We propose a new approach to learned optimization where we represent the computation of an optimizer's update step using a neural network. The parameters of the optimizer are then learned by training on a set of optimization tasks with the objective to perform minimization efficiently. Our innovation is a new neural network architecture, Optimus, for the learned optimizer inspired by the classic BFGS algorithm. As in BFGS, we estimate a preconditioning matrix as a sum of rank-one updates but use a Transformerbased neural network to predict these updates jointly with the step length and direction. In contrast to several recent learned optimization-based approaches [24, 27], our formulation allows for conditioning across the dimensions of the parameter space of the target problem while remaining applicable to optimization tasks of variable dimensionality without retraining. We demonstrate the advantages of our approach on a benchmark composed of objective functions traditionally used for the evaluation of optimization algorithms, as well as on the real world-task of physics-based visual reconstruction of articulated 3d human motion.

In recent years, impressive results have been achieved in robotic manipulation. While many efforts focus on generating collision-free reference signals, few allow safe contact between the robot bodies and the environment. However, in human's daily manipulation, contact between arms and obstacles is prevalent and even necessary. This paper investigates the benefit of allowing safe contact during robotic manipulation and advocates generating and tracking compliance reference signals in both operational and null spaces. In addition, to optimize the collision-allowed trajectories, we present a hybrid solver that integrates sampling- and gradient-based approaches. We evaluate the proposed method on a goal-reaching task in five simulated and real-world environments with different collisional conditions. We show that allowing safe contact improves goal-reaching efficiency and provides feasible solutions in highly collisional scenarios where collision-free constraints cannot be enforced. Moreover, we demonstrate that planning in null space, in addition to operational space, improves trajectory safety. Further information is available at https://rolandzhu.github.io/ContactReach/.

Deep learning has shown that learned functions can dramatically outperform hand-designed functions on perceptual tasks. Analogously, this suggests that learned optimizers may similarly outperform current hand-designed optimizers, especially for specific problems. However, learned optimizers are notoriously difficult to train and have yet to demonstrate wall-clock speedups over hand-designed optimizers, and thus are rarely used in practice. Typically, learned optimizers are trained by truncated backpropagation through an unrolled optimization process. The resulting gradients are either strongly biased (for short truncations) or have exploding norm (for long truncations). In this work we propose a training scheme which overcomes both of these difficulties, by dynamically weighting two unbiased gradient estimators for a variational loss on optimizer performance. This allows us to train neural networks to perform optimization of a specific task faster than tuned first-order methods. Moreover, by training the optimizer against validation loss (as opposed to training loss), we are able to learn optimizers that train networks to generalize better than first order methods. We demonstrate these results on problems where our learned optimizer trains convolutional networks faster in wall-clock time compared to tuned first-order methods and with an improvement in test loss.

Much of model-based reinforcement learning involves learning a model of an agent's world, and training an agent to leverage this model to perform a task more efficiently. While these models are demonstrably useful for agents, every naturally occurring model of the world of which we are aware---e.g., a brain---arose as the byproduct of competing evolutionary pressures for survival, not minimization of a supervised forward-predictive loss via gradient descent. That useful models can arise out of the messy and slow optimization process of evolution suggests that forward-predictive modeling can arise as a side-effect of optimization under the right circumstances. Crucially, this optimization process need not explicitly be a forward-predictive loss. In this work, we introduce a modification to traditional reinforcement learning which we call observational dropout, whereby we limit the agents ability to observe the real environment at each timestep. In doing so, we can coerce an agent into learning a world model to fill in the observation gaps during reinforcement learning. We show that the emerged world model, while not explicitly trained to predict the future, can help the agent learn key skills required to perform well in its environment. Videos of our results available at https://learningtopredict.github.io/