The physical design of a robot and the policy that controls its motion are inherently coupled, and should be determined according to the task and environment. In an increasing number of applications, data-driven and learning-based approaches, such as deep reinforcement learning, have proven effective at designing control policies. For most tasks, the only way to evaluate a physical design with respect to such control policies is empirical-i.e., by picking a design and training a control policy for it. Since training these policies is time-consuming, it is computationally infeasible to train separate policies for all possible designs as a means to identify the best one. In this work, we address this limitation by introducing a method that jointly optimizes over the physical design and control network. Our approach maintains a distribution over designs and uses reinforcement learning to optimize a control policy to maximize expected reward over the design distribution. We give the controller access to design parameters to allow it to tailor its policy to each design in the distribution. Throughout training, we shift the distribution towards higher-performing designs, eventually converging to a design and control policy that are jointly optimal. We evaluate our approach in the context of legged locomotion, and demonstrate that it discovers novel designs and walking gaits, outperforming baselines across different settings.

The ability of robots to estimate their location is crucial for a wide variety of autonomous operations. In settings where GPS is unavailable, measurements of transmissions from fixed beacons provide an effective means of estimating a robot's location as it navigates. The accuracy of such a beacon-based localization system depends both on how beacons are distributed in the environment, and how the robot's location is inferred based on noisy and potentially ambiguous measurements. We propose an approach for making these design decisions automatically and without expert supervision, by explicitly searching for the placement and inference strategies that, together, are optimal for a given environment. Since this search is computationally expensive, our approach encodes beacon placement as a differential neural layer that interfaces with a neural network for inference. This formulation allows us to employ standard techniques for training neural networks to carry out the joint optimization. We evaluate this approach on a variety of environments and settings, and find that it is able to discover designs that enable high localization accuracy.

Despite the success of kernel-based nonparametric methods, kernel selection still requires considerable expertise, and is often described as a “black art.” We present a sophisticated method for automatically searching for an appropriate kernel from an infinite space of potential choices. Previous efforts in this direction have focused on traversing a kernel grammar, only examining the data via computation of marginal likelihood. Our proposed search method is based on Bayesian optimization in model space, where we reason about model evidence as a function to be maximized. We explicitly reason about the data distribution and how it induces similarity between potential model choices in terms of the explanations they can offer for observed data. In this light, we construct a novel kernel between models to explain a given dataset. Our method is capable of finding a model that explains a given dataset well without any human assistance, often with fewer computations of model evidence than previous approaches, a claim we demonstrate empirically.