Stochastic methods tackle inexact Hessian and gradient computations in large-scale non-convex optimization.
problem Efficiently solving non-convex optimization problems with inexact Hessian and gradient computations.
method Stochastic trust region and cubic regularization methods with inexact gradient, Hessian, and function values.
result Achieves ε-approximate second-order optimality with similar iteration complexity as exact computations.
Inexact Riemannian optimization converges to stationary points efficiently.
problem Analyzing convergence and complexity of inexact Riemannian optimization.
method Tangential Block Majorization-Minimization (tBMM) framework.
result tBMM converges to an ε-stationary point within O(ε⁻²) iterations.
Proposes a method for anomaly detection with inexact labels.
problem Handling anomaly detection with inexact labels.
method Trains an anomaly score function using a neural network-based unsupervised method, maximizing the inexact AUC.
result Improves anomaly detection performance with inexact labels and outperforms existing methods.
New algorithm tackles complex optimization problems with inexact and stochastic methods.
problem Solving complex optimization problems with inexact and stochastic methods.
method Developed ICGALP algorithm for composite minimization problems with inexact computations.
result Convergence of Lagrangian to an optimum and asymptotic feasibility of the affine constraint.
Study on reproducibility in optimization with bounds on limits.
problem Limits of reproducibility in noisy or error-prone optimization procedures.
method Defined a quantitative measure of reproducibility and analyzed convex optimization settings.
result Revealed a fundamental trade-off between computation and reproducibility.
Second order Sobolev metrics are a useful tool in the shape analysis of curves. In this paper we combine these metrics with varifold-based inexact matching to explore a new strategy of computing geodesics between unparametrized curves. We describe the numerical method used for solving the inexact matching problem, appl…
New methods solve complex optimization problems in machine learning.
problem Challenges in stochastic bilevel optimization with constraints and high variables.
method Inexact bilevel stochastic gradient methods for constrained and unconstrained lower-level problems.
result Comprehensive convergence theory for both unconstrained and constrained cases.
The paper analyzes inexact variants of iterative methods for solving optimization problems.
problem Solving optimization problems with inexact sub-problems.
method Inexact variants of stochastic gradient descent, Newton, proximal point, and subspace ascent methods.
result Iteration complexity results for inexact variants of various iterative 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…
Paper shows how gradient concentration helps in learning from inexact data.
problem Learning from inexact and stochastic training data.
method Combines probabilistic gradient concentration with inexact optimization techniques.
result Derives sharp test error guarantees for learning.
New characterization limits sampling with inexact scores.
problem Limiting sampling with inexact scores for unbiased results.
method Characterized types of inexact score oracle access.
result Weaker error assumptions rule out tractability of unbiased sampling.
Develops accelerated fixed-point methods with delayed oracles for scientific computing.
problem Approximating fixed points of nonexpansive operators.
method Combines Nesterov's acceleration and KM iteration with delayed inexact oracles.
result Establishes improved convergence rates for fixed-point approximation.
Study optimizes decisions in real-time using inexact simulation solutions.
problem Real-time decision-making in simulation optimization with inexact solutions.
method Optimize then predict (OTP) approach, analyzing bias and variance in simulation-optimization algorithms.
result Unified analysis framework for OTP, establishing convergence rates and optimal allocation of computational budget.
Proposes a stochastic method for solving trilevel optimization problems.
problem Efficient and theoretically sound methods for trilevel optimization.
method Stochastic gradient descent method for unconstrained trilevel optimization.
result First convergence theory for stochastic methods in trilevel optimization.
New algorithm extends LMC to more complex potentials.
problem Addressing limitations of existing LMC methods.
method Inexact Proximal Langevin Algorithm (IPLA).
result Improved convergence rates and broader applicability.
Proposes STRON method for large-scale machine learning problems.
problem Large-scale machine learning problems.
method Stochastic Trust Region Inexact Newton (STRON) method using CG to solve trust region subproblem with progressive subsampling.
result Empirical results show efficacy of STRON method.
In this paper we consider the problem of minimizing a convex function using a randomized block coordinate descent method. One of the key steps at each iteration of the algorithm is determining the update to a block of variables. Existing algorithms assume that in order to compute the update, a particular subproblem is …
Inexact acquisition solutions in BO lead to sublinear cumulative regret.
problem Inexact maximization of acquisition functions in Bayesian optimization.
method Define inaccuracy measure, establish cumulative regret bounds for GP-UCB and GP-TS.
result Inexact BO algorithms can achieve sublinear cumulative regret under appropriate inaccuracy conditions.
Develops methods for spectral estimation and rare-event prediction in complex systems.
problem Challenges in understanding dynamics in complex systems with many degrees of freedom.
method Inexact iterative numerical linear algebra methods for spectral estimation and rare-event prediction.
result Demonstrates methods on low-dimensional and high-dimensional models, showing their effectiveness.
This paper analyzes the bias of inexact MCMC methods in high dimensions.
problem Understanding the bias of inexact MCMC methods in high-dimensional spaces.
method Establishing bounds on Wasserstein distances between inexact MCMC methods and target distributions.
result The asymptotic bias of ULA and uHMC depends on key quantities related to the target distribution or the stationary probability measure of the scheme.
Paper tackles BNSL with IP, improving quality of solutions.
problem Bayesian Network Structure Learning (BNSL) with IP formulations.
method Inexact column generation using difference-of-submodular optimization.
result Improved solutions quality compared to state-of-the-art approaches.
New method solves complex constrained optimization problems.
problem Constrained nonconvex-nonconcave minimax optimization problems.
method Inexact proximal gradient method using sequential convex programming.
result Established complexity guarantees for approximate stationary points.
Evolutionary forms, as well as exterior forms, are skew-symmetric differential forms. But in contrast to the exterior forms, the basis of evolutionary forms is deforming manifolds (with unclosed metric forms). Such forms possess a peculiarity, namely, the closed inexact exterior forms are obtained from that. The closur…
We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing system has access to a local empirical loss function, constructed with i.i.d. data sa…
Accelerates stochastic optimization for convex and strongly convex problems.
problem Improving convergence rates in noisy stochastic optimization.
method Extends Catalyst approach to stochastic settings, handles inexact proximal operators.
result Achieves optimal worst-case complexity for noise-dominated regions.
New method tackles inexact bilevel optimization for faster parameter learning.
problem Nested optimization problems in bilevel learning with computationally difficult exact solutions.
method Inexact derivative-free optimization algorithms for approximate lower-level solutions.
result Global convergence and worst-case complexity for the proposed approach.
New algorithm solves phase retrieval with adaptive stopping criteria.
problem Robust phase retrieval problem as nonsmooth, nonconvex optimization.
method Inexact proximal linear algorithm with adaptive stopping criteria.
result Proposed methods are more efficient than existing methods.
Unbiased method for Bayesian posterior means using kinetic Langevin dynamics.
problem Estimating Bayesian posterior means efficiently and accurately.
method Combines advanced splitting methods with enhanced gradient approximations in a multilevel Monte Carlo approach.
result The method achieves unbiased estimates with finite variance and central limit theorem properties.
Optimizes solving complex min-max problems with stochastic and nonconvex elements.
problem Min-max problems with stochastic and nonconvex elements.
method Combines conic nonexpansiveness, refined inexact Halpern iteration, and multilevel Monte Carlo estimator.
result Optimal or best-known complexity guarantees for $ρ< rac{1}{L}$, improving previous results.
We propose novel first-order stochastic approximation algorithms for canonical correlation analysis (CCA). Algorithms presented are instances of inexact matrix stochastic gradient (MSG) and inexact matrix exponentiated gradient (MEG), and achieve ε-suboptimality in the population objective in $\operatorname{poly}(\fr…
We analyze the performance of alternating minimization for loss functions optimized over two variables, where each variable may be restricted to lie in some potentially nonconvex constraint set. This type of setting arises naturally in high-dimensional statistics and signal processing, where the variables often reflect…
Paper proposes iLPA for solving DC composite optimization problems, with applications to matrix completion with outliers.
problem Solving nonconvex and nonsmooth DC composite optimization problems.
method Inexact linearized proximal algorithm (iLPA) for DC composite optimization problems.
result The iLPA achieves local R-linear convergence rate under the Kurdyka-Łöjasiewicz property.
In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties of this method, both in the exact and inexact setting, in the case when the obje…
New method tackles nonconvex-nonconcave problems with local KL condition.
problem Nonconvex-nonconcave minimax problems under varying KL conditions.
method Inexact proximal gradient method for KL-structured subproblems.
result Complexity guarantees for approximate stationary points.
Exact minibatch MH method improves scalability for large datasets.
problem Inexactness in minibatch MH methods causes inference errors.
method TunaMH proposes an exact minibatch MH method with a tunable batch size.
result TunaMH is asymptotically optimal in terms of batch size.
In this paper, we consider the convergence of an abstract inexact nonconvex and nonsmooth algorithm. We promise a pseudo sufficient descent condition and a pseudo relative error condition, which are both related to an auxiliary sequence, for the algorithm; and a continuity condition is assumed to hold. In fact, a lot o…
The paper studies the solution of stochastic optimization problems in which approximations to the gradient and Hessian are obtained through subsampling. We first consider Newton-like methods that employ these approximations and discuss how to coordinate the accuracy in the gradient and Hessian to yield a superlinear ra…
In kernel methods, the kernels are often required to be positive definite, which restricts the use of many indefinite kernels. To consider those non-positive definite kernels, in this paper, we aim to build an indefinite kernel learning framework for kernel logistic regression. The proposed indefinite kernel logistic r…
Distributed algorithms are often beset by the straggler effect, where the slowest compute nodes in the system dictate the overall running time. Coding-theoretic techniques have been recently proposed to mitigate stragglers via algorithmic redundancy. Prior work in coded computation and gradient coding has mainly focuse…
Improved analysis for fair federated learning reduces dependence on noise floor.
problem Asymptotic stationarity in group fair federated learning with reduced noise floor dependence.
method DS FedProxGrad framework with inexact local proximal solutions and fairness regularization.
result Algorithm converges asymptotically to stationarity without dependence on a noise floor.
Inexact subgradient methods work well for semialgebraic functions with additive errors.
problem Approximate gradients in machine learning and optimization.
method Inexact subgradient methods with persistent additive errors in semialgebraic functions.
result Iterates eventually fluctuate near the critical set with a proximity of O(ερ), where ε is the magnitude of subgradient evaluation errors. ERNN improves RNN accuracy and stability with time-delayed self-feedback.
problem Inaccuracy and instability in RNNs.
method Augmenting RNN with a time-delayed self-feedback loop to stabilize hidden state transitions.
result ERNN achieves state-of-the-art results on benchmark datasets.
New algorithm for computing Wasserstein barycenters with guarantees.
problem Computing Wasserstein barycenters with varying regularization strengths.
method Damped Sinkhorn iterations followed by exact maximization/minimization steps.
result First non-asymptotic convergence guarantees for approximating Wasserstein barycenters.
IRCUR accelerates RPCA by using CUR decomposition for efficient low rank estimation.
problem Dimension reduction in robust principal component analysis.
method IRCUR employs CUR decomposition to update the low rank component efficiently.
result IRCUR achieves significant computational efficiency compared to existing algorithms.
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 propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic variance-reduced gradient descent algorithm (SVRG) and other randomized incremental opti…
To improve the efficiency of Monte Carlo estimation, practitioners are turning to biased Markov chain Monte Carlo procedures that trade off asymptotic exactness for computational speed. The reasoning is sound: a reduction in variance due to more rapid sampling can outweigh the bias introduced. However, the inexactness …
We consider variants of trust-region and cubic regularization methods for non-convex optimization, in which the Hessian matrix is approximated. Under mild conditions on the inexact Hessian, and using approximate solution of the corresponding sub-problems, we provide iteration complexity to achieve ε-approximate seco…