The recently introduced Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) is an evolutionary algorithm capable of producing a large archive of diverse, high-performing solutions in a single run. It works by discretizing a continuous feature space into unique regions according to the desired discretization per dimension. While simple, this algorithm has a main drawback: it cannot scale to high-dimensional feature spaces since the number of regions increase exponentially with the number of dimensions. In this paper, we address this limitation by introducing a simple extension of MAP-Elites that has a constant, pre-defined number of regions irrespective of the dimensionality of the feature space. Our main insight is that methods from computational geometry could partition a high-dimensional space into well-spread geometric regions. In particular, our algorithm uses a centroidal Voronoi tessellation (CVT) to divide the feature space into a desired number of regions; it then places every generated individual in its closest region, replacing a less fit one if the region is already occupied. We demonstrate the effectiveness of the new "CVT-MAP-Elites" algorithm in high-dimensional feature spaces through comparisons against MAP-Elites in maze navigation and hexapod locomotion tasks.

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 dataefficient 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, blackbox 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).

Most policy search algorithms require thousands of training episodes to find an effective policy, which is often infeasible with a physical robot. This survey article focuses on the extreme other end of the spectrum: how can a robot adapt with only a handful of trials (a dozen) and a few minutes? By analogy with the word "big-data", we refer to this challenge as "micro-data reinforcement learning". We show that a first strategy is to leverage prior knowledge on the policy structure (e.g., dynamic movement primitives), on the policy parameters (e.g., demonstrations), or on the dynamics (e.g., simulators). A second strategy is to create data-driven surrogate models of the expected reward (e.g., Bayesian optimization) or the dynamical model (e.g., model-based policy search), so that the policy optimizer queries the model instead of the real system. Overall, all successful micro-data algorithms combine these two strategies by varying the kind of model and prior knowledge. The current scientific challenges essentially revolve around scaling up to complex robots, designing generic priors, and optimizing the computing time.1 In some rare cases, a process can be "optimally efficient". 2 It is challenging to put a precise limit for "micro-data learning" as each domain has different experimental constraints, this is why we will refer in this article to "a few minutes" or a "a few trials". The commonly used word "big-data" has a similar "fuzzy" limit that depends on the exact domain. 3 Planning-based and model-predictive control [59] methods do not search for policy parameters, this is why they do not fit into the scope of this paper. Although trajectory-based policies and planning-based methods share the same goal, they usually search in a different space: planning algorithms search in the state-action space (e.g., joint positions/velocities), whereas policy methods will search for the optimal parameters of the policy, which can encode a Chatzilygeroudis, Vassiliades, Stulp, Calinon and Mouret arXiv | 1 arXiv:1807.02303v4 [cs.RO] 31 May 2019 Chatzilygeroudis, Vassiliades, Stulp, Calinon and Mouret arXiv | 2This is basically sampling the distribution over trajectories, P (τ |θ), which is feasible since the sampling is performed with the models. When applying the same policy (i.e., a policy with the same parameters θ), the trajectories τ (and consequently r)Chatzilygeroudis, Vassiliades, Stulp, Calinon and Mouret arXiv | 9