Related papers: Approximation to Deep Q-Network by Stochastic Dela…
We establish a continuous-time framework for analyzing Deep Q-Networks (DQNs) via stochastic control and Forward-Backward Stochastic Differential Equations (FBSDEs). Considering a continuous-time Markov Decision Process (MDP) driven by a…
Despite the great empirical success of deep reinforcement learning, its theoretical foundation is less well understood. In this work, we make the first attempt to theoretically understand the deep Q-network (DQN) algorithm (Mnih et al.,…
This paper proposes a new theoretical lens to view Wasserstein generative adversarial networks (WGANs). To minimize the Wasserstein-1 distance between the true data distribution and our estimate of it, we derive a distribution-dependent…
We provide an analysis of the squared Wasserstein-2 ($W_2$) distance between two probability distributions associated with two stochastic differential equations (SDEs). Based on this analysis, we propose the use of a squared $W_2$…
This paper provides a theoretical understanding of Deep Q-Network (DQN) with the $\varepsilon$-greedy exploration in deep reinforcement learning. Despite the tremendous empirical achievement of the DQN, its theoretical characterization…
Deep Q-Networks algorithm (DQN) was the first reinforcement learning algorithm using deep neural network to successfully surpass human level performance in a number of Atari learning environments. However, divergent and unstable behaviour…
The deep Q-network (DQN) and return-based reinforcement learning are two promising algorithms proposed in recent years. DQN brings advances to complex sequential decision problems, while return-based algorithms have advantages in making use…
The quantum Wasserstein distance (W-distance) is a fundamental metric for quantifying the distinguishability of quantum operations, with critical applications in quantum error correction. However, computing the W-distance remains…
Topological Data Analysis methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially…
Several real-world scenarios, such as remote control and sensing, are comprised of action and observation delays. The presence of delays degrades the performance of reinforcement learning (RL) algorithms, often to such an extent that…
In order to solve the problem of frequent deceleration of unmanned vehicles when approaching obstacles, this article uses a Deep Q-Network (DQN) and its extension, the Double Deep Q-Network (DDQN), to develop a local navigation system that…
This paper investigates a project with stochastic activity durations and cash flows under discrete scenarios, where activities must satisfy precedence constraints generating cash inflows and outflows. The objective is to maximize expected…
Deep Q-learning Network (DQN) is a successful way which combines reinforcement learning with deep neural networks and leads to a widespread application of reinforcement learning. One challenging problem when applying DQN or other…
Inspired by Double Q-learning algorithm, the Double-DQN (DDQN) algorithm was originally proposed in order to address the overestimation issue in the original DQN algorithm. The DDQN has successfully shown both theoretically and empirically…
In this paper, we analyze the scalability of a recent Wasserstein-distance approach for training stochastic neural networks (SNNs) to reconstruct multidimensional random field models. We prove a generalization error bound for reconstructing…
This paper presents a distributionally robust Q-Learning algorithm (DrQ) which leverages Wasserstein ambiguity sets to provide idealistic probabilistic out-of-sample safety guarantees during online learning. First, we follow past work by…
Optimal Transport has sparked vivid interest in recent years, in particular thanks to the Wasserstein distance, which provides a geometrically sensible and intuitive way of comparing probability measures. For computational reasons, the…
We study in this paper a weak approximation to stochastic variance reduced gradient Langevin dynamics by stochastic delay differential equations in Wasserstein-1 distance, and obtain a uniform error bound. Our approach is via a refined…
The nested distance builds on the Wasserstein distance to quantify the difference of stochastic processes, including also the information modelled by filtrations. The Sinkhorn divergence is a relaxation of the Wasserstein distance, which…
In this work, we propose a novel generalized Wasserstein-2 distance approach for efficiently training stochastic neural networks to reconstruct random field models, where the target random variable comprises both continuous and categorical…