The most data-efficient algorithms for reinforcement learning (RL) in robotics are based on uncertain dynamical models: after each episode, they first learn a dynamical model of the robot, then they use an optimization algorithm to find a policy that maximizes the expected return given the model and its uncertainties. It is often believed that this optimization can be tractable only if analytical, gradient-based algorithms are used; however, these algorithms require using specific families of reward functions and policies, which greatly limits the flexibility of the overall approach. In this paper, we introduce a novel model-based RL algorithm, called Black-DROPS (Black-box Data-efficient RObot Policy Search) that: (1) does not impose any constraint on the reward function or the policy (they are treated as black-boxes), (2) is as data-efficient as the state-of-the-art algorithm for data-efficient RL in robotics, and (3) is as fast (or faster) than analytical approaches when several cores are available. The key idea is to replace the gradient-based optimization algorithm with a parallel, black-box algorithm that takes into account the model uncertainties. We demonstrate the performance of our new algorithm on two standard control benchmark problems (in simulation) and a low-cost robotic manipulator (with a real robot).
Direct policy search (PS) methods have been successful in robotics as they can easily be applied in high-dimensional continuous state-action RL problems @cite_3 . REINFORCE @cite_40 is an early policy gradient method which performs exploration of the action space using probabilistic policies. It suffers, however, from slow convergence due to the high variance in its gradient estimates. Policy gradients with parameter-based exploration (PGPE) @cite_36 address this problem by transferring exploration to parameter space. In particular, PGPE samples deterministic policies at the start of each episode by maintaining a separate Gaussian distribution for each parameter of the policy, whose mean and variance are adapted during training. The PoWER (Policy learning by Weighting Exploration with the Returns) algorithm @cite_32 uses probability-weighted averaging, which has the property of following the natural gradient without computing it @cite_32 . PoWER, however, assumes that the immediate rewards sum to a constant number and are always positive, which complicates the design of reward functions. The Policy Improvements with Path Integrals (PI @math ) @cite_14 algorithm does not make such an assumption. When the reward function is compatible with both PoWER and PI @math , the algorithms have identical performance @cite_14 .
@cite_14 @cite_36 @cite_32 @cite_3 @cite_40
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With the goal to generate more scalable algorithms with higher efficiency and fewer open parameters, reinforcement learning (RL) has recently moved towards combining classical techniques from optimal control and dynamic programming with modern learning techniques from statistical estimation theory. In this vein, this paper suggests to use the framework of stochastic optimal control with path integrals to derive a novel approach to RL with parameterized policies. While solidly grounded in value function estimation and optimal control based on the stochastic Hamilton-Jacobi-Bellman (HJB) equations, policy improvements can be transformed into an approximation problem of a path integral which has no open algorithmic parameters other than the exploration noise. The resulting algorithm can be conceived of as model-based, semi-model-based, or even model free, depending on how the learning problem is structured. The update equations have no danger of numerical instabilities as neither matrix inversions nor gradient learning rates are required. Our new algorithm demonstrates interesting similarities with previous RL research in the framework of probability matching and provides intuition why the slightly heuristically motivated probability matching approach can actually perform well. Empirical evaluations demonstrate significant performance improvements over gradient-based policy learning and scalability to high-dimensional control problems. Finally, a learning experiment on a simulated 12 degree-of-freedom robot dog illustrates the functionality of our algorithm in a complex robot learning scenario. We believe that Policy Improvement with Path Integrals (PI2) offers currently one of the most efficient, numerically robust, and easy to implement algorithms for RL based on trajectory roll-outs. We present a model-free reinforcement learning method for partially observable Markov decision problems. Our method estimates a likelihood gradient by sampling directly in parameter space, which leads to lower variance gradient estimates than those obtained by policy gradient methods such as REINFORCE. For several complex control tasks, including robust standing with a humanoid robot, we show that our method outperforms well-known algorithms from the fields of policy gradients, finite difference methods and population based heuristics. We also provide a detailed analysis of the differences between our method and the other algorithms. 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™ robot arm. Policy search is a subfield in reinforcement learning which focuses on finding good parameters for a given policy parametrization. It is well suited for robotics as it can cope with high-dimensional state and action spaces, one of the main challenges in robot learning. We review recent successes of both model-free and model-based policy search in robot learning.Model-free policy search is a general approach to learn policies based on sampled trajectories. We classify model-free methods based on their policy evaluation strategy, policy update strategy, and exploration strategy and present a unified view on existing algorithms. Learning a policy is often easier than learning an accurate forward model, and, hence, model-free methods are more frequently used in practice. However, for each sampled trajectory, it is necessary to interact with the robot, which can be time consuming and challenging in practice. Model-based policy search addresses this problem by first learning a simulator of the robot's dynamics from data. Subsequently, the simulator generates trajectories that are used for policy learning. For both model-free and model-based policy search methods, we review their respective properties and their applicability to robotic systems. This article presents a general class of associative reinforcement learning algorithms for connectionist networks containing stochastic units. These algorithms, called REINFORCE algorithms, are shown to make weight adjustments in a direction that lies along the gradient of expected reinforcement in both immediate-reinforcement tasks and certain limited forms of delayed-reinforcement tasks, and they do this without explicitly computing gradient estimates or even storing information from which such estimates could be computed. Specific examples of such algorithms are presented, some of which bear a close relationship to certain existing algorithms while others are novel but potentially interesting in their own right. Also given are results that show how such algorithms can be naturally integrated with backpropagation. We close with a brief discussion of a number of additional issues surrounding the use of such algorithms, including what is known about their limiting behaviors as well as further considerations that might be used to help develop similar but potentially more powerful reinforcement learning algorithms.