Related papers: Continuous Inventory Models of Diffusion Type: Lon…
The paper considers the optimal control problem of inventory of a discrete product in regeneration scheme with a Poisson flow of customer requirements. In the system deferred demand is allowed, the volume of which is limited by a given…
In this paper, we introduce a modification of the free boundary problem related to optimal stopping problems for diffusion processes. This modification allows the application of this PDE method in cases where the usual regularity…
Diffusion models have recently emerged as effective generative frameworks for trajectory optimization, capable of producing high-quality and diverse solutions. However, training these models in a purely data-driven manner without explicit…
Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding…
Consider a set of discounted optimal stopping problems for a one-parameter family of objective functions and a fixed diffusion process, started at a fixed point. A standard problem in stochastic control/optimal stopping is to solve for the…
Consistency Models (CM) (Song et al., 2023) accelerate score-based diffusion model sampling at the cost of sample quality but lack a natural way to trade-off quality for speed. To address this limitation, we propose Consistency Trajectory…
Understanding the spread of infectious diseases requires integrating movement, physical constraints, and spatial configurations into epidemiological models. In this study, we investigate how particle diffusivity, hardcore interactions, and…
We consider a production-inventory control model with finite capacity and two different production rates, assuming that the cumulative process of customer demand is given by a compound Poisson process. It is possible at any time to switch…
This paper studies a diffusion model that arises as the limit of a queueing system scheduling problem in the asymptotic heavy traffic regime of Halfin and Whitt. The queueing system consists of several customer classes and many servers…
The coupling between advection and diffusion in position space can often lead to enhanced mass transport compared to diffusion without flow. An important framework used to characterize the long-time diffusive transport in position space is…
We consider the problem of parameter estimation for a class of continuous-time state space models. In particular, we explore the case of a partially observed diffusion, with data also arriving according to a diffusion process. Based upon a…
In a previous paper, we established strong existence and uniqueness for a reflected diffusion $(X,S)$ with values in $\bar D\times \mathbbm{R}^p$, solving the following pair of stochastic differential equations: $$ dX_t = \sigma(X_t)dB_t +…
In this paper we investigate an optimal dividend problem with transaction costs, where the surplus process is modelled by a refracted L\'evy process and the ruin time is considered with Parisian delay. Presence of the transaction costs…
This paper introduces Diffusion Policy, a new way of generating robot behavior by representing a robot's visuomotor policy as a conditional denoising diffusion process. We benchmark Diffusion Policy across 12 different tasks from 4…
We give new approximation algorithms for the submodular joint replenishment problem and the inventory routing problem, using an iterative rounding approach. In both problems, we are given a set of $N$ items and a discrete time horizon of…
Optimal control problems are inherently hard to solve as the optimization must be performed simultaneously with updating the underlying system. Starting from an initial guess, Howard's policy improvement algorithm separates the step of…
Trajectory generation for mobile robots in unstructured environments faces a critical dilemma: balancing kinematic smoothness for safe execution with terminal precision for fine-grained tasks. Existing generative planners often struggle…
Diffusion-based models for robotic control, including vision-language-action (VLA) and vision-action (VA) policies, have demonstrated significant capabilities. Yet their advancement is constrained by the high cost of acquiring large-scale…
Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for…
Traditional solvable optimal control theory predominantly focuses on quadratic costs due to their analytical tractability, yet they often fail to capture critical non-linearities inherent in real-world systems including water, energy,…