This work studies the problem of sequential control in an unknown, nonlinear dynamical system, where we model the underlying system dynamics as an unknown function in a known Reproducing Kernel Hilbert Space. This framework yields a general setting that permits discrete and continuous control inputs as well as non-smooth, non-differentiable dynamics. Our main result, the Lower Confidence-based Continuous Control (LC3) algorithm, enjoys a near-optimal $O(\sqrt{T})$ regret bound against the optimal controller in episodic settings, where $T$ is the number of episodes. The bound has no explicit dependence on dimension of the system dynamics, which could be infinite, but instead only depends on information theoretic quantities. We empirically show its application to a number of nonlinear control tasks and demonstrate the benefit of exploration for learning model dynamics.

The remarkable successes of deep learning in speech recognition and computer vision have motivated efforts to adapt similar techniques to other problem domains, including reinforcement learning (RL). Consequently, RL methods have produced rich motor behaviors on simulated robot tasks, with their success largely attributed to the use of multi-layer neural networks. This work is among the first to carefully study what might be responsible for these recent advancements. Our main result calls this emerging narrative into question by showing that much simpler architectures -- based on linear and RBF parameterizations -- achieve comparable performance to state of the art results. We not only study different policy representations with regard to performance measures at hand, but also towards robustness to external perturbations. We again find that the learned neural network policies --- under the standard training scenarios --- are no more robust than linear (or RBF) policies; in fact, all three are remarkably brittle. Finally, we then directly modify the training scenarios in order to favor more robust policies, and we again do not find a compelling case to favor multi-layer architectures. Overall, this study suggests that multi-layer architectures should not be the default choice, unless a side-by-side comparison to simpler architectures shows otherwise. More generally, we hope that these results lead to more interest in carefully studying the architectural choices, and associated trade-offs, for training generalizable and robust policies.

While a lot of progress has recently been made in dynamic motion planning for humanoid robots, much of this work has remained limited to simulation. Here we show that executing the resulting trajectories on a Darwin-OP robot, even with local feedback derived from the optimizer, does not result in stable movements. We then develop a new trajectory optimization method, adapting our earlier CIO algorithm to plan through ensembles of perturbed models. This makes the plan robust to model uncertainty, and leads to successful execution on the robot. We obtain a high rate of task completion without trajectory divergence (falling) in dynamic forward walking, sideways walking, and turning, and a similarly high success rate in getting up from the floor (the robot broke before we could quantify the latter). Even though the planning is still done offline, the present work represents a significant step towards automating the tedious scripting of complex movements.

We present a method for training recurrent neural networks to act as near-optimal feedback controllers. It is able to generate stable and realistic behaviors for a range of dynamical systems and tasks -- swimming, flying, biped and quadruped walking with different body morphologies. It does not require motion capture or task-specific features or state machines. The controller is a neural network, having a large number of feed-forward units that learn elaborate state-action mappings, and a small number of recurrent units that implement memory states beyond the physical system state. The action generated by the network is defined as velocity. Thus the network is not learning a control policy, but rather the dynamics under an implicit policy. Essential features of the method include interleaving supervised learning with trajectory optimization, injecting noise during training, training for unexpected changes in the task specification, and using the trajectory optimizer to obtain optimal feedback gains in addition to optimal actions.

We describe an accurate approach to state estimation which fuses any available sensor data with physical consistency priors. This is done by combining the advantages of recursive estimation and fixed-lag smoothing: at each step we re-estimate the trajectory over a time window into the past, but also use a recursive prior obtained from the previous time step via internal simulation. We also incorporate a physics engine into the estimator, which makes it possible to adjust the state estimates so that the inferred contact interactions are consistent with the observed accelerations. The estimator can utilize contact sensors to improve accuracy, but even in the absence of such sensors it reasons correctly about contact forces. Estimation speed and accuracy are demonstrated on a 28-DOF humanoid robot (Darwin) in a walking task. Timing tests and leave-one-out cross-validation show that the proposed approach can be used in real-time and is substantially more accurate than the EKF, without any over-fitting. A video of our results is attached.