Related papers: Universal Approximation Theorem of Deep Q-Networks

In recent years, deep learning has been connected with optimal control as a way to define a notion of a continuous underlying learning problem. In this view, neural networks can be interpreted as a discretization of a parametric Ordinary…

Maximum simulated likelihood estimation of mixed multinomial logit (MMNL) or probit models requires evaluation of a multidimensional integral. Quasi-Monte Carlo (QMC) methods such as shuffled and scrambled Halton sequences and modified…

Q-learning has long been one of the most popular reinforcement learning algorithms, and theoretical analysis of Q-learning has been an active research topic for decades. Although researches on asymptotic convergence analysis of Q-learning…

Mixed precision quantization has become an important technique for optimizing the execution of deep neural networks (DNNs). Certified robustness, which provides provable guarantees about a model's ability to withstand different adversarial…

Optimizing large-scale wireless networks, including optimal resource management, power allocation, and throughput maximization, is inherently challenging due to their non-observable system dynamics and heterogeneous and complex nature.…

We analyse quantile temporal-difference learning (QTD), a distributional reinforcement learning algorithm that has proven to be a key component in several successful large-scale applications of reinforcement learning. Despite these…

For the past couple of decades, numerical optimization has played a central role in addressing wireless resource management problems such as power control and beamformer design. However, optimization algorithms often entail considerable…

Optimal trade execution is an important problem faced by essentially all traders. Much research into optimal execution uses stringent model assumptions and applies continuous time stochastic control to solve them. Here, we instead take a…

This paper investigates the approximation properties of deep neural networks with piecewise-polynomial activation functions. We derive the required depth, width, and sparsity of a deep neural network to approximate any H\"{o}lder smooth…

In this paper, a novel Deep Q-Network (DQN) based scheduling method to optimize delay time and fairness among entanglement requests in quantum repeater networks is proposed. The scheduling of requests determines which pairs of end nodes…

Meshing is a critical, but user-intensive process necessary for stable and accurate simulations in computational fluid dynamics (CFD). Mesh generation is often a bottleneck in CFD pipelines. Adaptive meshing techniques allow the mesh to be…

Deep neural networks (DNNs) and Kolmogorov-Arnold networks (KANs) are popular methods for function approximation due to their flexibility and expressivity. However, they typically require a large number of trainable parameters to produce a…

We present a distributed quasi-Newton (DQN) method, which enables a group of agents to compute an optimal solution of a separable multi-agent optimization problem locally using an approximation of the curvature of the aggregate objective…

Q-learning, which seeks to learn the optimal Q-function of a Markov decision process (MDP) in a model-free fashion, lies at the heart of reinforcement learning. When it comes to the synchronous setting (such that independent samples for all…

A deep learning approach to reinforcement learning led to a general learner able to train on visual input to play a variety of arcade games at the human and superhuman levels. Its creators at the Google DeepMind's team called the approach:…

This work presents the first finite-time analysis for the last-iterate convergence of average-reward $Q$-learning with an asynchronous implementation. A key feature of the algorithm we study is the use of adaptive stepsizes, which serve as…

We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial differential equations). As an application, we apply the…

In this paper, we provide a theoretical analysis of the inductive biases in convolutional neural networks (CNNs). We start by examining the universality of CNNs, i.e., the ability to approximate any continuous functions. We prove that a…

In distributed software-defined networks (SDN), multiple physical SDN controllers, each managing a network domain, are implemented to balance centralized control, scalability and reliability requirements. In such networking paradigm,…

In this paper, we propose forward and backward stochastic differential equations (FBSDEs) based deep neural network (DNN) learning algorithms for the solution of high dimensional quasilinear parabolic partial differential equations (PDEs),…