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Variable division and optimization (D\&O) is a frequently utilized algorithm design paradigm in Evolutionary Algorithms (EAs). A D\&O EA divides a variable into partial variables and then optimize them respectively. A complicated problem is…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N coupled stochastic variables with the Dirichlet distribution as its asymptotic solution. To ensure a bounded…
Motivated by distributed statistical learning over uncertain communication networks, we study distributed stochastic optimization by networked nodes to cooperatively minimize a sum of convex cost functions. The network is modeled by a…
We consider the setting of multiscale overdamped Langevin stochastic differential equations, and study the problem of learning the drift function of the homogenized dynamics from continuous-time observations of the multiscale system. We…
We introduce a novel alignment method for diffusion models from distribution optimization perspectives while providing rigorous convergence guarantees. We first formulate the problem as a generic regularized loss minimization over…
We introduce a scheme for deriving an optimally-parametrised Langevin dynamics of few collective variables from data generated in molecular dynamics simulations. The drift and the position-dependent diffusion profiles governing the Langevin…
Of stochastic differential equations, diffusion processes have been adopted in numerous applications, as more relevant and flexible models. This paper studies diffusion processes in a different setting, where for a given stationary…
Aligning text-to-image (T2I) diffusion models with human preferences has emerged as a critical research challenge. While recent advances in this area have extended preference optimization techniques from large language models (LLMs) to the…
Guaranteeing real-time and accurate object detection simultaneously is paramount in autonomous driving environments. However, the existing object detection neural network systems are characterized by a tradeoff between computation time and…
In this paper, a deep reinforcement learning (DRL)-based approach to the Lyapunov optimization is considered to minimize the time-average penalty while maintaining queue stability. A proper construction of state and action spaces is…
We consider stochastic control with discretionary stopping for the drift of a diffusion process over an infinite time horizon. The objective is to choose a control process and a stopping time to minimize the expectation of a convex terminal…
New one-leg multistep time discretizations of nonlinear evolution equations are investigated. The main features of the scheme are the preservation of the nonnegativity and the entropy-dissipation structure of the diffusive equations. The…
The diffusion model has shown success in generating high-quality and diverse solutions to trajectory optimization problems. However, diffusion models with neural networks inevitably make prediction errors, which leads to constraint…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
We study a stochastic program where the probability distribution of the uncertain problem parameters is unknown and only indirectly observed via finitely many correlated samples generated by an unknown Markov chain with $d$ states. We…
Linear Parameter-Varying (LPV) systems with jumps and piecewise differentiable parameters is a class of hybrid LPV systems for which no tailored stability analysis and stabilization conditions have been obtained so far. We fill this gap…
Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the…
This paper studies Distributionally Robust Optimization (DRO), a fundamental framework for enhancing the robustness and generalization of statistical learning and optimization. An effective ambiguity set for DRO must involve distributions…
We consider the method of Reduction of Dissipativity Domain to prove global Lyapunov stability of Discrete Time Recurrent Neural Networks. The standard and advanced criteria for Absolute Stability of these essentially nonlinear systems…