Related papers: Mirrored Langevin Dynamics
In the framework of real Hilbert spaces we study continuous in time dynamics as well as numerical algorithms for the problem of approaching the set of zeros of a single-valued monotone and continuous operator $V$. The starting poin is a…
In this paper, we study the problem of sampling from log-concave distributions supported on convex, compact sets, with a particular focus on the randomized midpoint discretization of both vanilla and kinetic Langevin diffusions in this…
In this paper, we propose a systematic approach for extending first-order optimization algorithms, originally designed for unconstrained strongly convex problems, to handle closed and convex set constraints. We show that the resulting…
This paper addresses a distributed convex optimization problem with a class of coupled constraints, which arise in a multi-agent system composed of multiple communities modeled by cliques. First, we propose a fully distributed…
In this work, we consider the problem of minimizing the sum of Moreau envelopes of given functions, which has previously appeared in the context of meta-learning and personalized federated learning. In contrast to the existing theory that…
We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…
Subspace learning and matrix factorization problems have great many applications in science and engineering, and efficient algorithms are critical as dataset sizes continue to grow. Many relevant problem formulations are non-convex, and in…
In recent years, a variety of gradient-based first-order methods have been developed to solve bi-level optimization problems for learning applications. However, theoretical guarantees of these existing approaches heavily rely on the…
In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems and…
We introduce a suite of new particle-based algorithms for sampling in constrained domains which are entirely learning rate free. Our approach leverages coin betting ideas from convex optimisation, and the viewpoint of constrained sampling…
We propose smoothed primal-dual algorithms for solving stochastic and smooth nonconvex optimization problems with linear inequality constraints. Our algorithms are single-loop and only require a single stochastic gradient based on one…
Learning-to-optimize is an emerging framework that seeks to speed up the solution of certain optimization problems by leveraging training data. Learned optimization solvers have been shown to outperform classical optimization algorithms in…
Distributed gradient descent algorithms have come to the fore in modern machine learning, especially in parallelizing the handling of large datasets that are distributed across several workers. However, scant attention has been paid to…
We present a general technique for the analysis of first-order methods. The technique relies on the construction of a duality gap for an appropriate approximation of the objective function, where the function approximation improves as the…
We consider the task of sampling with respect to a log concave probability distribution. The potential of the target distribution is assumed to be composite, \textit{i.e.}, written as the sum of a smooth convex term, and a nonsmooth convex…
In this report, we study decentralized stochastic optimization to minimize a sum of smooth and strongly convex cost functions when the functions are distributed over a directed network of nodes. In contrast to the existing work, we use…
We introduce a novel method for solving density-based topology optimization problems: Sigmoidal Mirror descent with a Projected Latent variable (SiMPL). The SiMPL method (pronounced as ``the simple method'') optimizes a design using only…
Motion planning under differential constraints is a classic problem in robotics. To date, the state of the art is represented by sampling-based techniques, with the Rapidly-exploring Random Tree algorithm as a leading example. Yet, the…
Safety is an essential requirement for reinforcement learning systems. The newly emerging framework of robust constrained Markov decision processes allows learning policies that satisfy long-term constraints while providing guarantees under…
This paper improves the state-of-the-art rate of a first-order algorithm for solving entropy regularized optimal transport. The resulting rate for approximating the optimal transport (OT) has been improved from…