arXiv research

Introduces a new divergence measure for optimal transport.

Innovative method solves nonconvex optimization on manifolds.

APO optimizes neural network parameters by amortizing proximal point methods.

In machine learning research, the proximal gradient methods are popular for solving various optimization problems with non-smooth regularization. Inexact proximal gradient methods are extremely important when exactly solving the proximal operator is time-consuming, or the proximal operator does not have an analytic sol…

Variational Proximal Policy Optimization improves reinforcement learning from human feedback.

A new method solves convex optimization problems on manifolds efficiently.

Improved bounds for proximal gradient algorithms with computational errors.

Optimal scaling for proximal MALA in high dimensions confirmed.

A new method reformulates Optimal Transport Conditional Flow Matching using proximal operators.

Optimizes convergence rate of stochastic proximal algorithms for composite convex problems.

CFR-Pro enhances treatment effect estimation by incorporating local proximity.

New method reduces variance in stochastic optimization with high confidence.

Develops a new SPP algorithm with variance reduction for weakly convex optimization.

Adaptive methods improve gradient descent and proximal gradient for convex optimization.

Improved sampling guarantees for weakly log-concave distributions.

A new method tackles nonconvex optimization with penalties and proximal terms.

Proximal algorithms applied to current deformation into cycles.

Stochastic version of proximal distance algorithm analyzed and validated.

Stochastic proximal point algorithm with momentum converges faster and is more stable than standard methods.

Deriving and applying Proximal Policy Optimization to GFlowNets for efficient training of discrete sampling policies

PDNS tackles multimodal sampling challenges using proximal point method.

Proposes a Riemannian optimization for policy improvement in MDPs.

Many machine learning techniques sacrifice convenient computational structures to gain estimation robustness and modeling flexibility. However, by exploring the modeling structures, we find these "sacrifices" do not always require more computational efforts. To shed light on such a "free-lunch" phenomenon, we study the…

Generative flows learn distributions on low-dimensional manifolds robustly via Wasserstein proximals.

In this paper, we propose a probabilistic optimization method, named probabilistic incremental proximal gradient (PIPG) method, by developing a probabilistic interpretation of the incremental proximal gradient algorithm. We explicitly model the update rules of the incremental proximal gradient method and develop a syst…

In this work, we highlight a connection between the incremental proximal method and stochastic filters. We begin by showing that the proximal operators coincide, and hence can be realized with, Bayes updates. We give the explicit form of the updates for the linear regression problem and show that there is a one-to-one …

New algorithm solves phase retrieval with adaptive stopping criteria.

Develops minibatch stochastic proximal gradient for large-scale learning models.

The need for parameter estimation with massive datasets has reinvigorated interest in stochastic optimization and iterative estimation procedures. Stochastic approximations are at the forefront of this recent development as they yield procedures that are simple, general, and fast. However, standard stochastic approxima…

We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We prove that certain decompositions lead to a theoretically optimal condition number.…

We propose a new proximal, path-following framework for a class of constrained convex problems. We consider settings where the nonlinear---and possibly non-smooth---objective part is endowed with a proximity operator, and the constraint set is equipped with a self-concordant barrier. Our approach relies on the followin…

A new optimization method, BPM, converges linearly in non-convex, non-smooth problems.

We analyze the local convergence of proximal splitting algorithms to solve optimization problems that are convex besides a rank constraint. For this, we show conditions under which the proximal operator of a function involving the rank constraint is locally identical to the proximal operator of its convex envelope, hen…

PPOS improves PPO by smoothing the surrogate objective function.

New method finds linear relationships across multiple data blocks using proximal gradient descent with $\ell_1$ constraint.

Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is an iterative scheme born from the adaptation of proximal point algorithm to nois…

Variational inference is a powerful approach for approximate posterior inference. However, it is sensitive to initialization and can be subject to poor local optima. In this paper, we develop proximity variational inference (PVI). PVI is a new method for optimizing the variational objective that constrains subsequent i…

We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a collection of proximal operators that share the same quadratic form, or if the qu…

Two new methods solve nonsmooth optimization on Riemannian Stiefel manifold.

New algorithm stabilizes RL policy learning through divergence regularization.

Inserts proximal mapping into deep networks for better regularization.

In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form solutions of proximal operators and envelope representations based on the Moreau, Fo…

Study shows tractable generalization in RL is impossible but possible with Strong Proximity.

Paper proposes a novel metric learning algorithm using Riemannian optimization.

Proximal Policy Optimization (PPO) is a highly popular model-free reinforcement learning (RL) approach. However, we observe that in a continuous action space, PPO can prematurely shrink the exploration variance, which leads to slow progress and may make the algorithm prone to getting stuck in local optima. Drawing insp…

Generative adversarial networks (GANs) represent a zero-sum game between two machine players, a generator and a discriminator, designed to learn the distribution of data. While GANs have achieved state-of-the-art performance in several benchmark learning tasks, GAN minimax optimization still poses great theoretical and…

The paper accelerates ISTA and FISTA algorithms for composite optimization problems.

We develop model-based methods for solving stochastic convex optimization problems, introducing the approximate-proximal point, or aProx, family, which includes stochastic subgradient, proximal point, and bundle methods. When the modeling approaches we propose are appropriately accurate, the methods enjoy stronger conv…