Matthew A. Wright

Matthew A. Wright, Roberto Horowitz

This paper addresses an open problem in traffic modeling: the second-order macroscopic node problem. A second-order macroscopic traffic model, in contrast to a first-order model, allows for variation of driving behavior across subpopulations of vehicles in the flow. The second-order models are thus more descriptive (e.g., they have been used to model variable mixtures of behaviorally-different traffic, like car/truck traffic, autonomous/human-driven traffic, etc.), but are much more complex. The second-order node problem is a particularly complex problem, as it requires the resolution of discontinuities in traffic density and mixture characteristics, and solving of throughflows for arbitrary numbers of input and output roads to a node (in other words, this is an arbitrary-dimensional Riemann problem with two conserved quantities). In this paper, we extend the well-known "Generic Class of Node Model" constraints to the second order and present a simple solution algorithm to the second-order node problem. Our solution makes use of a recently-introduced dynamic system characterization of the first-order node model problem, which gives insight and intuition as to the continuous-time dynamics implicit in node models. We further argue that the common "supply and demand" construction of node models that decouples them from link models is not suitable to the second-order node problem. Our second-order node model and solution method have immediate applications in allowing modeling of behaviorally-complex traffic flows of contemporary interest (like partially-autonomous-vehicle flows) in arbitrary road networks.

Matthew A. Wright, Roberto Horowitz, Alex A. Kurzhanskiy

To help mitigate road congestion caused by the unrelenting growth of traffic demand, many transit authorities have implemented managed lane policies. Managed lanes typically run parallel to a freeway's standard, general-purpose (GP) lanes, but are restricted to certain types of vehicles. It was originally thought that managed lanes would improve the use of existing infrastructure through incentivization of demand-management behaviors like carpooling, but implementations have often been characterized by unpredicted phenomena that is often to detrimental system performance. This paper presents several macroscopic traffic modeling tools we have used for study of freeways equipped with managed lanes, or "managed lane-freeway networks." The proposed framework is based on the widely-used first-order kinematic wave theory. In this model, the GP and the managed lanes are modeled as parallel links connected by nodes, where certain type of traffic may switch between GP and managed lane links. Two types of managed lane topologies are considered: full-access, where vehicles can switch between the GP and the managed lanes anywhere; and separated, where such switching is allowed only at certain locations called gates. We also describe methods to incorporate in three phenomena into our model that are particular to managed lane-freeway networks. The inertia effect reflects drivers' inclination to stay in their lane as long as possible and switch only if this would obviously improve their travel condition. The friction effect reflects the empirically-observed driver fear of moving fast in a managed lane while traffic in the adjacent GP lanes moves slowly due to congestion. The smoothing effect describes how managed lanes can increase throughput at bottlenecks by reducing lane changes. We present simple models for each of these phenomena that fit within the general macroscopic theory.

Zhanghao Wu, Paras Jain, Matthew A. Wright et al.

Graph neural networks are powerful architectures for structured datasets. However, current methods struggle to represent long-range dependencies. Scaling the depth or width of GNNs is insufficient to broaden receptive fields as larger GNNs encounter optimization instabilities such as vanishing gradients and representation oversmoothing, while pooling-based approaches have yet to become as universally useful as in computer vision. In this work, we propose the use of Transformer-based self-attention to learn long-range pairwise relationships, with a novel "readout" mechanism to obtain a global graph embedding. Inspired by recent computer vision results that find position-invariant attention performant in learning long-range relationships, our method, which we call GraphTrans, applies a permutation-invariant Transformer module after a standard GNN module. This simple architecture leads to state-of-the-art results on several graph classification tasks, outperforming methods that explicitly encode graph structure. Our results suggest that purely-learning-based approaches without graph structure may be suitable for learning high-level, long-range relationships on graphs. Code for GraphTrans is available at https://github.com/ucbrise/graphtrans.

Ionel Gog, Sukrit Kalra, Peter Schafhalter et al.

We present Pylot, a platform for autonomous vehicle (AV) research and development, built with the goal to allow researchers to study the effects of the latency and accuracy of their models and algorithms on the end-to-end driving behavior of an AV. This is achieved through a modular structure enabled by our high-performance dataflow system that represents AV software pipeline components (object detectors, motion planners, etc.) as a dataflow graph of operators which communicate on data streams using timestamped messages. Pylot readily interfaces with popular AV simulators like CARLA, and is easily deployable to real-world vehicles with minimal code changes. To reduce the burden of developing an entire pipeline for evaluating a single component, Pylot provides several state-of-the-art reference implementations for the various components of an AV pipeline. Using these reference implementations, a Pylot-based AV pipeline is able to drive a real vehicle, and attains a high score on the CARLA Autonomous Driving Challenge. We also present several case studies enabled by Pylot, including evidence of a need for context-dependent components, and per-component time allocation. Pylot is open source, with the code available at https://github.com/erdos-project/pylot.

Matthew A. Wright, Joseph E. Gonzalez

Despite their ubiquity in core AI fields like natural language processing, the mechanics of deep attention-based neural networks like the Transformer model are not fully understood. In this article, we present a new perspective towards understanding how Transformers work. In particular, we show that the "dot-product attention" that is the core of the Transformer's operation can be characterized as a kernel learning method on a pair of Banach spaces. In particular, the Transformer's kernel is characterized as having an infinite feature dimension. Along the way we consider an extension of the standard kernel learning problem to a binary setting, where data come from two input domains and a response is defined for every cross-domain pair. We prove a new representer theorem for these binary kernel machines with non-Mercer (indefinite, asymmetric) kernels (implying that the functions learned are elements of reproducing kernel Banach spaces rather than Hilbert spaces), and also prove a new universal approximation theorem showing that the Transformer calculation can learn any binary non-Mercer reproducing kernel Banach space pair. We experiment with new kernels in Transformers, and obtain results that suggest the infinite dimensionality of the standard Transformer kernel is partially responsible for its performance. This paper's results provide a new theoretical understanding of a very important but poorly understood model in modern machine~learning.

Nicholas Rhinehart, Jeff He, Charles Packer et al.

Humans have a remarkable ability to make decisions by accurately reasoning about future events, including the future behaviors and states of mind of other agents. Consider driving a car through a busy intersection: it is necessary to reason about the physics of the vehicle, the intentions of other drivers, and their beliefs about your own intentions. If you signal a turn, another driver might yield to you, or if you enter the passing lane, another driver might decelerate to give you room to merge in front. Competent drivers must plan how they can safely react to a variety of potential future behaviors of other agents before they make their next move. This requires contingency planning: explicitly planning a set of conditional actions that depend on the stochastic outcome of future events. In this work, we develop a general-purpose contingency planner that is learned end-to-end using high-dimensional scene observations and low-dimensional behavioral observations. We use a conditional autoregressive flow model to create a compact contingency planning space, and show how this model can tractably learn contingencies from behavioral observations. We developed a closed-loop control benchmark of realistic multi-agent scenarios in a driving simulator (CARLA), on which we compare our method to various noncontingent methods that reason about multi-agent future behavior, including several state-of-the-art deep learning-based planning approaches. We illustrate that these noncontingent planning methods fundamentally fail on this benchmark, and find that our deep contingency planning method achieves significantly superior performance. Code to run our benchmark and reproduce our results is available at https://sites.google.com/view/contingency-planning

Matthew A. Wright, Roberto Horowitz

Many potential applications of reinforcement learning in the real world involve interacting with other agents whose numbers vary over time. We propose new neural policy architectures for these multi-agent problems. In contrast to other methods of training an individual, discrete policy for each agent and then enforcing cooperation through some additional inter-policy mechanism, we follow the spirit of recent work on the power of relational inductive biases in deep networks by learning multi-agent relationships at the policy level via an attentional architecture. In our method, all agents share the same policy, but independently apply it in their own context to aggregate the other agents' state information when selecting their next action. The structure of our architectures allow them to be applied on environments with varying numbers of agents. We demonstrate our architecture on a benchmark multi-agent autonomous vehicle coordination problem, obtaining superior results to a full-knowledge, fully-centralized reference solution, and significantly outperforming it when scaling to large numbers of agents.

Matthew A. Wright, Roberto Horowitz, Alex A. Kurzhanskiy

The propagation of traffic congestion along roads is a commonplace nonlinear phenomenon. When many roads are connected in a network, congestion can spill from one road to others as drivers queue to enter a congested road, creating further nonlinearities in the network dynamics. This paper considers the node model problem, which refers to methods for solving for cross-flows when roads meet at a junction. We present a simple hybrid dynamic system that, given a macroscopic snapshot of the roads entering and exiting a node, intuitively models the node's throughflows over time. This dynamic system produces solutions to the node model problem that are equal to those produced by many popular node models without intuitive physical meanings. We also show how the earlier node models can be rederived as executions of our dynamic system. The intuitive physical description supplied by our system provides a base for control of the road junction system dynamics, as well as the emergent network dynamics.