arXiv subjects

Keunwoo Lim

Publications and source records attributed to Keunwoo Lim.

5 recordsLinked to original sources

arXiv2026

Constrained Deep Inventory Management Using Forward-Backward SDEs

We study multi-product replenishment subject to aggregate operating limits imposed pathwise in place of expectation. On-hand and in-transit inventory, warehouse capacity and an emission allowance define a safe set, and the resulting multi-product lost-sales problem is posed as a safe stochastic optimal control problem. The Hamilton--Jacobi--Bellman (HJB) equation is represented as a system of forward--backward stochastic differential equations (FBSDEs) and solved by learning the value function and its gradient, with a quadratic program derived by control barrier function (CBF) is solved at each decision epoch. Because purchase orders enter the in-transit pipeline only, the in-transit constraints have relative degree one while the on-hand constraints have relative degree two. We extend the stochastic high-relative-degree construction of (Clark, 2021) from a single barrier to four coupled aggregate constraints of mixed relative degree, and we establish its initial-condition requirement by design.

math.OC↗

arXiv2025

A sliced Wasserstein and diffusion approach to random coefficient models

We propose a new minimum-distance estimator for linear random coefficient models. This estimator integrates the recently advanced sliced Wasserstein distance with the nearest neighbor methods, both of which enhance computational efficiency. We demonstrate that the proposed method is consistent in approximating the true distribution. Moreover, our formulation naturally leads to a diffusion process-based algorithm and is closely connected to treatment effect distribution estimation -- both of which are of independent interest and hold promise for broader applications.

math.ST↗

arXiv2024

Appropriate State-Dependent Friction Coefficient Accelerates Kinetic Langevin Dynamics

We consider the convergence of kinetic Langevin dynamics to its ergodic invariant measure, which is Gibbs distribution. Instead of the standard setup where the friction coefficient is a constant scalar, we investigate position-dependent friction coefficient and the possible accelerated convergence it enables. We show that by choosing this coefficient matrix to be $2\sqrt{\text{Hess}V}$, convergence is accelerated in the sense that no constant scalar friction coefficient can lead to faster convergence for a large subset of (nonlinear) strongly-convex potential $V$'s. The speed of convergence is quantified in terms of chi-square divergence from the target distribution, and proved using a Lyapunov approach, based on viewing sampling as optimization in the infinite dimensional space of probability distributions.

math.PR↗

arXiv2024

Cutoff Phenomenon for Cyclic Dynamics on Hypercube

The cutoff phenomena for Markovian dynamics have been observed and rigorously verified for a multitude of models, particularly for Glauber-type dynamics on spin systems. However, prior studies have barely considered irreversible chains. In this work, the cutoff phenomenon of certain cyclic dynamics are studied on the hypercube $Σ_{n} = Q^{V_{n}}$, where $Q = \{1, 2, 3\}$ and $V_{n} = \{1,...,n\}$. The main feature of these dynamics is the fact that they are represented by an irreversible Markov chain. Based on the coupling modifications suggested in a previous study of the cutoff phenomenon for the Curie-Weiss-Potts model, a comprehensive proof is presented.

math.PR↗

arXiv2024

Smoothed NPMLEs in nonparametric Poisson mixtures and beyond

We discuss nonparametric mixing distribution estimation under the Gaussian-smoothed optimal transport (GOT) distance. It is shown that a recently formulated conjecture -- that the Poisson nonparametric maximum likelihood estimator can achieve root-$n$ rate of convergence under the GOT distance -- holds up to some logarithmic terms. We also establish the same conclusion for other minimum-distance estimators, and discuss mixture models beyond the Poisson.

math.ST↗