16 accepted papers
We propose Frank–Wolfe (FW) algorithms with an adaptive Bregman step-size strategy for smooth adaptable (also called: relatively smooth) (weakly-) convex functions. This means that the gradient of the objective function is not necessarily Lipschitz continuous, and we only require the smooth adaptabl…
Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian manifold structure and performing optimization intrinsically on t…
In recent years, random subspace methods have been actively studied for large-dimensional nonconvex problems. Recent subspace methods have improved theoretical guarantees such as iteration complexity and local convergence rate while reducing computational costs by deriving descent directions in rand…
The K-means algorithm is one of the most widely studied clustering algorithms in machine learning. While extensive research has focused on its ability to achieve a globally optimal solution, there still lacks a rigorous analysis of its local optimality guarantees. In this paper, we first present con…
Deep learning with noisy labels presents significant challenges. In this work, we theoretically characterize the role of label noise from a feature learning perspective. Specifically, we consider a signal-noise data distribution, where each sample comprises a label-dependent signal and label-indepen…
In this study, we consider an optimization problem with uncertainty dependent on decision variables, which has recently attracted attention due to its importance in machine learning and pricing applications. In this problem, the gradient of the objective function cannot be obtained explicitly becaus…
Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian manifolds. We present several hypergradient estimation strategie…
Large language models (LLMs) have shown impressive capabilities across various tasks. However, training LLMs from scratch requires significant computational power and extensive memory capacity. Recent studies have explored low-rank structures on weights for efficient fine-tuning in terms of paramete…
Accurate outlier detection is not only a necessary preprocessing step, but can itself give important insights into the data. However, especially, for non-linear regression the detection of outliers is non-trivial, and actually ambiguous. We propose a new method that identifies outliers by finding a…
The Gaussian homotopy (GH) method is a popular approach to finding better stationary points for non-convex optimization problems by gradually reducing a parameter value $t$, which changes the problem to be solved from an almost convex one to the original target one. Existing GH-based methods repeate…
Although application examples of multilevel optimization have already been discussed since the 1990s, the development of solution methods was almost limited to bilevel cases due to the difficulty of the problem. In recent years, in machine learning, Franceschi et al. have proposed a method for solvi…
Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence results have been reported. We present two simple stochastic…
The unfairness of a regressor is evaluated by measuring the correlation between the estimator and the sensitive attribute (e.g., race, gender, age), and the coefficient of determination (CoD) is a natural extension of the correlation coefficient when more than one sensitive attribute exists. As is w…
Motivated by online advertising, we study a multiple-play multi-armed bandit problem with position bias that involves several slots and the latter slots yield fewer rewards. We characterize the hardness of the problem by deriving an asymptotic regret bound. We propose the Permutation Minimum Empiric…
Density ratio estimation is a vital tool in both machine learning and statistical community. However, due to the unbounded nature of density ratio, the estimation proceudre can be vulnerable to corrupted data points, which often pushes the estimated ratio toward infinity. In this paper, we present a…
In this paper we consider robust classifications and show equivalence between the regularized classifications. In general, robust classifications are used to create a classifier robust to data by taking into account the uncertainty of the data. Our result shows that regularized classifications inher…