Accelerating Cooperative Planning for Automated Vehicles with Learned Heuristics and Monte Carlo Tree Search

Efficient driving in urban traffic scenarios requires foresight. The observation of other traffic participants and the inference of their possible next actions depending on the own action is considered cooperative prediction and planning. Humans are well equipped with the capability to predict the actions of multiple interacting traffic participants and plan accordingly, without the need to directly communicate with others. Prior work has shown that it is possible to achieve effective cooperative planning without the need for explicit communication. However, the search space for cooperative plans is so large that most of the computational budget is spent on exploring the search space in unpromising regions that are far away from the solution. To accelerate the planning process, we combined learned heuristics with a cooperative planning method to guide the search towards regions with promising actions, yielding better solutions at lower computational costs

Topological Data Analysis of Convolutional Neural Networks Using Depthwise Separable Convolutions

In this dissertation, we present our contribution to a growing body of work combining the fields of Topological Data Analysis (TDA) and machine learning. The object of our analysis is the Convolutional Neural Network, or CNN, a predictive model with a large number of parameters organized using a grid-like geometry. This geometry is engineered to resemble patches of pixels in an image, and thus CNNs are a conventional choice for an image-classifying model. CNNs belong to a larger class of neural network models, which, starting at a random initialization state, undergo a gradual fitting (or training) process, often a variation of gradient descent. The goal of this descent process is to decrease the value of a loss function measuring the error associated with the model’s predictions, and ideally converge to a model minimizing the loss. While such neural networks are known for generating accurate predictions in a wide variety of contexts and having a significant scalability advantage over many other predictive models, they are notoriously difficult to analyze and understand holistically. TDA techniques, such as the persistent homology and Mapper algorithms, have been proposed as methods for exploring the CNN training process. As we will detail, Gunnar Carlsson and Richard Gabrielsson’s TDA work with CNNs has suggested fundamental similarities in the distributions underlying both 3-by-3 image patches in natural images and CNNs trained on these images, i.e., CNNs can learn topological information about their training data. Our work aims to expand this use of TDA to an alternate CNN construction, using the technique of depthwise separable convolution. This construction requires fewer parameters to be trained and requires fewer multiplcation/addition operations than the CNNs discussed in the work of Carlsson and Gabrielsson, which are characterized by what we call the standard convolution. However, we observe that, when trained on a dataset of chest X-Rays, these models are able not only to perform well, but also learn similar topological information to their standard-convolution counterparts