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).
A limitation of PGPE is that it does not consider any correlations between dimensions in parameter space. This can be addressed by the Natural Evolution Strategies (NES) @cite_28 and Covariance Matrix Adaptation ES (CMA-ES) @cite_29 families of algorithms, which are population-based Black-Box Optimizers (BBO). Both NES and CMA-ES iteratively update a search distribution by calculating an estimated gradient on the distribution parameters (mean and covariance matrix). At each generation, they sample a set of solutions (i.e., policy parameters) and rank them based on their fitness (i.e., expected return). NES performs gradient ascent along the natural gradient, which normalizes the update with respect to uncertainty. CMA-ES updates the distribution by exploiting the technique of evolution paths to average-out random effects over the generations. NES and CMA-ES are closely related, as the latter performs an approximate natural gradient ascent @cite_31 . Interestingly, a variant of PI @math with a simplified parameter perturbation and update method outperforms PI @math and was shown to be a special case of CMA-ES @cite_6 .
@cite_28 @cite_29 @cite_31 @cite_6
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This paper presents a novel evolutionary optimization strategy based on the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). This new approach is intended to reduce the number of generations required for convergence to the optimum. Reducing the number of generations, i.e., the time complexity of the algorithm, is important if a large population size is desired: (1) to reduce the effect of noise; (2) to improve global search properties; and (3) to implement the algorithm on (highly) parallel machines. Our method results in a highly parallel algorithm which scales favorably with large numbers of processors. This is accomplished by efficiently incorporating the available information from a large population, thus significantly reducing the number of generations needed to adapt the covariance matrix. The original version of the CMA-ES was designed to reliably adapt the covariance matrix in small populations but it cannot exploit large populations efficiently. Our modifications scale up the efficiency to population sizes of up to 10n, where n is the problem dimension. This method has been applied to a large number of test problems, demonstrating that in many cases the CMA-ES can be advanced from quadratic to linear time complexity. This paper presents Natural Evolution Strategies (NES), a recent family of black-box optimization algorithms that use the natural gradient to update a parameterized search distribution in the direction of higher expected fitness. We introduce a collection of techniques that address issues of convergence, robustness, sample complexity, computational complexity and sensitivity to hyperparameters. This paper explores a number of implementations of the NES family, such as general-purpose multi-variate normal distributions and separable distributions tailored towards search in high dimensional spaces. Experimental results show best published performance on various standard benchmarks, as well as competitive performance on others. This paper presents Natural Evolution Strategies (NES), a recent family of algorithms that constitute a more principled approach to black-box optimization than established evolutionary algorithms. NES maintains a parameterized distribution on the set of solution candidates, and the natural gradient is used to update the distribution's parameters in the direction of higher expected fitness. We introduce a collection of techniques that address issues of convergence, robustness, sample complexity, computational complexity and sensitivity to hyperparameters. This paper explores a number of implementations of the NES family, ranging from general-purpose multi-variate normal distributions to heavy-tailed and separable distributions tailored towards global optimization and search in high dimensional spaces, respectively. Experimental results show best published performance on various standard benchmarks, as well as competitive performance on others. CMA-ES is one of the most popular stochastic search algorithms. It performs favourably in many tasks without the need of extensive parameter tuning. The algorithm has many beneficial properties, including automatic step-size adaptation, efficient covariance updates that incorporates the current samples as well as the evolution path and its invariance properties. Its update rules are composed of well established heuristics where the theoretical foundations of some of these rules are also well understood. In this paper we will fully derive all CMA-ES update rules within the framework of expectation-maximisation-based stochastic search algorithms using information-geometric trust regions. We show that the use of the trust region results in similar updates to CMA-ES for the mean and the covariance matrix while it allows for the derivation of an improved update rule for the step-size. Our new algorithm, Trust-Region Co-variance Matrix Adaptation Evolution Strategy (TR-CMA-ES) is fully derived from first order optimization principles and performs favourably in compare to standard CMA-ES algorithm.