The paper connects a proximal method to stochastic filters and Bayes updates.
problem Large-scale optimization and probabilistic methods for regression.
method Explicit form of Bayes updates for linear regression and general sequential setting.
result The incremental proximal method can be realized by the Kalman filter for linear-quadratic cost functions.
Proposes a probabilistic optimization method for large-scale problems.
problem Large-scale regularized optimization problems.
method Develops a probabilistic interpretation of the incremental proximal gradient algorithm and uses Bayesian filtering.
result Makes it possible to solve large-scale problems using well-known Bayesian filters.
New method accelerates optimization for nonconvex problems in statistics.
problem Nonconvex optimization problems in statistics and machine learning.
method Adaptive momentum and block coordinate proximal gradient method with specific update rules.
result The method achieves provable local linear convergence in sparse linear regression problems.
Proposes variational Gaussian approximations for solving the Kushner equation.
problem Solving the Kushner equation for state estimation with observations.
method Tractable variational Gaussian approximations of proximal losses based on Wasserstein and Fisher metrics.
result The proposed method leads to a Gaussian flow consistent with Kalman-Bucy and Riccati flows.
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…
Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are statistically inefficient as estimators of the true parameter value. To address these tw…
LPOM approximates neural nets with proximal operators for efficient training.
problem Training feed-forward neural networks efficiently and avoiding gradient issues.
method Rewriting activation functions as proximal operators, using block coordinate descent.
result LPOM converges and performs well on MNIST and CIFAR-10.
PPOS improves PPO by smoothing the surrogate objective function.
problem Performance instability and optimization inefficiency in PPO.
method Use of a functional clipping method instead of a flat clipping method.
result PPOS conducts more accurate updates and outperforms other PPO variants.
SPU improves deep RL efficiency by optimizing non-parametric policies.
problem Improving sample efficiency in deep reinforcement learning.
method Formulates and solves a constrained optimization problem in non-parameterized space, converts to parameterized policy using supervised regression.
result SPU outperforms TRPO and PPO in various tasks.
AsyB-ProxSGD parallelizes model updates and stochastic gradient descent for large models and data.
problem Efficiently training large models and handling large datasets in parallel.
method AsyB-ProxSGD: model parallel proximal stochastic gradient algorithm for asynchronous systems.
result Achieves linear speedup with O(K1/4) number of workers for nonconvex problems. Develops a new SPP algorithm with variance reduction for weakly convex optimization.
problem Weakly convex, composite optimization problems.
method Inexact semismooth Newton framework with variance reduction for stochastic proximal point updates.
result Establishes convergence results for the proposed algorithm.
We make policy optimization algorithms batch size-invariant by decoupling proximal and behavior policies.
problem Some policy optimization algorithms do not have batch size-invariance, leading to inefficiencies.
method We decouple the proximal policy from the behavior policy to achieve batch size-invariance.
result Our approach makes policy optimization algorithms more efficient and allows them to use stale data more effectively.
NASP uses proximal gradient descent to speed up neural architecture search.
problem Efficiently search for high-performance neural architectures.
method Differentiable Neural Architecture Search using Proximal gradient descent.
result NASP achieves 10 times speedup over DARTS while maintaining high performance.
Stochastic version of proximal distance algorithm analyzed and validated.
problem Optimization of constrained estimation problems.
method Stochastic proximal distance algorithm, with convergence guarantees and finite error bounds.
result Convergence guarantees and finite error bounds for the first time.
Improved greedy 2-coordinate updates for optimization problems with constraints.
problem Minimizing smooth functions subject to constraints.
method Exploiting a connection to steepest descent in the 1-norm, we give faster convergence rates and efficient computation.
result Greedy selection converges faster than random selection and can be computed in O(nlogn) time. DE-PSGLD samples from constrained distributions in a decentralized manner.
problem Sampling from log-concave distributions with constraints.
method Decentralized Proximal Stochastic Gradient Langevin Dynamics with proximal regularization.
result DE-PSGLD converges to a regularized Gibbs distribution and maintains posterior concentration.
Unified framework for training neural networks with non-smooth, non-convex regularizers.
problem Training neural networks with non-smooth, non-convex regularizers.
method ProxGen framework for stochastic proximal gradient descent.
result ProxGen framework achieves the same convergence rate as standard methods and outperforms subgradient-based approaches.
A new method tackles nonconvex optimization with penalties and proximal terms.
problem Nonconvex optimization problems with equality and inequality constraints.
method Inexact proximal augmented Lagrangian method (P-ALM) with adaptive penalty and proximal parameters.
result Effective convergence properties and numerical superiority over traditional methods.
A new PGA algorithm ensures stable, robust, and noise-immune solutions for non-negative inverse problems.
problem Stable convergence and suboptimal solutions in inverse problems due to negative values and high sensitivity to hyperparameters.
method A novel multiplicative update proximal gradient algorithm (SSO-PGA) that enforces non-negativity and boundedness through a learnable sigmoid-based operator.
result Significantly surpasses traditional PGA and other state-of-the-art algorithms in performance and stability.
Unified view connects CoCoA and ADMM for distributed ERM.
problem Connection between CoCoA and ADMM for distributed ERM.
method Unified primal-dual perspective reformulation.
result Unified ADMM variants perform at least as good as CoCoA in ridge-regularized ERM.
In this paper we propose a randomized primal-dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints. Assuming mere convexity, we establish its O(1/t) convergence rate in terms of the objective value and feasibility m…
Paper proposes a new method to optimize robot body structure and control policy.
problem Optimizing robot body structure and control policy in a coupled manner.
method Revisits co-design problem as a Stackelberg game, incorporating control adaptation dynamics.
result Stackelberg PPO outperforms standard PPO in stability and performance.
Unified Lagrangian-based methods for nonsmooth nonconvex optimization.
problem Minimizing nonsmooth nonconvex functions with constraints.
method Developed a unified framework for Lagrangian-based methods using subgradient updates.
result Global convergence guarantees for the proposed framework under mild conditions.
APO optimizes neural network parameters by amortizing proximal point methods.
problem Optimizing neural network parameters online and adaptively.
method APO framework that meta-learns proximal point parameters.
result APO can recover and outperform existing optimizers and schedules.
The study analyzes methods for solving non-convex, non-smooth optimization problems.
problem Finding critical points of non-convex and non-smooth functions.
method Gradient descent, proximal update, Frank-Wolfe update methods for general and continuous sub-analytic functions.
result Established rates of convergence and faster rates for specific function classes.
One-bit proximal method speeds up nonconvex stochastic optimization.
problem Reducing communication in distributed SGD for large datasets.
method Stochastic proximal gradient method using one-bit per update.
result The method achieves convergence rates similar to uncompressed SGD.
Proposes a semi-implicit back propagation method for neural networks.
problem Challenges in training neural networks, especially gradient vanishing and small step sizes.
method Proposes a semi-implicit back propagation method using error back propagation and proximal methods.
result The proposed method leads to better performance in terms of loss decreasing and training/validation accuracy compared to SGD and ProxBP.
Randomized SINDy learns dynamic data structures using probabilistic methods.
problem Learning time-dependent data structures in dynamic systems.
method Sequential machine learning with a probabilistic approach, incorporating feature augmentation and Tikhonov regularization.
result Demonstrated effectiveness in regression and binary classification using real-world data.
ITSPACE improves covariance alignment faster than other methods.
problem Optimizing covariance matrices for machine learning tasks.
method Proximal majorization-minimization method that directly optimizes the Bures-Wasserstein objective.
result ITSPACE achieves lower BW gap solutions faster than other methods.
A new adaptive clipping method improves PPO's performance in reinforcement learning.
problem Inefficient policy updates in PPO leading to poor performance.
method Adaptive clipping mechanism in PPO-λ algorithm. result PPO-λ achieves better performance than PPO on various tasks. Paper introduces a new policy optimization method using importance sampling.
problem Stable and low variance policy learning with small policy updates.
method Derives an alternative objective using importance sampling and introduces an approximation to balance bias and variance.
result The new algorithm improves on-policy policy optimization on continuous control benchmarks.
We present a distributed proximal-gradient method for optimizing the average of convex functions, each of which is the private local objective of an agent in a network with time-varying topology. The local objectives have distinct differentiable components, but they share a common nondifferentiable component, which has…
Consider the stochastic composition optimization problem where the objective is a composition of two expected-value functions. We propose a new stochastic first-order method, namely the accelerated stochastic compositional proximal gradient (ASC-PG) method, which updates based on queries to the sampling oracle using tw…
New algorithm accelerates single-pass SGD for generalized linear prediction.
problem Improving single-pass non-quadratic stochastic optimization.
method Data-dependent proximal method incorporating dual-momentum acceleration.
result Momentum acceleration resolves open problem in streaming setting.
The L1-regularized models are widely used for sparse regression or classification tasks. In this paper, we propose the orthant-wise passive descent algorithm (OPDA) for optimizing L1-regularized models, as an improved substitute of proximal algorithms, which are the standard tools for optimizing the models nowada…
Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning. In theory, under certain conditions, this problem can be solved in polynomial time via a natural convex relaxation, known as Compressive …
Revisits PPO design choices, exposing failure modes and proposing alternatives.
problem Failure modes of standard PPO in new environments.
method Revisits standard PPO design choices, exposes failure modes, and proposes alternative approaches.
result Alternative design choices prevent failure modes in new environments.
Paper finds a fast method for a matrix norm proximal operator.
problem Optimizing mixed ℓ1,∞ matrix norms efficiently. method Closed-form computation using soft-thresholding, iterative algorithm for thresholds.
result Mixed ℓ1,∞ prox can be computed in closed form. New method optimizes hyperparameters for non-smooth problems efficiently.
problem Efficiently tuning hyperparameters for non-smooth cost functions.
method Combines hyperparameter search with proximal gradient updates.
result Method converges to local optimum of LOO validation error.
This work optimizes bid strategies for online auctions using measure-valued optimization.
problem Optimizing bid strategies in first-price auctions to maximize expected surplus.
method Formulates the problem as convex optimization over the joint distribution of shading parameters, adapts the distribution after each auction using a Wasserstein-proximal update.
result The proposed algorithm encourages bids on values with high expected surplus.
AutoAnchor uses cross-attention to improve text-to-image model unlearning.
problem Mitigating harmful or copyrighted content in text-to-image models.
method Two-stage framework that automatically synthesizes manifold-proximal anchors using cross-attention consistency loss.
result Effective robust and unbiased unlearning across various baselines.
A new method for RLHF using proximal point Nash learning.
problem Capturing real human preferences in RLHF.
method Proximal point Nash learning, embedding self-play updates into a proximal point framework.
result High-probability last-iterate convergence for the combined method.
New method improves matrix factorization speed and accuracy.
problem Matrix factorization optimization problems suffer from biased solutions and lack of convergence guarantees.
method Proposes a novel Bregman distance for matrix factorization, enabling non-alternating schemes with convergence proof.
result Convergence to a stationary point proved for matrix factorization problems.
AGS-CL selectively updates penalties based on node importance for continual learning.
problem Catastrophic forgetting in continual learning.
method Adaptive Group Sparsity (AGS) with proximal gradient descent.
result Significantly outperforms baselines on various continual learning benchmarks.
Paper proposes distributed optimization for federated learning with theoretical guarantees.
problem Privacy-preserving cross-organizational data collaboration in machine learning.
method Augmented Lagrangian technique for diverse communication topologies, termination criteria, and parameter update mechanisms.
result The proposed framework recovers classical optimization methods and provides strong performance in large-scale federated learning.
In many learning tasks, structural models usually lead to better interpretability and higher generalization performance. In recent years, however, the simple structural models such as lasso are frequently proved to be insufficient. Accordingly, there has been a lot of work on "superposition-structured" models where mul…
Estimates MoE models with feature selection for high-dimensional data.
problem Estimation and feature selection in Mixtures-of-Experts models with high-dimensional predictors.
method Regularized maximum likelihood estimation with proximal-Newton EM algorithm.
result Good performance in recovering sparse solutions, parameter estimation, and clustering of heterogeneous data.
The paper addresses nonconvex penalized LAD estimation in partial linear models using DNNs.
problem Challenges in nonconvex penalized LAD estimation with DNNs in partial linear models.
method Parameterizes nonparametric term with DNNs, formulates penalized LAD problem, introduces proximal subgradient method.
result Establishes consistency, convergence rate, and asymptotic normality of the estimator.