Study optimizes sampling to avoid extreme tail risks in unknown heavy-tailed distributions.
problem Identify optimal alternative with minimal extreme tail risk from unknown heavy-tailed distributions.
method Data-driven sequential sampling policies to maximize likelihood of selecting the optimal alternative.
result Proposed methods outperform existing approaches in identifying the optimal alternative.
AutoLoss learns optimal schedules for alternating optimization tasks.
problem Optimizing different task objectives with alternating updates.
method Meta-learning framework to learn and determine the optimization schedule.
result AutoLoss improves convergence quality on multiple ML tasks.
Optimized concentric helices minimize the ropelength of non-alternating torus knots.
problem Optimizing the ropelength of non-alternating torus knots.
method Optimized geometry and combinatorics of concentric helices.
result Optimized ropelength of concentric helices is approximately 7.83Q^(3/2).
Alternative proof of Michael-Simon-Sobolev inequality using optimal transport.
problem Proving the Michael-Simon-Sobolev inequality for submanifolds of codimension 2.
method Optimal transport techniques.
result Sharpness of the inequality for submanifolds of codimension 2.
Investigates optimal consumption and investment using alternative data sources.
problem Optimal consumption and investment decisions under hidden economic regimes.
method Develops a novel duality theory for a jump-diffusion process with alternative data.
result Provides conditions for using control approach based on dynamic programming.
We propose a method for finding alternate features missing in the Lasso optimal solution. In ordinary Lasso problem, one global optimum is obtained and the resulting features are interpreted as task-relevant features. However, this can overlook possibly relevant features not selected by the Lasso. With the proposed met…
Alt-GDA outperforms Sim-GDA in minimax games with near-optimal local convergence.
problem Minimax optimization convergence rate comparison
method Alternating Gradient Descent-Ascent (Alt-GDA) vs. Simultaneous Gradient Descent-Ascent (Sim-GDA)
result Alt-GDA achieves near-optimal local convergence rate for strongly convex-strongly concave problems, while Sim-GDA converges slower.
Gaussian kernel tests are optimal against smooth alternatives.
problem Understanding the statistical properties of nonparametric tests using Gaussian kernels.
method Analysis of Gaussian kernel-based goodness-of-fit, homogeneity, and independence tests.
result Gaussian kernel tests are minimax optimal against smooth alternatives in all three settings.
A meta-learning approach improves the performance of alternating minimization for non-convex optimization problems.
problem Optimizing non-convex problems with multiple variables using alternating minimization.
method Meta-learning based alternating minimization (MLAM) to replace handcrafted updating rules.
result The proposed MLAM method outperforms traditional AM-based methods in various non-convex optimization problems.
TSSM splits neural networks for parallel training with minimal accuracy loss.
problem Accuracy degradation in parallel training of deep neural networks.
method TSSM reformulates alternating minimization to achieve parallelism with minimal accuracy loss.
result TSSM achieves significant speedup without accuracy loss on multiple datasets.
Alternative method improves SVM for data classification.
problem SVM's weaknesses in time processing, optimization, multi-class generalization, and unbalanced classes.
method Minimum distance to optimal subspaces containing mapped classes.
result Improved performance with fewer shortcomings.
Alternative optimizer outperforms gradient descent in weakly-supervised CNN segmentation.
problem Training deep neural networks with complex loss functions.
method Demonstrated an alternative optimizer (ADM) outperforming gradient descent.
result Gradient descent performs poorly with certain loss functions, while an alternative optimizer achieves state-of-the-art results.
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.
Stochastic algorithm achieves sublinear convergence for bi-objective optimization.
problem Optimizing two conflicting functions using gradient or subgradient descent.
method Stochastic alternating algorithm with varying steps for each objective.
result Achieves sublinear convergence rate of O(1/T) under strong convexity.
Proposes an efficient alternative to nonconvex-nonconcave min-max optimization.
problem Min-max optimization challenges in nonconvex-nonconcave settings.
method Introduces ε-greedy adversarial equilibrium model and proves its existence.
result Existence of ε-greedy adversarial equilibrium for smooth bounded functions.
Flexible framework for CMTF with ADMM for various constraints and couplings.
problem Challenges in data fusion from multiple sources with varying characteristics.
method Flexible algorithmic framework using AO and ADMM for various constraints, loss functions, and couplings.
result Accurate and computationally efficient results for various loss functions, including KL divergence.
The use of alternative measures to evaluate classifier performance is gaining attention, specially for imbalanced problems. However, the use of these measures in the classifier design process is still unsolved. In this work we propose a classifier designed specifically to optimize one of these alternative measures, nam…
Study shows a linear quadratic regulator's imitation learning converges globally.
problem Global convergence of imitation learning for linear quadratic regulators.
method Analyzed alternating gradient algorithm and established Q-linear rate of convergence.
result Established a unique saddle point for globally optimal policy and reward function.
Chirality affects the curvature of molecular networks, influencing their shape and stability.
problem Understanding how chirality influences the curvature of molecular networks.
method Langevin dynamics simulations and constrained gradient optimization of square lattice networks.
result Linking chirality dictates the sign of Gaussian curvature in molecular chainmail networks.
New algorithm improves convergence rates for convex optimization problems.
problem Convex optimization problems with noisy stochastic data.
method Stochastic proximal point algorithm with weak linear regularity condition.
result Achieves $\mathcal{O}\left(\frac{1}{k}
ight)$ convergence rate for SPP.
Introduces a new geometric method for optimal experimental design.
problem Restrictive invariance properties of traditional OED approaches based on probability densities.
method Mutual transport dependence (MTD) using optimal transport theory.
result Demonstrates high-quality designs and flexibility compared to standard methods.
Paper proposes an algorithm for PARAFAC2-based CMTF models with various constraints.
problem Jointly analyze matrices and tensors with irregular/ragged data.
method Alternating Optimization (AO) and ADMM for fitting PARAFAC2-based CMTF models with various constraints.
result Accurately recovers underlying patterns using various constraints and linear couplings.
Games generalize the single-objective optimization paradigm by introducing different objective functions for different players. Differentiable games often proceed by simultaneous or alternating gradient updates. In machine learning, games are gaining new importance through formulations like generative adversarial netwo…
This paper presents a model to describe contractual dispute resolution by mediation in situations where a defaulting supplier is near insolvent. While each party has internal constraints, and if alternate performances are available, such as more costly alternative goods, the proposed approach allows the mediator to fin…
Chandrasekaran, Parrilo and Willsky (2010) proposed a convex optimization problem to characterize graphical model selection in the presence of unobserved variables. This convex optimization problem aims to estimate an inverse covariance matrix that can be decomposed into a sparse matrix minus a low-rank matrix from sam…
Paper formulates mutual information optimal control for discrete-time systems.
problem Optimal control of discrete-time linear systems with mutual information.
method Formulates MIOCP as an extension of MEOCP, derives optimal policy and prior, proposes alternating minimization algorithm.
result Proposes an alternating minimization algorithm for MIOCP.
Paper develops efficient AltMin algorithm for SRPCP robust matrix recovery.
problem SRPCP model robust matrix recovery with universal penalty parameter.
method Tuning-free alternating minimization (AltMin) algorithm with closed-form subproblems.
result Efficient AltMin algorithm confirms robustness and efficiency.
Quasi-alternating links of determinant 1, 2, 3, and 5 were previously classified by Greene and Teragaito, who showed that the only such links are two-bridge. In this paper, we extend this result by showing that all quasi-alternating links of determinant at most 7 are connected sums of two-bridge links, which is optimal…
Paper tackles risk-sensitive decision-making under uncertainty.
problem Risk-sensitive decision-making problem under uncertainty.
method Formulated as a stochastic control problem, delineated necessary optimality conditions.
result Illustrative examples from optimal betting and inventory management support the theory.
We present an objective function for learning with unlabeled data that utilizes auxiliary expectation constraints. We optimize this objective function using a procedure that alternates between information and moment projections. Our method provides an alternate interpretation of the posterior regularization framework (…
DANTE trains neural networks using an alternating minimization approach.
problem Training neural networks with mixed activation functions efficiently.
method DANTE uses alternating minimization and quasi-convexity to handle neural networks with both differentiable and non-differentiable activation functions.
result DANTE-trained neural networks are promising and competitive in terms of quality and training speed.
Paper tackles efficient SGD methods for constrained bilevel optimization.
problem Stochastic bilevel optimization with equality constraints.
method Alternating implicit projected SGD and its variants.
result Achieves sample complexity matching state-of-the-art for unconstrained problems.
We propose two new alternating direction methods to solve "fully" nonsmooth constrained convex problems. Our algorithms have the best known worst-case iteration-complexity guarantee under mild assumptions for both the objective residual and feasibility gap. Through theoretical analysis, we show how to update all the al…
Understanding the evolution of human society, as a complex adaptive system, is a task that has been looked upon from various angles. In this paper, we simulate an agent-based model with a high enough population tractably. To do this, we characterize an entity called \textit{society}, which helps us reduce the complexit…
Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Levy process. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. The objective is to find a dividend poli…
A new framework tackles CASH problem with alternating optimization and Rising Bandits.
problem Efficiently solving the Combined Algorithm Selection and Hyperparameter optimization (CASH) problem.
method Alternating optimization framework using BO for HPO and Rising Bandits for algorithm selection.
result Demonstrated superiority over competitive baselines in extensive experiments.
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…
New method solves sparse PCA and CCA with guaranteed convergence.
problem Sparse PCA and CCA for large-scale data analysis.
method Alternating manifold proximal gradient method.
result Unified convergence analysis for the proposed method.
New methods solve non-Lipschitz smooth problems with guaranteed convergence.
problem Non-Lipschitz smooth problems in machine learning and signal processing.
method Bregman-divergence based algorithms for relatively smooth problems.
result Guaranteed convergence to second-order stationary points for any relatively smooth problem.
New method recovers matrices with nonlinear structures using optimization on Grassmann manifold.
problem Recovering high-rank matrices with nonlinear structures like subspaces or clusters.
method Formulated as rank minimization of a nonlinear feature map, approximated by constrained non-convex optimization on the Grassmann manifold, using Riemannian and alternating minimization schemes.
result Global convergence and worst-case complexity bounds for alternating minimization scheme, leading to unique limit point.
We give an alternative proof for the fact that in n-dimensional Alexandrov spaces with curvature bounded below there exists a unique optimal transport plan from any purely (n−1)-unrectifiable starting measure, and that this plan is induced by an optimal map.
Derives FACT, an alternative to NFA for neural networks, explaining feature learning.
problem Understanding how neural networks learn representations.
method First-principles approach using first-order optimality conditions.
result FACT explains why NFA holds and provides a principled alternative.
Gradient methods converge better for alternating updates in bilinear zero-sum games.
problem Understanding the dynamics of gradient algorithms for bilinear zero-sum games.
method Systematic analysis of popular gradient updates for simultaneous and alternating versions of bilinear zero-sum games.
result Alternating updates converge better than simultaneous ones, with optimal parameter setup and rates.
Proposes a partitioned least squares model for feature grouping.
problem Modeling with feature groups to assess variable importance.
method Two methods: alternating least squares and exact reformulation.
result Exact method provides better results in less time.
Study improves efficiency of MIMO systems' sum rate estimation.
problem Maximizing sum rate in MIMO systems with PAPC constraints.
method Proposes two new low-complexity approaches: alternating optimization and machine learning.
result Demonstrates superior performance compared to existing methods.
LCBO tackles constrained optimization in high dimensions, offering a polynomial convergence rate.
problem Bayesian optimization for high-dimensional constrained problems.
method LCBO uses local descent and uncertainty-driven exploration, proving polynomial convergence rate.
result LCBO achieves a polynomial convergence rate for KKT residuals in high dimensions.
Recently, Andrews and Clutterbuck [AC13] gave a new proof of the optimal lower eigenvalue bound on manifolds via modulus of continuity for solutions of the heat equation. In this short note, we give an alternative proof of Theorem 2 in [AC13]. More precisely, following Ni's method ([Ni13, Section 6]) we give an ellipti…
AGD converges in polynomial iterations to optimal matrix factorization.
problem Matrix factorization optimization with alternating gradient descent.
method Alternating gradient descent with fixed step size, proving convergence in polynomial iterations.
result AGD reaches ε-optimal factorization in T iterations with high probability.