New algorithms adapt to both gradient norms and comparator norms in online learning.
problem Adapting to both gradient norms and comparator norms in online learning.
method Developed parameter-free and scale-free algorithms for unbounded online convex optimization.
result Improved regret bounds for scale-invariant online prediction with linear models.
AdaGrad-Norm achieves optimal convergence rates for non-convex objectives without tuning.
problem Optimal convergence rates for non-convex, smooth objectives with adaptive step sizes.
method Adaptive SGD (AdaGrad-Norm) with self-tuning step sizes, analyzing under unbounded gradients and affine variance scaling.
result AdaGrad-Norm achieves order optimal convergence rate of $\mathcal{O}\left(\frac{\mathrm{poly}\log(T)}{\sqrt{T}}
ight)$ under optimal assumptions.
AdaGrad-Norm achieves linear convergence for certain functions.
problem Proving linear convergence for specific types of functions.
method Introducing RUIG, a measure of gradient balance; developing a two-stage framework.
result AdaGrad-Norm achieves linear convergence for certain functions.
New algorithms reduce regret for convex bandits with small comparator norms.
problem Optimizing in bandit convex optimization with varying comparator norms.
method Developed algorithms using techniques from full-information setting and new gradient estimators.
result Regret bounds are small when comparator norm is small.
Adaptive norms improve neural network optimization with second-order methods.
problem Optimizing neural networks with second-order methods.
method Regularized Newton methods with adaptive norms, interpreting adaptive gradient methods as trust region methods.
result Ellipsoidal constraints outperform spherical constraints in terms of backpropagations and asymptotic loss value.
A new algorithm estimates mean adaptively to covariance, faster and more flexible than existing methods.
problem Estimating mean of a distribution with unknown covariance efficiently and privately.
method Adaptive differentially private algorithm with optimal convergence rates and near-linear sample complexity.
result Achieves optimal rates of convergence with respect to the Mahalanobis norm ∣∣⋅∣∣Σ. New bounds adaptively control spectral complexity of trained Transformers.
problem Understanding why Transformers generalize well in machine learning.
method Spectrum-adaptive post hoc generalization bounds for multi-layer Transformers.
result Bounds adaptively trade off spectral complexity against dimension and depth factors.
This work is substituted by the paper in arXiv:2011.14066. Stochastic gradient descent is the de facto algorithm for training deep neural networks (DNNs). Despite its popularity, it still requires fine tuning in order to achieve its best performance. This has led to the development of adaptive methods, that claim autom…
A new method for learning function parameters in operators using data-adaptive RKHS.
problem Learning function parameters in operators with robustness to noise and numerical error.
method Data Adaptive RKHS Tikhonov Regularization (DARTR) method.
result DARTR leads to an accurate estimator robust to noise and numerical error, converging at a consistent rate as data refines.
Proposes a new regression method using Lp-norms for non-Gaussian noise.
problem Non-Gaussian noise in residuals affects the performance of local least squares regression.
method Introduces local polynomial Lp-norm regression, replacing weighted least squares with weighted Lp-norm estimation. result Demonstrates superior performance over local least squares in one-dimensional data and higher dimensions.
New method certifies neural network function space norms from point evaluations.
problem Certifying neural network function space norms from point evaluations alone.
method Combining interval arithmetic enclosures, adaptive marking/refinement, and quadrature-based aggregation.
result Certified computation of Lp, W1,p, and W2,p norms. This work proposes an adaptive trace lasso regularized L1-norm based graph cut method for dimensionality reduction of Hyperspectral images, called as `Trace Lasso-L1 Graph Cut' (TL-L1GC). The underlying idea of this method is to generate the optimal projection matrix by considering both the sparsity as well as the corr…
Proposes a new adaptive gradient method based on gradient differences.
problem Manual tuning of stepsize in vanilla gradient methods.
method Adaptation driven by cumulative squared norms of gradient differences.
result More robust than AdaGrad in various settings.
Kernel adaptive filters, a class of adaptive nonlinear time-series models, are known by their ability to learn expressive autoregressive patterns from sequential data. However, for trivial monotonic signals, they struggle to perform accurate predictions and at the same time keep computational complexity within desired …
New nonconvex regularizer speeds up low-rank matrix completion.
problem Low-rank matrix completion with good theoretical and empirical performance.
method Proposes a new nonconvex regularizer with adaptive shrinkage, scalable, and fast optimization.
result Proposed method achieves state-of-the-art recovery performance and is the fastest.
DoRA improves adaptation efficiency for large models by factoring norms and fusing kernels.
problem High-rank DoRA is computationally expensive and infeasible on common GPUs.
method Factored norms and fused Triton kernels to reduce memory and speed up computation.
result Fused implementation is up to 2.0x faster for inference and 1.9x faster for gradient computation.
This paper explores adaptive methods in over-parameterized linear regression.
problem Understanding why neural networks generalize well in over-parameterized settings.
method Characterizes two sub-classes of adaptive methods and their generalization performance.
result Adaptive methods in over-parameterized linear regression converge to the minimum norm solution.
A new tensor p-shrinkage nuclear norm improves low-rank tensor completion.
problem Estimating tensors from partial observations with low rank.
method Proposed tensor p-shrinkage nuclear norm (p-TNN) and an efficient algorithm.
result Upper bound of recovery error provided for the LRTC model.
New methods improve online matrix optimization with reduced computational cost.
problem Online matrix optimization with operator norm constraints.
method Gradient-based prediction scheme with smoothed potentials for nuclear norm.
result Adaptive matrix optimizers match Shampoo's regret up to a constant factor.
New bounds on adaptivity cost in stochastic optimization.
problem Understanding the cost of changing strategies in stochastic optimization.
method Proving impossibility results for adaptivity in non-smooth stochastic convex optimization.
result Lower bounds on the price of adaptivity for different levels of uncertainty.
In this paper, we propose a novel linear discriminant analysis criterion via the Bhattacharyya error bound estimation based on a novel L1-norm (L1BLDA) and L2-norm (L2BLDA). Both L1BLDA and L2BLDA maximize the between-class scatters which are measured by the weighted pairwise distances of class means and meanwhile mini…
Using the ℓ1-norm to regularize the estimation of the parameter vector of a linear model leads to an unstable estimator when covariates are highly correlated. In this paper, we introduce a new penalty function which takes into account the correlation of the design matrix to stabilize the estimation. This norm, ca…
We discuss the problem of adaptive discrete-time signal denoising in the situation where the signal to be recovered admits a "linear oracle" -- an unknown linear estimate that takes the form of convolution of observations with a time-invariant filter. It was shown by Juditsky and Nemirovski (2009) that when the $\ell_2…
This paper presents a normalization mechanism called Instance-Level Meta Normalization (ILM~Norm) to address a learning-to-normalize problem. ILM~Norm learns to predict the normalization parameters via both the feature feed-forward and the gradient back-propagation paths. ILM~Norm provides a meta normalization mechanis…
We consider the empirical risk minimization problem for linear supervised learning, with regularization by structured sparsity-inducing norms. These are defined as sums of Euclidean norms on certain subsets of variables, extending the usual ℓ1-norm and the group ℓ1-norm by allowing the subsets to overlap. T…
Existing approaches for training neural networks with user-level differential privacy (e.g., DP Federated Averaging) in federated learning (FL) settings involve bounding the contribution of each user's model update by clipping it to some constant value. However there is no good a priori setting of the clipping norm acr…
This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse Column-wise Inverse Operator, to address these two issues. We analyze an adaptive …
We show how the discovery of robust scalable numerical solvers for arbitrary bounded linear operators can be automated as a Game Theory problem by reformulating the process of computing with partial information and limited resources as that of playing underlying hierarchies of adversarial information games. When the so…
GAS-Norm improves deep learning time series forecasting in non-stationary settings.
problem Deep learning models struggle with non-stationary time series data.
method Combines GAS model for adaptive normalization with deep neural networks.
result Improves deep learning performance in 21 out of 25 settings.
DNNs can learn complex functions efficiently by breaking the curse of dimensionality.
problem Learning complex functions efficiently in high-dimensional spaces.
method Combining compositionality and symmetry learning with generalization bounds.
result DNNs can learn functions with bounded F1-norm efficiently, reducing the curse of dimensionality. A novel one-class classifier fusion method for robust anomaly detection.
problem Fundamental challenges in ensemble-based anomaly detection.
method Locally adaptive learning with dynamic ℓp-norm constraints and interior-point optimization.
result Significantly improved computational efficiency and superior performance across diverse anomaly types.
Algorithm reduces regret in online learning with varying norms.
problem Online convex optimization with changing norms.
method Adaptive online learning algorithm that adjusts to varying norms without tuning.
result Achieves improved regret bounds for full-matrix AdaGrad.
A new method combines classifiers using possibility distributions and adaptive t-norms.
problem Aggregating predictions from multiple classifiers trained on overlapping datasets.
method Proposes a new approach to aggregate classifier predictions using possibility theory and adaptive t-norms.
result Proves the proposed approach possesses desirable robustness properties.
We present a proof due to Duistermaat that the gradient flow of the norm squared of the moment map defines a deformation retract of the appropriate piece of the manifold onto the zero level set of the moment map. Duistermaat's proof is an adaptation of Lojasiewicz's argument for analytic functions to functions which ar…
We propose an adaptive optimization method for deep learning that dynamically adjusts batch size.
problem Optimizing deep learning models with varying sensitivity to batch size selection.
method Adaptive regularization with dynamically determined stochastic batch size based on gradient norms.
result Our method outperforms state-of-the-art optimization algorithms in generalization and robustness.
New approach to adaptively select bandwidths in nonparametric regression.
problem Adaptive bandwidth selection in nonparametric regression.
method Inspired by ℓ2-norms of interval projections, introduces a new bandwidth selection procedure. result Obtains non-asymptotic risk bounds for local polynomial regression methods that adapt to local Hölder exponent.
We develop a novel family of algorithms for the online learning setting with regret against any data sequence bounded by the empirical Rademacher complexity of that sequence. To develop a general theory of when this type of adaptive regret bound is achievable we establish a connection to the theory of decoupling inequa…
The k-nearest neighbour (k-NN) classifier is one of the oldest and most important supervised learning algorithms for classifying datasets. Traditionally the Euclidean norm is used as the distance for the k-NN classifier. In this thesis we investigate the use of alternative distances for the k-NN classifier. We …
A new fast adversarial attack finds minimal perturbations to change class.
problem Evaluating robustness of neural networks against adversarial attacks.
method White-box adversarial attack minimizing perturbation size.
result Outperforms or matches state-of-the-art attacks.
We study the adaptive estimation of copula correlation matrix Σ for the semi-parametric elliptical copula model. In this context, the correlations are connected to Kendall's tau through a sine function transformation. Hence, a natural estimate for Σ is the plug-in estimator Σ^ with Kendall's tau statistic. We …
New robust estimator for high-dimensional data with outliers and leverage points.
problem Robust regression in high-dimensional datasets with gross contamination.
method Adaptive τ-Lasso estimator with an adaptive ℓ1-norm penalty.
result Adaptive τ-Lasso has the oracle property and robustness to outliers and high-leverage points.
This paper adapts Thurston's earthquake metric to Riemann surfaces with marked points.
problem Defining a norm and metric on Teichmüller spaces for surfaces of arbitrary genus.
method Adapting Thurston's earthquake norm to Riemann surfaces with marked points and using complex Legendre transforms.
result Establishes a complete analogue of Thurston's earthquake norm in the conformal setting.
In this paper, we present GASG21 (Grassmannian Adaptive Stochastic Gradient for L2,1 norm minimization), an adaptive stochastic gradient algorithm to robustly recover the low-rank subspace from a large matrix. In the presence of column outliers, we reformulate the batch mode matrix L2,1 norm minimization with…
Improved generalization bounds for multi-class CNNs without explicit class dependence.
problem Generalization error bounds for deep learning with multi-class CNNs.
method Adapted Rademacher analysis to incorporate weight sharing, reducing dependence on the number of classes.
result Bounds have no explicit dependence on the number of classes, scaling with the norm of weight matrices.
New framework assesses regularization norms in ill-posed problems, revealing L2 instability and proposing adaptive fractional RKHS solutions.
problem Comparative analysis of regularization norms in ill-posed problems.
method Small noise analysis framework for Tikhonov and RKHS regularizations.
result Optimal convergence rates achieved with adaptive fractional RKHS, but hyper-parameters decay too fast.
Weight normalization and reparametrized gradient descent adaptively regularize weights and converge to minimum l2 norm solutions.
problem Adapting to non-convex weight normalization for convergence to minimum l2 norm solutions.
method Weight normalization and reparametrized projected gradient descent (rPGD) for overparametrized least-squares regression.
result rPGD converges close to the minimum l2 norm solution, even for far-from-zero initializations.
New algorithm bounds MAB regret for unknown scale and magnitude of losses.
problem Adversarial Multi Armed Bandits with unknown scale and magnitude of losses.
method Design a bandit Follow The Regularized Leader (FTRL) algorithm with adaptive learning rate.
result First MAB bounds that adapt to L2 and L1 norms of losses. DFR reduces the computational cost of sparse-group lasso and adaptive sparse-group lasso.
problem Sparse-group lasso's computational expense and need for tuning.
method Dual Feature Reduction (DFR) using strong screening rules and dual norms.
result DFR drastically reduces computational cost without affecting solution optimality.