Related papers: Deep Contract Design via Discontinuous Networks
The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts…
Whereas recovery of the manifold from data is a well-studied topic, approximation rates for functions defined on manifolds are less known. In this work, we study a regression problem with inputs on a $d^*$-dimensional manifold that is…
Innovation in the physical layer of communication systems has traditionally been achieved by breaking down the transceivers into sets of processing blocks, each optimized independently based on mathematical models. Conversely, deep learning…
Deep learning methods have gained popularity in recent years through the media and the relative ease of implementation through open source packages such as Keras. We investigate the applicability of popular recurrent neural networks in…
Deep Neural Networks (DNNs) have emerged as a powerful mechanism and are being increasingly deployed in real-world safety-critical domains. Despite the widespread success, their complex architecture makes proving any formal guarantees about…
Deep neural network with rectified linear units (ReLU) is getting more and more popular recently. However, the derivatives of the function represented by a ReLU network are not continuous, which limit the usage of ReLU network to situations…
Large electricity customers (e.g., large data centers) can exhibit huge and variable electricity demands, which poses significant challenges for the electricity suppliers to plan for sufficient capacity. Thus, it is desirable to design…
The nonlinearity of activation functions used in deep learning models are crucial for the success of predictive models. There are several commonly used simple nonlinear functions, including Rectified Linear Unit (ReLU) and Leaky-ReLU…
A contract is an economic tool used by a principal to incentivize one or more agents to exert effort on her behalf, by defining payments based on observable performance measures. A key challenge addressed by contracts -- known in economics…
In deep learning, dense layer connectivity has become a key design principle in deep neural networks (DNNs), enabling efficient information flow and strong performance across a range of applications. In this work, we model densely connected…
The NP-hard problem of optimizing a shallow ReLU network can be characterized as a combinatorial search over each training example's activation pattern followed by a constrained convex problem given a fixed set of activation patterns. We…
Optimal designs are usually model-dependent and likely to be sub-optimal if the postulated model is not correctly specified. In practice, it is common that a researcher has a list of candidate models at hand and a design has to be found…
In a framework close to the one developed by Holmstr\"om and Milgrom [44], we study the optimal contracting scheme between a Principal and several Agents. Each hired Agent is in charge of one project, and can make efforts towards managing…
We demonstrate that deep neural networks with the ReLU activation function can efficiently approximate the solutions of various types of parametric linear transport equations. For non-smooth initial conditions, the solutions of these PDEs…
Deep learning has been widely used in many fields, but the model training process usually consumes massive computational resources and time. Therefore, designing an efficient neural network training method with a provable convergence…
We study a new class of contract design problems where a principal delegates the execution of multiple projects to a set of agents. The principal's expected reward from each project is a combinatorial function of the agents working on it.…
Interpretable machine learning (IML) becomes increasingly important in highly regulated industry sectors related to the health and safety or fundamental rights of human beings. In general, the inherently IML models should be adopted because…
Recent research reveals that deep learning is an effective way of solving high dimensional Hamilton-Jacobi-Bellman equations. The resulting feedback control law in the form of a neural network is computationally efficient for real-time…
The increasing deployment of AI is shaping the future landscape of the internet, which is set to become an integrated ecosystem of AI agents. Orchestrating the interaction among AI agents necessitates decentralized, self-sustaining…
While deep learning has outperformed other methods for various tasks, theoretical frameworks that explain its reason have not been fully established. To address this issue, we investigate the excess risk of two-layer ReLU neural networks in…