10 accepted papers
We study the Hamiltonian flow for optimization (HF-opt), which simulates the Hamiltonian dynamics for some integration time and resets the velocity to $0$ to decrease the objective function; this is the optimization analogue of the Hamiltonian Monte Carlo algorithm for sampling. For short integratio…
In this work, we consider monotone Riemannian Variational Inequality Problems (RVIPs), which encompass both Riemannian convex optimization and minimax optimization as particular cases. In Euclidean space, the last-iterates of both the extragradient (EG) and past extragradient (PEG) methods converge…
Hamiltonian Monte Carlo (HMC) is a popular method in sampling. While there are quite a few works of studying this method on various aspects, an interesting question is how to choose its integration time to achieve acceleration. In this work, we consider accelerating the process of sampling from a di…
Quasar convexity is a condition that allows some first-order methods to efficiently minimize a function even when the optimization landscape is non-convex. Previous works develop near-optimal accelerated algorithms for minimizing this class of functions, however, they require a subroutine of binary…
Missing data problems have many manifestations across many scientific fields. A fundamental type of missing data problem arises when samples are \textit{truncated}, i.e., samples that lie in a subset of the support are not observed. Statistical estimation from truncated samples is a classical proble…
We consider a setting that a model needs to adapt to a new domain under distribution shifts, given that only unlabeled test samples from the new domain are accessible at test time. A common idea in most of the related works is constructing pseudo-labels for the unlabeled test samples and applying gr…
In this paper we study two-player bilinear zero-sum games with constrained strategy spaces. An instance of natural occurrences of such constraints is when mixed strategies are used, which correspond to a probability simplex constraint. We propose and analyze the alternating mirror descent algorithm,…
Heavy Ball (HB) nowadays is one of the most popular momentum methods in non-convex optimization. It has been widely observed that incorporating the Heavy Ball dynamic in gradient-based methods accelerates the training process of modern machine learning models. However, the progress on establishing i…
We present a family of algorithms, called descent algorithms, for optimizing convex and non-convex functions. We also introduce a new first-order algorithm, called rescaled gradient descent (RGD), and show that RGD achieves a faster convergence rate than gradient descent provided the function is str…
We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability distribution $\nu = e^{-f}$ on $\R^n$. We prove a convergence guarantee in Kullback-Leibler (KL) divergence assuming $\nu$ satisfies log-Sobolev inequality and $f$ has bounded Hessian. Notably, we do not assume convexit…