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The paper presents necessary and sufficient conditions for the order reduction of optimal control systems. Exploring the corresponding Hamiltonian system allows to solve the order reduction problem in terms of dynamical systems,…
The average cost optimality is known to be a challenging problem for partially observable stochastic control, with few results available beyond the finite state, action, and measurement setup, for which somewhat restrictive conditions are…
Diffusion policies have emerged as a mainstream paradigm for building vision-language-action (VLA) models. Although they demonstrate strong robot control capabilities, their training efficiency remains suboptimal. In this work, we identify…
Score-based generative models like the diffusion model have been testified to be effective in modeling multi-modal data from image generation to reinforcement learning (RL). However, the inference process of diffusion model can be slow,…
Schrodinger Bridges (SBs) are diffusion processes that steer, in finite time, a given initial distribution to another final one while minimizing a suitable cost functional. Although various methods for computing SBs have recently been…
Current robotic pick-and-place policies typically require consistent gripper configurations across training and inference. This constraint imposes high retraining or fine-tuning costs, especially for imitation learning-based approaches,…
Diffusion policies have emerged as powerful generative models for offline policy learning, whose sampling process can be rigorously characterized by a score function guiding a stochastic differential equation (SDE). However, the same…
This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion factor process. The…
Inventory control with unknown demand distribution is considered, with emphasis placed on the case involving discrete nonperishable items. We focus on an adaptive policy which in every period uses, as much as possible, the optimal…
We establish well-posedness for a class of systems of SDEs with non-Lipschitz coefficients in the diffusion and jump terms and with two sources of interdependence: a monotone function of all the components in the drift of each SDE and the…
For optimal control of diffusions under several criteria, due to computational or analytical reasons, many studies have a apriori assumed control policies to be Lipschitz or smooth, often with no rigorous analysis on whether this…
Diffusion models have gained attention for their ability to represent complex distributions and incorporate uncertainty, making them ideal for robust predictions in the presence of noisy or incomplete data. In this study, we develop and…
We study a dynamic scheduling problem for a multi-class queueing network with a large pool of statistically identical servers. The arrival processes are Poisson, and service times and patience times are assumed to be exponentially…
We consider a processor sharing queue where the number of jobs served at any time is limited to $K$, with the excess jobs waiting in a buffer. We use random counting measures on the positive axis to model this system. The limit of this…
The model of this paper gives a convenient strategy that a bank in the federal funds market can use in order to maximize its profit in a contemporaneous reserve requirement (CRR) regime. The reserve requirements are determined by the demand…
We consider a distribution warehouse where both the inbound inventory replenishment and outbound dispatch decisions are subject to fixed (as well as per-unit) transportation charges and demand is stochastic. In order to realize scale…
In the classical quickest detection problem, one must detect as quickly as possible when a Brownian motion without drift "changes" into a Brownian motion with positive drift. The change occurs at an unknown "disorder" time with exponential…
We focus on Optimal Transport PDE on the unit sphere $\mathbb{S}^2$ with a particular type of cost function $c(x,y) = F(x \cdot y, x \cdot \hat{e}, y \cdot \hat{e})$ which we call cost functions with preferential direction, where $\hat{e}…
A distributed order fractional diffusion equation is considered. Distributed order derivatives are fractional derivatives that have been integrated over the order of the derivative within a given range. In this paper sub-diffusive cases are…
In this paper we consider an energy storage optimization problem in finite time in a model with partial information that allows for a changing economic environment. The state process consists of the storage level controlled by the storage…