BZPEERPapers, people, evidence and research paths
Menu

Discover

SearchFind papers, people, topics, institutions and opportunities from one place.GraphSee how papers, authors, topics and evidence connect.

Research tools

HomeContinue from the papers, people and topics that matter now.CollectionsTurn saved papers into reading lists, evidence maps and shareable context.ResearchReconstruct the path that led you from search to paper to question.CollaborationMove from a paper, topic or expert request into a focused thread.PublishCreate full-text research articles with metadata, formulas and versions.

Network

ExpertsFind specialists whose work and reviews explain why they can help.CommunitiesJoin research groups organized around papers, topics and shared evidence.

Opportunities

ListingsBrowse roles, calls and collaborations connected to real research context.

Account

Log inReturn to your saved papers, graph views and active threads.Create accountStart saving papers, building a research trail and joining teams.
Log inCreate account

Source author record

Akiko Takeda

Akiko Takeda appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
math.OCMachine LearningArtificial Intelligencemath.PR

Catalog footprint

What is connected

12works
4topics
4close collaborators

Actions

Connect this record

Log in to claim
Open graphBrowse works

Research graph

See the researcher in context

Open full explorer

Inspect adjacent papers, topics, institutions and collaborators without losing the researcher page.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Published work

12 published item(s)

preprint2026arXiv

Randomized Subspace Nesterov Accelerated Gradient

Randomized-subspace methods reduce the cost of first-order optimization by using only low-dimensional projected-gradient information, a feature that is attractive in forward-mode automatic differentiation and communication-limited settings. While Nesterov acceleration is well understood for full-gradient and coordinate-based methods, obtaining accelerated methods for general subspace sketches that use only projected-gradient information and can improve over full-dimensional Nesterov acceleration in oracle complexity is technically nontrivial. We develop randomized-subspace Nesterov accelerated gradient methods for smooth convex and smooth strongly convex optimization under matrix smoothness and generic sketch moment assumptions. The key technical ingredient is a three-sequence formulation tailored to matrix smoothness, which recovers the corresponding classical Nesterov methods in the full-dimensional case. The resulting theory establishes accelerated oracle-complexity guarantees and makes explicit how matrix smoothness and the sketch distribution enter the complexity. It also provides a unified basis for comparing sketch families and identifying when randomized-subspace acceleration improves over full-dimensional Nesterov acceleration in oracle complexity.

0 citations0 reviewsNo code linkedOpen access
preprint2025arXiv

Complexity and convergence analysis of a single-loop SDCAM for Lipschitz composite optimization and beyond

We develop and analyze a single-loop algorithm for minimizing the sum of a Lipschitz differentiable function $f$, a prox-friendly proper closed function $g$ (with a closed domain on which $g$ is continuous) and the composition of another prox-friendly proper closed function $h$ (whose domain is closed on which $h$ is continuous) with a continuously differentiable mapping $c$ (that is Lipschitz continuous and Lipschitz differentiable on the convex closure of the domain of $g$). Such models arise naturally in many contemporary applications, where $f$ is the loss function for data misfit, and $g$ and $h$ are nonsmooth functions for inducing desirable structures in $x$ and $c(x)$. Existing single-loop algorithms mainly focus either on the case where $h$ is Lipschitz continuous or the case where $h$ is an indicator function of a closed convex set. In this paper, we develop a single-loop algorithm for more general possibly non-Lipschitz $h$. Our algorithm is a single-loop variant of the successive difference-of-convex approximation method (SDCAM) proposed in [22]. We show that when $h$ is Lipschitz, our algorithm exhibits an iteration complexity that matches the best known complexity result for obtaining an $(ε_1,ε_2,0)$-stationary point. Moreover, we show that, by assuming additionally that dom $g$ is compact, our algorithm exhibits an iteration complexity of $\tilde{O}(ε^{-4})$ for obtaining an $(ε,ε,ε)$-stationary point when $h$ is merely continuous and real-valued. Furthermore, we consider a scenario where $h$ does not have full domain and establish vanishing bounds on successive changes of iterates. Finally, in all three cases mentioned above, we show that one can construct a subsequence such that any accumulation point $x^*$ satisfies $c(x^*)\in$ dom $h$, and if a standard constraint qualification holds at $x^*$, then $x^*$ is a stationary point.

0 citations0 reviewsNo code linkedOpen access
preprint2024arXiv

Accelerated-gradient-based generalized Levenberg--Marquardt method with oracle complexity bound and local quadratic convergence

Minimizing the sum of a convex function and a composite function appears in various fields. The generalized Levenberg--Marquardt (LM) method, also known as the prox-linear method, has been developed for such optimization problems. The method iteratively solves strongly convex subproblems with a damping term. This study proposes a new generalized LM method for solving the problem with a smooth composite function. The method enjoys three theoretical guarantees: iteration complexity bound, oracle complexity bound, and local convergence under a Hölderian growth condition. The local convergence results include local quadratic convergence under the quadratic growth condition; this is the first to extend the classical result for least-squares problems to a general smooth composite function. In addition, this is the first LM method with both an oracle complexity bound and local quadratic convergence under standard assumptions. These results are achieved by carefully controlling the damping parameter and solving the subproblems by the accelerated proximal gradient method equipped with a particular termination condition. Experimental results show that the proposed method performs well in practice for several instances, including classification with a neural network and nonnegative matrix factorization.

0 citations0 reviewsNo code linkedOpen access
preprint2024arXiv

Stochastic Approach for Price Optimization Problems with Decision-dependent Uncertainty

Price determination is a central research topic of revenue management in marketing. The important aspect in pricing is controlling the stochastic behavior of demand, and the previous studies have tackled price optimization problems with uncertainties. However, many of those studies assumed that uncertainties are independent of decision variables (i.e., prices) and did not consider situations where demand uncertainty depends on price. Although some price optimization studies have dealt with decision-dependent uncertainty, they make application-specific assumptions in order to obtain an optimal solution or an approximation solution. To handle a wider range of applications with decision-dependent uncertainty, we propose a general non-convex stochastic optimization formulation. This approach aims to maximize the expectation of a revenue function with respect to a random variable representing demand under a decision-dependent distribution. We derived an unbiased stochastic gradient estimator by using a well-tuned variance reduction parameter and used it for a projected stochastic gradient descent method to find a stationary point of our problem. We conducted synthetic experiments and simulation experiments with real data on a retail service application. The results show that the proposed method outputs solutions with higher total revenues than baselines.

0 citations0 reviewsNo code linkedOpen access
preprint2024arXiv

Universal heavy-ball method for nonconvex optimization under Hölder continuous Hessians

We propose a new first-order method for minimizing nonconvex functions with Lipschitz continuous gradients and Hölder continuous Hessians. The proposed algorithm is a heavy-ball method equipped with two particular restart mechanisms. It finds a solution where the gradient norm is less than $ε$ in $O(H_ν^{\frac{1}{2 + 2 ν}} ε^{- \frac{4 + 3 ν}{2 + 2 ν}})$ function and gradient evaluations, where $ν\in [0, 1]$ and $H_ν$ are the Hölder exponent and constant, respectively. Our algorithm is $ν$-independent and thus universal; it automatically achieves the above complexity bound with the optimal $ν\in [0, 1]$ without knowledge of $H_ν$. In addition, the algorithm does not require other problem-dependent parameters as input, including the gradient's Lipschitz constant or the target accuracy $ε$. Numerical results illustrate that the proposed method is promising.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Random projection of Linear and Semidefinite problem with linear inequalities

The Johnson-Lindenstrauss Lemma states that there exist linear maps that project a set of points of a vector space into a space of much lower dimension such that the Euclidean distance between these points is approximately preserved. This lemma has been previously used to prove that we can randomly aggregate, using a random matrix whose entries are drawn from a zero-mean sub-Gaussian distribution, the equality constraints of an Linear Program (LP) while preserving approximately the value of the problem. In this paper we extend these results to the inequality case by introducing a random matrix with non-negative entries that allows to randomly aggregate inequality constraints of an LP while preserving approximately the value of the problem. By duality, the approach we propose allows to reduce both the number of constraints and the dimension of the problem while obtaining some theoretical guarantees on the optimal value. We will also show an extension of our results to certain semidefinite programming instances.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Controllability maximization of large-scale systems using projected gradient method

In this work, we formulate two controllability maximization problems for large-scale networked dynamical systems such as brain networks: The first problem is a sparsity constraint optimization problem with a box constraint. The second problem is a modified problem of the first problem, in which the state transition matrix is Metzler. In other words, the second problem is a realization problem for a positive system. We develop a projected gradient method for solving the problems, and prove global convergence to a stationary point with locally linear convergence rate. The projections onto the constraints of the first and second problems are given explicitly. Numerical experiments using the proposed method provide non-trivial results. In particular, the controllability characteristic is observed to change with increase in the parameter specifying sparsity, and the change rate appears to be dependent on the network structure.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Convex Fairness Constrained Model Using Causal Effect Estimators

Recent years have seen much research on fairness in machine learning. Here, mean difference (MD) or demographic parity is one of the most popular measures of fairness. However, MD quantifies not only discrimination but also explanatory bias which is the difference of outcomes justified by explanatory features. In this paper, we devise novel models, called FairCEEs, which remove discrimination while keeping explanatory bias. The models are based on estimators of causal effect utilizing propensity score analysis. We prove that FairCEEs with the squared loss theoretically outperform a naive MD constraint model. We provide an efficient algorithm for solving FairCEEs in regression and binary classification tasks. In our experiment on synthetic and real-world data in these two tasks, FairCEEs outperformed an existing model that considers explanatory bias in specific cases.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

A New Dynamic Pricing Model based on Convex Hull Pricing

This paper presents a new dynamic pricing model (a.k.a. real-time pricing) that reflects startup costs of generators. Dynamic pricing, which is a method to control demand by pricing electricity at hourly (or more often) intervals, has been studied by many researchers. They assume that the cost functions of suppliers are convex, although they may be nonconvex because of the startup costs of generators in practice. We provide a dynamic pricing model that takes into account such cost functions within the settings of unit commitment problems (UCPs). Our model gives convex hull price (CHP), which has not been used in the context of dynamic pricing, though it is known that the CHP minimizes the uplift payment which is disadvantageous to suppliers for a given demand. In addition, we apply an iterative algorithm based on the subgradient method to solve our model. Numerical experiments show the efficiency of our model on reducing uplift payments. The prices determined by our algorithm give sufficiently small uplift payments in a realistic computational time.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Breakdown Point of Robust Support Vector Machine

The support vector machine (SVM) is one of the most successful learning methods for solving classification problems. Despite its popularity, SVM has a serious drawback, that is sensitivity to outliers in training samples. The penalty on misclassification is defined by a convex loss called the hinge loss, and the unboundedness of the convex loss causes the sensitivity to outliers. To deal with outliers, robust variants of SVM have been proposed, such as the robust outlier detection algorithm and an SVM with a bounded loss called the ramp loss. In this paper, we propose a robust variant of SVM and investigate its robustness in terms of the breakdown point. The breakdown point is a robustness measure that is the largest amount of contamination such that the estimated classifier still gives information about the non-contaminated data. The main contribution of this paper is to show an exact evaluation of the breakdown point for the robust SVM. For learning parameters such as the regularization parameter in our algorithm, we derive a simple formula that guarantees the robustness of the classifier. When the learning parameters are determined with a grid search using cross validation, our formula works to reduce the number of candidate search points. The robustness of the proposed method is confirmed in numerical experiments. We show that the statistical properties of the robust SVM are well explained by a theoretical analysis of the breakdown point.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

A Conjugate Property between Loss Functions and Uncertainty Sets in Classification Problems

In binary classification problems, mainly two approaches have been proposed; one is loss function approach and the other is uncertainty set approach. The loss function approach is applied to major learning algorithms such as support vector machine (SVM) and boosting methods. The loss function represents the penalty of the decision function on the training samples. In the learning algorithm, the empirical mean of the loss function is minimized to obtain the classifier. Against a backdrop of the development of mathematical programming, nowadays learning algorithms based on loss functions are widely applied to real-world data analysis. In addition, statistical properties of such learning algorithms are well-understood based on a lots of theoretical works. On the other hand, the learning method using the so-called uncertainty set is used in hard-margin SVM, mini-max probability machine (MPM) and maximum margin MPM. In the learning algorithm, firstly, the uncertainty set is defined for each binary label based on the training samples. Then, the best separating hyperplane between the two uncertainty sets is employed as the decision function. This is regarded as an extension of the maximum-margin approach. The uncertainty set approach has been studied as an application of robust optimization in the field of mathematical programming. The statistical properties of learning algorithms with uncertainty sets have not been intensively studied. In this paper, we consider the relation between the above two approaches. We point out that the uncertainty set is described by using the level set of the conjugate of the loss function. Based on such relation, we study statistical properties of learning algorithms using uncertainty sets.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

A Unified Robust Classification Model

A wide variety of machine learning algorithms such as support vector machine (SVM), minimax probability machine (MPM), and Fisher discriminant analysis (FDA), exist for binary classification. The purpose of this paper is to provide a unified classification model that includes the above models through a robust optimization approach. This unified model has several benefits. One is that the extensions and improvements intended for SVM become applicable to MPM and FDA, and vice versa. Another benefit is to provide theoretical results to above learning methods at once by dealing with the unified model. We give a statistical interpretation of the unified classification model and propose a non-convex optimization algorithm that can be applied to non-convex variants of existing learning methods.

0 citations0 reviewsNo code linkedOpen access