathematical models that allow one to formally analyze and compare the performance of supervised-learning algorithms such as their sample complexity. While existing models such as PAC (Probably Approximately Correct) have played an influential role in understanding the nature of supervised learning, they have not been as successful in reinforcement learning (RL). Here, the fundamental barrier is the need for active exploration in sequential decision problems. An RL agent tries to maximize long-term utility by exploiting its knowledge about the problem, but this knowledge has to be acquired by the agent itself through exploring the problem that may reduce short-term utility. The need for active exploration is common in many problems in daily life, engineering, and sciences. For example, a Backgammon program strives to take good moves to maximize the probability of winning a game, but sometimes it may try novel and possibly harmful moves to discover how the opponent reacts in the hope of discovering a better game-playing strategy. It has been known since the early days of RL that a good tradeoff between exploration and exploitation is critical for the agent to learn fast (i.e., to reach near-optimal strategies

Abstract—Many complex robot motor skills can be represented using elementary movements, and there exist efficient techniques for learning parametrized motor plans using demonstrations and self-improvement. However, in many cases, the robot currently needs to learn a new elementary movement even if a parametrized motor plan exists that covers a similar, related situation. Clearly, a method is needed that modulates the elementary movement through the meta-parameters of its representation. In this paper, we show how to learn such mappings from circumstances to meta-parameters using reinforcement learning. We introduce an appropriate reinforcement learning algorithm based on a kernelized version of the reward-weighted regression. We compare this algorithm to several previous methods on a toy example and show that it performs well in comparison to standard algorithms. Subsequently, we show two robot applications of the presented setup; i.e., the generalization of throwing movements in darts, and of hitting movements in table tennis. We show that both tasks can be learned successfully using simulated and real robots. I.

Recently, fitted Q-iteration (FQI) based methods have become more popular due to their increased sample efficiency, a more stable learning process and the higher quality of the resulting policy. However, these methods remain hard to use for continuous action spaces which frequently occur in real-world tasks, e.g., in robotics and other technical applications. The greedy action selection commonly used for the policy improvement step is particularly problematic as it is expensive for continuous actions, can cause an unstable learning process, introduces an optimization bias and results in highly non-smooth policies unsuitable for real-world systems. In this paper, we show that by using a soft-greedy action selection the policy improvement step used in FQI can be simplified to an inexpensive advantageweighted regression. With this result, we are able to derive a new, computationally efficient FQI algorithm which can even deal with high dimensional action spaces. 1

We present Fitness Expectation Maximization (FEM), a novel method for performing ‘black box ’ function optimization. FEM searches the fitness landscape of an objective function using an instantiation of the well-known Expectation Maximization algorithm, producing search points to match the sample distribution weighted according to higher expected fitness. FEM updates both candidate solution parameters and the search policy, which is represented as a multinormal distribution. Inheriting EM’s stability and strong guarantees, the method is both elegant and competitive with some of the best heuristic search methods in the field, and performs well on a number of unimodal and multimodal benchmark tasks. To illustrate the potential practical applications of the approach, we also show experiments on finding the parameters for a controller of the challenging non-Markovian double pole balancing task.

Abstract. Direct policy search is a promising reinforcement learning framework in particular for controlling in continuous, high-dimensional systems such as anthropomorphic robots. Policy search often requires a large number of samples for obtaining a stable policy update estimator due to its high flexibility. However, this is prohibitive when the sampling cost is expensive. In this paper, we extend an EM-based policy search method so that previously collected samples can be efficiently reused. The usefulness of the proposed method, called Reward-weighted Regression with sample Reuse (R 3), is demonstrated through a robot learning experiment. 1

Abstract Learning robots that can acquire new motor skills and refine existing one has been a long standing vision of robotics, artificial intelligence, and the cognitive sciences. Early steps towards this goal in the 1980s made clear that reasoning and human insights will not suffice. Instead, new hope has been offered by the rise of modern machine learning approaches. However, to date, it becomes increasingly clear that off-the-shelf machine learning approaches will not suffice for motor skill learning as these methods often do not scale into the high-dimensional domains of manipulator and humanoid robotics nor do they fulfill the real-time requirement of our domain. As an alternative, we propose to break the generic skill learning problem into parts that we can understand well from a robotics point of view. After designing appropriate learning approaches for these basic components, these will serve as the ingredients of a general approach to motor skill learning. In this paper, we discuss our recent and current progress in this direction. For doing so, we present our work on learning to control, on learning elementary movements as well as our steps towards learning of complex tasks. We show several evaluations both using real robots as well as physically realistic simulations. 1

Abstract. It has been a long-standing goal in the adaptive control community to reduce the generically difficult, general reinforcement learning (RL) problem to simpler problems solvable by supervised learning. While this approach is today’s standard for value function-based methods, fewer approaches are known that apply similar reductions to policy search methods. Recently, it has been shown that immediate RL problems can be solved by reward-weighted regression, and that the resulting algorithm is an expectation maximization (EM) algorithm with strong guarantees. In this paper, we extend this algorithm to the episodic case and show that it can be used in the context of LSTM recurrent neural networks (RNNs). The resulting RNN training algorithm is equivalent to a weighted self-modeling supervised learning technique. We focus on partially observable Markov decision problems (POMDPs) where it is essential that the policy is nonstationary in order to be optimal. We show that this new reward-weighted logistic regression used in conjunction with an RNN architecture can solve standard benchmark POMDPs with ease. 1

Expectation-Maximization methods for solving (PO)MDPs

Abstract — Recent advances on path integral stochastic optimal control [2],[3] provide new insights on the optimal control of nonlinear stochastic systems which are linear in controls, with state independent and time invariant control transition matrix. Under theses assumptions, the Hamilton-Jacobi-Belman equation is formulated and linearized with the use of the logarithmic transformation of the optimal value function. The resulting HJB is a linear second order partial differential equation which is solved to an approximation based on the Feynman- Kac formula [6]. In this work we review the theory of path integral control and derive the linearized HJB equation for systems with state dependent control transition matrix. In addition we derive the path integral formulation for the general class of systems with state dimensionality that is higher than the dimensionality of the controls. Furthermore, by a modified inverse dynamics controller, we apply path integral stochastic optimal control over the new control space. Simulations are illustrated and future developments and extensions are discussed. I.