Related papers: From Sampling to Optimization on Discrete Domains …
In this paper, we provide a family of dynamic programming based algorithms to sample nearly-shortest self avoiding walks between two points of the integer lattice $\mathbb{Z}^2$. We show that if the shortest path of between two points has…
Devising mechanisms with good beyond-worst-case input-dependent performance has been an important focus of differential privacy, with techniques such as smooth sensitivity, propose-test-release, or inverse sensitivity mechanism being…
Community detection is one of the fundamental problems of network analysis, for which a number of methods have been proposed. Most model-based or criteria-based methods have to solve an optimization problem over a discrete set of labels to…
Set packing is a fundamental problem that generalises some well-known combinatorial optimization problems and knows a lot of applications. It is equivalent to hypergraph matching and it is strongly related to the maximum independent set…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
Most current sampling algorithms for high-dimensional distributions are based on MCMC techniques and are approximate in the sense that they are valid only asymptotically. Rejection sampling, on the other hand, produces valid samples, but is…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
Two complementary techniques for analyzing search spaces are proposed: (i) an algorithm to detect search points with potential to be local optima; and (ii) a slightly adjusted Wang-Landau sampling algorithm to explore larger search spaces.…
We consider the minimax estimation problem of a discrete distribution with support size $k$ under privacy constraints. A privatization scheme is applied to each raw sample independently, and we need to estimate the distribution of the raw…
The sampling problem under local differential privacy has recently been studied with potential applications to generative models, but a fundamental analysis of its privacy-utility trade-off (PUT) remains incomplete. In this work, we define…
The non-smooth finite-sum minimization is a fundamental problem in machine learning. This paper develops a distributed stochastic proximal-gradient algorithm with random reshuffling to solve the finite-sum minimization over time-varying…
This work focuses on off-policy evaluation (OPE) with function approximation in infinite-horizon undiscounted Markov decision processes (MDPs). For MDPs that are ergodic and linear (i.e. where rewards and dynamics are linear in some known…
Non-negative matrix factorization (NMF) is a key technique for feature extraction and widely used in source separation. However, existing algorithms may converge to poor local minima, or to one of several minima with similar objective value…
We consider the problem of inference in discrete probabilistic models, that is, distributions over subsets of a finite ground set. These encompass a range of well-known models in machine learning, such as determinantal point processes and…
Sampling from constrained distributions has a wide range of applications, including in Bayesian optimization and robotics. Prior work establishes convergence and feasibility guarantees for constrained sampling, but assumes that the feasible…
We study differentially private (DP) algorithms for stochastic convex optimization: the problem of minimizing the population loss given i.i.d. samples from a distribution over convex loss functions. A recent work of Bassily et al. (2019)…
In this paper, we showcase the interplay between discrete and continuous optimization in network-structured settings. We propose the first fully decentralized optimization method for a wide class of non-convex objective functions that…
Given a directed graph $G$ on $n$ vertices with a special vertex $s$, the directed minimum degree spanning tree problem requires computing a incoming spanning tree rooted at $s$ whose maximum tree in-degree is the smallest among all such…
The denoising diffusion probabilistic model (DDPM) has emerged as a mainstream generative model in generative AI. While sharp convergence guarantees have been established for the DDPM, the iteration complexity is, in general, proportional…