Data Efficient Reinforcement Learning for Legged Robots

We present a model-based framework for robot locomotion that achieves walking based on only 4.5 minutes (45,000 control steps) of data collected on a quadruped robot. To accurately model the robot's dynamics over a long horizon, we introduce a loss function that tracks the model's prediction over multiple timesteps. We adapt model predictive control to account for planning latency, which allows the learned model to be used for real time control. Additionally, to ensure safe exploration during model learning, we embed prior knowledge of leg trajectories into the action space. The resulting system achieves fast and robust locomotion. Unlike model-free methods, which optimize for a particular task, our planner can use the same learned dynamics for various tasks, simply by changing the reward function. To the best of our knowledge, our approach is more than an order of magnitude more sample efficient than current model-free methods.

Teleoperator Imitation with Continuous-time Safety

Learning to effectively imitate human teleoperators, with generalization to unseen and dynamic environments, is a promising path to greater autonomy enabling robots to steadily acquire complex skills from supervision. We propose a new motion learning technique rooted in contraction theory and sum-of-squares programming for estimating a control law in the form of a polynomial vector field from a given set of demonstrations. Notably, this vector field is provably optimal for the problem of minimizing imitation loss while providing continuous-time guarantees on the induced imitation behavior. Our method generalizes to new initial and goal poses of the robot and can adapt in real-time to dynamic obstacles during execution, with convergence to teleoperator behavior within a well-defined safety tube. We present an application of our framework for pick-and-place tasks in the presence of moving obstacles on a 7-DOF KUKA IIWA arm. The method compares favorably to other learning-from-demonstration approaches on benchmark handwriting imitation tasks.

When random search is not enough: Sample-Efficient and Noise-Robust Blackbox Optimization of RL Policies

Interest in derivative-free optimization (DFO) and "evolutionary strategies" (ES) has recently surged in the Reinforcement Learning (RL) community, with growing evidence that they match state of the art methods for policy optimization tasks. However, blackbox DFO methods suffer from high sampling complexity since they require a substantial number of policy rollouts for reliable updates. They can also be very sensitive to noise in the rewards, actuators or the dynamics of the environment. In this paper we propose to replace the standard ES derivative-free paradigm for RL based on simple reward-weighted averaged random perturbations for policy updates, that has recently become a subject of voluminous research, by an algorithm where gradients of blackbox RL functions are estimated via regularized regression methods. In particular, we propose to use L1/L2 regularized regression-based gradient estimation to exploit sparsity and smoothness, as well as LP decoding techniques for handling adversarial stochastic and deterministic noise. Our methods can be naturally aligned with sliding trust region techniques for efficient samples reuse to further reduce sampling complexity. This is not the case for standard ES methods requiring independent sampling in each epoch. We show that our algorithms can be applied in locomotion tasks, where training is conducted in the presence of substantial noise, e.g. for learning in sim transferable stable walking behaviors for quadruped robots or training quadrupeds how to follow a path. We further demonstrate our methods on several $\mathrm{OpenAI}$ $\mathrm{Gym}$ $\mathrm{Mujoco}$ RL tasks. We manage to train effective policies even if up to $25\%$ of all measurements are arbitrarily corrupted, where standard ES methods produce sub-optimal policies or do not manage to learn at all. Our empirical results are backed by theoretical guarantees.

Learning Stabilizable Dynamical Systems via Control Contraction Metrics

We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key idea is to develop a new control-theoretic regularizer for dynamics fitting rooted in the notion of stabilizability, which guarantees that the learned system can be accompanied by a robust controller capable of stabilizing any open-loop trajectory that the system may generate. By leveraging tools from contraction theory, statistical learning, and convex optimization, we provide a general and tractable semi-supervised algorithm to learn stabilizable dynamics, which can be applied to complex underactuated systems. We validated the proposed algorithm on a simulated planar quadrotor system and observed notably improved trajectory generation and tracking performance with the control-theoretic regularized model over models learned using traditional regression techniques, especially when using a small number of demonstration examples. The results presented illustrate the need to infuse standard model-based reinforcement learning algorithms with concepts drawn from nonlinear control theory for improved reliability.

Structured Evolution with Compact Architectures for Scalable Policy Optimization

We present a new method of blackbox optimization via gradient approximation with the use of structured random orthogonal matrices, providing more accurate estimators than baselines and with provable theoretical guarantees. We show that this algorithm can be successfully applied to learn better quality compact policies than those using standard gradient estimation techniques. The compact policies we learn have several advantages over unstructured ones, including faster training algorithms and faster inference. These benefits are important when the policy is deployed on real hardware with limited resources. Further, compact policies provide more scalable architectures for derivative-free optimization (DFO) in high-dimensional spaces. We show that most robotics tasks from the OpenAI Gym can be solved using neural networks with less than 300 parameters, with almost linear time complexity of the inference phase, with up to 13x fewer parameters relative to the Evolution Strategies (ES) algorithm introduced by Salimans et al. (2017). We do not need heuristics such as fitness shaping to learn good quality policies, resulting in a simple and theoretically motivated training mechanism.

Optimizing Simulations with Noise-Tolerant Structured Exploration

We propose a simple drop-in noise-tolerant replacement for the standard finite difference procedure used ubiquitously in blackbox optimization. In our approach, parameter perturbation directions are defined by a family of structured orthogonal matrices. We show that at the small cost of computing a Fast Walsh-Hadamard/Fourier Transform (FWHT/FFT), such structured finite differences consistently give higher quality approximation of gradients and Jacobians in comparison to vanilla approaches that use coordinate directions or random Gaussian perturbations. We find that trajectory optimizers like Iterative LQR and Differential Dynamic Programming require fewer iterations to solve several classic continuous control tasks when our methods are used to linearize noisy, blackbox dynamics instead of standard finite differences. By embedding structured exploration in a quasi-Newton optimizer (LBFGS), we are able to learn agile walking and turning policies for quadruped locomotion, that successfully transfer from simulation to actual hardware.We theoretically justify our methods via bounds on the quality of gradient reconstruction and provide a basis for applying them also to nonsmooth problems.

Learning Contracting Vector Fields For Stable Imitation Learning

We propose a new non-parametric framework for learning incrementally stable dynamical systems x' = f(x) from a set of sampled trajectories. We construct a rich family of smooth vector fields induced by certain classes of matrix-valued kernels, whose equilibria are placed exactly at a desired set of locations and whose local contraction and curvature properties at various points can be explicitly controlled using convex optimization. With curl-free kernels, our framework may also be viewed as a mechanism to learn potential fields and gradient flows. We develop large-scale techniques using randomized kernel approximations in this context. We demonstrate our approach, called contracting vector fields (CVF), on imitation learning tasks involving complex point-to-point human handwriting motions.

Manifold Regularization for Kernelized LSTD

Policy evaluation or value function or Q-function approximation is a key procedure in reinforcement learning (RL). It is a necessary component of policy iteration and can be used for variance reduction in policy gradient methods. Therefore its quality has a significant impact on most RL algorithms. Motivated by manifold regularized learning, we propose a novel kernelized policy evaluation method that takes advantage of the intrinsic geometry of the state space learned from data, in order to achieve better sample efficiency and higher accuracy in Q-function approximation. Applying the proposed method in the Least-Squares Policy Iteration (LSPI) framework, we observe superior performance compared to widely used parametric basis functions on two standard benchmarks in terms of policy quality.

Hierarchically Compositional Kernels for Scalable Nonparametric Learning

We propose a novel class of kernels to alleviate the high computational cost of large-scale nonparametric learning with kernel methods. The proposed kernel is defined based on a hierarchical partitioning of the underlying data domain, where the Nystr\"om method (a globally low-rank approximation) is married with a locally lossless approximation in a hierarchical fashion. The kernel maintains (strict) positive-definiteness. The corresponding kernel matrix admits a recursively off-diagonal low-rank structure, which allows for fast linear algebra computations. Suppressing the factor of data dimension, the memory and arithmetic complexities for training a regression or a classifier are reduced from $O(n^2)$ and $O(n^3)$ to $O(nr)$ and $O(nr^2)$, respectively, where $n$ is the number of training examples and $r$ is the rank on each level of the hierarchy. Although other randomized approximate kernels entail a similar complexity, empirical results show that the proposed kernel achieves a matching performance with a smaller $r$. We demonstrate comprehensive experiments to show the effective use of the proposed kernel on data sizes up to the order of millions.