Diffusion models (DMs) create samples from a data distribution by starting from random noise and iteratively solving a reverse-time ordinary differential equation (ODE). Because each step in the iterative solution requires an expensive neural function evaluation (NFE), there has been significant interest in approximately solving these diffusion ODEs with only a few NFEs without modifying the underlying model. However, in the few NFE regime, we observe that tracking the true ODE evolution is fundamentally impossible using traditional ODE solvers. In this work, we propose a new method that learns a good solver for the DM, which we call Solving for the Solver (S4S). S4S directly optimizes a solver to obtain good generation quality by learning to match the output of a strong teacher solver. We evaluate S4S on six different pre-trained DMs, including pixel-space and latent-space DMs for both conditional and unconditional sampling. In all settings, S4S uniformly improves the sample quality relative to traditional ODE solvers. Moreover, our method is lightweight, data-free, and can be plugged in black-box on top of any discretization schedule or architecture to improve performance. Building on top of this, we also propose S4S-Alt, which optimizes both the solver and the discretization schedule. By exploiting the full design space of DM solvers, with 5 NFEs, we achieve an FID of 3.73 on CIFAR10 and 13.26 on MS-COCO, representing a $1.5\times$ improvement over previous training-free ODE methods.

Decision-makers often adaptively influence downstream competitive agents' behavior to minimize their cost, yet in doing so face critical challenges: $(i)$ decision-makers might not *a priori* know the agents' objectives; $(ii)$ agents might *learn* their responses, introducing stochasticity and non-stationarity into the decision-making process; and $(iii)$ there may be additional non-strategic environmental stochasticity. Characterizing convergence of this complex system is contingent on how the decision-maker controls for the tradeoff between the induced drift and additional noise from the learning agent behavior and environmental stochasticity. To understand how the learning agents' behavior is influenced by the decision-maker’s actions, we first consider a decision-maker that deploys an arbitrary sequence of actions which induces a sequence of games and corresponding equilibria. We characterize how the drift and noise in the agents' stochastic algorithms decouples from their optimization error. Leveraging this decoupling and accompanying finite-time efficiency estimates, we design decision-maker algorithms that control the induced drift relative to the agent noise. This enables efficient finite-time tracking of game theoretic equilibrium concepts that adhere to the incentives of the players' collective learning processes.

We present JRDB, a novel egocentric dataset collected from our social mobile manipulator JackRabbot. The dataset includes 64 minutes of annotated multimodal sensor data including stereo cylindrical 360${}^\circ$RGB video at 15 fps, 3D point clouds from two 16 planar rays Velodyne LiDARs, line 3D point clouds from two Sick Lidars, audio signal, RGB-D video at 30 fps, 360${}^\circ$spherical image from a fisheye camera and encoder values from the robot's wheels. Our dataset incorporates data from traditionally underrepresented scenes such as indoor environments and pedestrian areas, all from the ego-perspective of the robot, both stationary and navigating. The dataset has been annotated with over 2.4 million bounding boxes spread over five individual cameras and 1.8 million associated 3D cuboids around all people in the scenes totaling over 3500 time consistent trajectories. Together with our dataset and the annotations, we launch a benchmark and metrics for 2D and 3D person detection and tracking. With this dataset, which we plan on extending with further types of annotation in the future, we hope to provide a new source of data and a test-bench for research in the areas of egocentric robot vision, autonomous navigation, and all perceptual tasks around social robotics in human environments.