Nearest Neighbour Score Estimators for Diffusion Generative Models

Score function estimation is the cornerstone of both training and sampling from diffusion generative models. Despite this fact, the most commonly used estimators are either biased neural network approximations or high variance Monte Carlo estimators based on the conditional score. We introduce a novel nearest neighbour score function estimator which utilizes multiple samples from the training set to dramatically decrease estimator variance. We leverage our low variance estimator in two compelling applications. Training consistency models with our estimator, we report a significant increase in both convergence speed and sample quality. In diffusion models, we show that our estimator can replace a learned network for probability-flow ODE integration, opening promising new avenues of future research.

A Diffusion-Model of Joint Interactive Navigation

Simulation of autonomous vehicle systems requires that simulated traffic participants exhibit diverse and realistic behaviors. The use of prerecorded real-world traffic scenarios in simulation ensures realism but the rarity of safety critical events makes large scale collection of driving scenarios expensive. In this paper, we present DJINN - a diffusion based method of generating traffic scenarios. Our approach jointly diffuses the trajectories of all agents, conditioned on a flexible set of state observations from the past, present, or future. On popular trajectory forecasting datasets, we report state of the art performance on joint trajectory metrics. In addition, we demonstrate how DJINN flexibly enables direct test-time sampling from a variety of valuable conditional distributions including goal-based sampling, behavior-class sampling, and scenario editing.

Analyzing and Improving Greedy 2-Coordinate Updates for Equality-Constrained Optimization via Steepest Descent in the 1-Norm

We consider minimizing a smooth function subject to a summation constraint over its variables. By exploiting a connection between the greedy 2-coordinate update for this problem and equality-constrained steepest descent in the 1-norm, we give a convergence rate for greedy selection under a proximal Polyak-Lojasiewicz assumption that is faster than random selection and independent of the problem dimension $n$. We then consider minimizing with both a summation constraint and bound constraints, as arises in the support vector machine dual problem. Existing greedy rules for this setting either guarantee trivial progress only or require $O(n^2)$ time to compute. We show that bound- and summation-constrained steepest descent in the L1-norm guarantees more progress per iteration than previous rules and can be computed in only $O(n \log n)$ time.

Realistically distributing object placements in synthetic training data improves the performance of vision-based object detection models

When training object detection models on synthetic data, it is important to make the distribution of synthetic data as close as possible to the distribution of real data. We investigate specifically the impact of object placement distribution, keeping all other aspects of synthetic data fixed. Our experiment, training a 3D vehicle detection model in CARLA and testing on KITTI, demonstrates a substantial improvement resulting from improving the object placement distribution.

Video Killed the HD-Map: Predicting Driving Behavior Directly From Drone Images

The development of algorithms that learn behavioral driving models using human demonstrations has led to increasingly realistic simulations. In general, such models learn to jointly predict trajectories for all controlled agents by exploiting road context information such as drivable lanes obtained from manually annotated high-definition (HD) maps. Recent studies show that these models can greatly benefit from increasing the amount of human data available for training. However, the manual annotation of HD maps which is necessary for every new location puts a bottleneck on efficiently scaling up human traffic datasets. We propose a drone birdview image-based map (DBM) representation that requires minimal annotation and provides rich road context information. We evaluate multi-agent trajectory prediction using the DBM by incorporating it into a differentiable driving simulator as an image-texture-based differentiable rendering module. Our results demonstrate competitive multi-agent trajectory prediction performance when using our DBM representation as compared to models trained with rasterized HD maps.

Noise Is Not the Main Factor Behind the Gap Between SGD and Adam on Transformers, but Sign Descent Might Be

The success of the Adam optimizer on a wide array of architectures has made it the default in settings where stochastic gradient descent (SGD) performs poorly. However, our theoretical understanding of this discrepancy is lagging, preventing the development of significant improvements on either algorithm. Recent work advances the hypothesis that Adam and other heuristics like gradient clipping outperform SGD on language tasks because the distribution of the error induced by sampling has heavy tails. This suggests that Adam outperform SGD because it uses a more robust gradient estimate. We evaluate this hypothesis by varying the batch size, up to the entire dataset, to control for stochasticity. We present evidence that stochasticity and heavy-tailed noise are not major factors in the performance gap between SGD and Adam. Rather, Adam performs better as the batch size increases, while SGD is less effective at taking advantage of the reduction in noise. This raises the question as to why Adam outperforms SGD in the full-batch setting. Through further investigation of simpler variants of SGD, we find that the behavior of Adam with large batches is similar to sign descent with momentum.

Target-based Surrogates for Stochastic Optimization

We consider minimizing functions for which it is expensive to compute the (possibly stochastic) gradient. Such functions are prevalent in reinforcement learning, imitation learning and adversarial training. Our target optimization framework uses the (expensive) gradient computation to construct surrogate functions in a target space (e.g. the logits output by a linear model for classification) that can be minimized efficiently. This allows for multiple parameter updates to the model, amortizing the cost of gradient computation. In the full-batch setting, we prove that our surrogate is a global upper-bound on the loss, and can be (locally) minimized using a black-box optimization algorithm. We prove that the resulting majorization-minimization algorithm ensures convergence to a stationary point of the loss. Next, we instantiate our framework in the stochastic setting and propose the $SSO$ algorithm, which can be viewed as projected stochastic gradient descent in the target space. This connection enables us to prove theoretical guarantees for $SSO$ when minimizing convex functions. Our framework allows the use of standard stochastic optimization algorithms to construct surrogates which can be minimized by any deterministic optimization method. To evaluate our framework, we consider a suite of supervised learning and imitation learning problems. Our experiments indicate the benefits of target optimization and the effectiveness of $SSO$.

Vehicle Type Specific Waypoint Generation

We develop a generic mechanism for generating vehicle-type specific sequences of waypoints from a probabilistic foundation model of driving behavior. Many foundation behavior models are trained on data that does not include vehicle information, which limits their utility in downstream applications such as planning. Our novel methodology conditionally specializes such a behavior predictive model to a vehicle-type by utilizing byproducts of the reinforcement learning algorithms used to produce vehicle specific controllers. We show how to compose a vehicle specific value function estimate with a generic probabilistic behavior model to generate vehicle-type specific waypoint sequences that are more likely to be physically plausible then their vehicle-agnostic counterparts.

Improved Policy Optimization for Online Imitation Learning

We consider online imitation learning (OIL), where the task is to find a policy that imitates the behavior of an expert via active interaction with the environment. We aim to bridge the gap between the theory and practice of policy optimization algorithms for OIL by analyzing one of the most popular OIL algorithms, DAGGER. Specifically, if the class of policies is sufficiently expressive to contain the expert policy, we prove that DAGGER achieves constant regret. Unlike previous bounds that require the losses to be strongly-convex, our result only requires the weaker assumption that the losses be strongly-convex with respect to the policy's sufficient statistics (not its parameterization). In order to ensure convergence for a wider class of policies and losses, we augment DAGGER with an additional regularization term. In particular, we propose a variant of Follow-the-Regularized-Leader (FTRL) and its adaptive variant for OIL and develop a memory-efficient implementation, which matches the memory requirements of FTL. Assuming that the loss functions are smooth and convex with respect to the parameters of the policy, we also prove that FTRL achieves constant regret for any sufficiently expressive policy class, while retaining $O(\sqrt{T})$ regret in the worst-case. We demonstrate the effectiveness of these algorithms with experiments on synthetic and high-dimensional control tasks.

Conditional Permutation Invariant Flows

We present a novel, conditional generative probabilistic model of set-valued data with a tractable log density. This model is a continuous normalizing flow governed by permutation equivariant dynamics. These dynamics are driven by a learnable per-set-element term and pairwise interactions, both parametrized by deep neural networks. We illustrate the utility of this model via applications including (1) complex traffic scene generation conditioned on visually specified map information, and (2) object bounding box generation conditioned directly on images. We train our model by maximizing the expected likelihood of labeled conditional data under our flow, with the aid of a penalty that ensures the dynamics are smooth and hence efficiently solvable. Our method significantly outperforms non-permutation invariant baselines in terms of log likelihood and domain-specific metrics (offroad, collision, and combined infractions), yielding realistic samples that are difficult to distinguish from real data.