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Recent advancements in diffusion models and diffusion bridges primarily focus on finite-dimensional spaces, yet many real-world problems necessitate operations in infinite-dimensional function spaces for more natural and interpretable…
The Feynman path integral formalism has inspired the development of memory-efficient and parallelizable classical algorithms for simulating quantum computers. We adapt this approach for the calculation of probability amplitudes of…
Stochastic Optimal Control (SOC) problems arise in systems influenced by uncertainty, such as autonomous robots or financial models. Traditional methods like dynamic programming are often intractable for high-dimensional, nonlinear systems…
The Schr\"odinger bridge problem (SBP) is gaining increasing attention in generative modeling and showing promising potential even in comparison with the score-based generative models (SGMs). SBP can be interpreted as an entropy-regularized…
The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and the regularization of density paths (potential energy). These combinations yield different…
This paper deals with an optimization problem over a network of agents, where the cost function is the sum of the individual objectives of the agents and the constraint set is the intersection of local constraints. Most existing methods…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…
Expectations of path integrals of killed stochastic processes play a central role in several applications across physics, chemistry, and finance. Simulation-based evaluation of these functionals is often biased and numerically expensive due…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. This imperfect communication poses a fundamental…
Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore…
Sparse dictionary learning is a popular method for representing signals as linear combinations of a few elements from a dictionary that is learned from the data. In the classical setting, signals are represented as vectors and the…
We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…
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 study generative modeling for time series using entropic optimal transport and the Schr\"odinger bridge (SB) framework, with a focus on applications in finance and energy modeling. Extending the diffusion-based approach of Hamdouche,…
We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…
Path-integral techniques are a powerful tool used in open quantum systems to provide an exact solution for the non-Markovian dynamics. However, the exponential scaling of the tensor size with quantum memory length of these techniques limits…
In this paper, we describe a new method to compute the minimum of a real polynomial function and the ideal defining the points which minimize this polynomial function, assuming that the minimizer ideal is zero-dimensional. Our method is a…
We propose an algorithm to approximate solutions of global optimization problems in Sobolev spaces that follows the spirit of Consensus-based algorithms in finite dimensions. The main ingredient are Gaussian processes. In fact, we exploit…
We reformulate a class of non-linear stochastic optimal control problems introduced by Todorov (2007) as a Kullback-Leibler (KL) minimization problem. As a result, the optimal control computation reduces to an inference computation and…