Related papers: Fully lifted random duality theory
We study learning optimal policies from a logged dataset, i.e., offline RL, with function approximation. Despite the efforts devoted, existing algorithms with theoretic finite-sample guarantees typically assume exploratory data coverage or…
In this paper we revisited the classical problem of max-sum equivalence of randomly weighted sums in two dimensions. In opposite to the most papers in literature, we consider that there exists some interdependence between the primary random…
Opportunistic detection rules (ODRs) are variants of fixed-sample-size detection rules in which the statistician is allowed to make an early decision on the alternative hypothesis opportunistically based on the sequentially observed…
Evaluations of Deep Reinforcement Learning (DRL) methods are an integral part of scientific progress of the field. Beyond designing DRL methods for general intelligence, designing task-specific methods is becoming increasingly prominent for…
Conventional reinforcement learning (RL) algorithms exhibit broad generality in their theoretical formulation and high performance on several challenging domains when combined with powerful function approximation. However, developing RL…
Partially Observable Markov Decision Processes (POMDPs) can model complex sequential decision-making problems under stochastic and uncertain environments. A main reason hindering their broad adoption in real-world applications is the lack…
Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is…
This paper studies distributionally robust regret-optimal (DRRO) control with purified output feedback for linear systems subject to additive disturbances and measurement noise. These uncertainties (including the initial system state) are…
Deep Reinforcement Learning (DRL) has achieved great success in solving complicated decision-making problems. Despite the successes, DRL is frequently criticized for many reasons, e.g., data inefficient, inflexible and intractable reward…
To overcome the curses of dimensionality and modeling of Dynamic Programming (DP) methods to solve Markov Decision Process (MDP) problems, Reinforcement Learning (RL) methods are adopted in practice. Contrary to traditional RL algorithms…
Global pooling is one of the most significant operations in many machine learning models and tasks, which works for information fusion and structured data (like sets and graphs) representation. However, without solid mathematical…
Out-of-distribution (OOD) generalization is a challenging machine learning problem yet highly desirable in many high-stake applications. Existing methods suffer from overly pessimistic modeling with low generalization confidence. As…
We study the problem of maximizing the probability that (i) an electric component or financial institution $X$ does not default before another component or institution $Y$ and (ii) that $X$ and $Y$ default jointly within the class of all…
We explore the limit of stochastic differential equations driven by some random processes satisfying singularly perturbed second order stochastic differential equations. The main tool we employ is the universal limit theorem in rough path…
This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis…
Optimal control (OC) algorithms such as Differential Dynamic Programming (DDP) take advantage of the derivatives of the dynamics to efficiently control physical systems. Yet, in the presence of nonsmooth dynamical systems, such class of…
We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality…
Distributionally robust optimization (DRO) incorporates robustness against uncertainty in the specification of probabilistic models. This paper focuses on mitigating the curse of dimensionality in data-driven DRO problems with optimal…
This paper concerns the central issues of model robustness and sample efficiency in offline reinforcement learning (RL), which aims to learn to perform decision making from history data without active exploration. Due to uncertainties and…
The directed preferential attachment model is revisited. A new exact characterization of the limiting in- and out-degree distribution is given by two \emph{independent} pure birth processes that are observed at a common exponentially…