New bounds for agnostic learning with average smoothness.
problem Distribution-free nonparametric regression with average smoothness.
method Distribution-free uniform convergence bounds and agnostic learning algorithm.
result Distribution-free uniform convergence bounds for average-smoothness classes in the agnostic setting.
Improved learning rates with new smoothness measure.
problem Learning with noisy data and unknown function class.
method Generalized Hölder smoothness to average smoothness, proving upper and lower bounds.
result Achieved nearly optimal learning rates in realizable and agnostic settings.
Averaged SGD optimizes a smoothed objective, leading to better generalization.
problem Improving generalization performance in machine learning models.
method Analyzed the smoothed objective function of SGD and proved that averaged SGD can optimize this smoothed function efficiently.
result Averaged SGD can efficiently optimize a smoothed objective, leading to better generalization.
New theory for nonsmooth systems helps optimize and control complex functions.
problem Optimizing and controlling systems with nonsmooth functions.
method Higher-order averaging theory with nonsmooth near-identity transformation and lexicographic differentiation.
result Closed formula for nonsmooth first and second-order averaging.
This paper analyzes the convergence of Federated Average under relaxed assumptions.
problem Lack of theoretical analysis for Federated Average under assumptions beyond smoothness.
method Relaxing assumptions of strong smoothness to semi-smoothness and semi-Lipschitz properties, and introducing a bound on the gradient.
result Provides a theoretical convergence study on Federated Learning under new assumptions.
New algorithm for federated learning with non-smooth regularizers.
problem Federated Learning with non-smooth composite optimization problems.
method Proposed Federated Dual Averaging (FedDualAvg) algorithm to overcome convergence issues.
result FedDualAvg outperforms other algorithms in federated composite optimization.
Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness assumptions, which do not apply to many modern applications of SGD with non-smooth object…
The paper analyzes MACD using operator theory.
problem Understanding the mathematical foundation of MACD.
method Developed a functional-analytic framework interpreting MACD as a phase-corrected, smoothed derivative operator.
result MACD is structurally equivalent to a band-pass filter and can be expressed as a finite difference of delayed and doubly averaged signals.
DSPI connects natural policy gradient to policy iteration, proving global convergence.
problem Optimizing policies in reinforcement learning.
method DSPI framework, combining smoothed policy iteration and natural policy gradient.
result DSPI achieves geometric convergence and optimal complexity for policy optimization.
Last iterate of Extragradient algorithm converges slower than averaged iterates in saddle point problems.
problem Smooth convex-concave saddle point problems
method Analysis of Extragradient (EG) algorithm convergence rates
result The last iterate of EG converges at a rate of O(1/√T), compared to O(1/T) for averaged iterates
Improved averaging method for noisy observations converges strongly.
problem Noisy observations from random dynamical systems require stable estimates.
method Introduced p-EMA, a modified exponential moving average with subharmonic weight decay. result Stochastic convergence guarantees for p-EMA under mild assumptions. Inverse depth scaling found in LLMs due to similar layers averaging error.
problem Understanding how depth affects loss in large language models.
method Analysis of LLMs and toy residual networks.
result Loss scales inversely proportional to depth in LLMs.
SQR Averaging improves probabilistic electricity price forecasting.
problem Accurate short-term price forecasting in electricity markets.
method Smoothing Quantile Regression Averaging.
result SQR Averaging leads to profit increases of up to 3.5% in day-ahead power trading.
New algorithms optimize spectral risk measures, improving interpolation between average and worst-case performance.
problem Optimizing spectral risk measures for learning systems.
method Developed stochastic algorithms to optimize spectral risk measures by characterizing their subdifferential and addressing challenges like biasedness of subgradient estimates and non-smoothness.
result Our approach outperforms out-of-the-box stochastic subgradient and dual averaging methods in optimizing spectral risk measures.
Discrete exterior calculus shows natural properties of wedge product and averaging.
problem Naturalness of discrete exterior calculus operations.
method Showed naturalness of discrete wedge product and averaging interpretation.
result Discrete wedge product is natural and equals Wilson's cochain product.
Regularization improves robustness of smoothed classifiers.
problem Certifying robustness of smoothed classifiers.
method Regularizing prediction consistency over Gaussian noise.
result Significantly improved certified robustness with less training costs.
This paper presents a tensor multiplication based smoothing algorithm that follows a two step denoising method. Unlike other traditional averaging approaches, our approach uses an element based normal voting tensor to compute smooth surfaces. By introducing a binary optimization on the proposed tensor together with a l…
GPA improves LLM training speed by 8.71% for Llama-160M models.
problem Training Large Language Models (LLMs) with high memory overhead and slow convergence.
method Generalized Primal Averaging (GPA) extends Nesterov's method to eliminate memory-intensive two-loop structure.
result GPA achieves up to 10.13% speedup over AdamW in training Llama-1B model.
tl;dr: no, it cannot, at least not on average on the standard archive problems. We assess whether using six smoothing algorithms (moving average, exponential smoothing, Gaussian filter, Savitzky-Golay filter, Fourier approximation and a recursive median sieve) could be automatically applied to time series classificatio…
Optimal weight windows are found by projecting the origin onto a convex polytope.
problem Finding the best weight windows for a weighted moving average smoother.
method Formulated as a quadratic program and projection onto a convex polytope.
result Optimal weight windows are symmetrical and decrease in weight away from the center.
Deterministic method for certifying neural network robustness.
problem Certifying neural network robustness against adversarial attacks.
method Equivalence between training and Gaussian averaging for robustness certification.
result Comparable certified accuracy and robustness to stochastic methods but with single model evaluation.
Paper establishes lower bounds for finite-sum optimization problems using novel construction methods.
problem Lower complexity bounds for finite-sum optimization problems with various component functions.
method Developed novel approach to construct hard instances and analyzed PIFO algorithms.
result Established lower complexity bounds for convex-concave and nonconvex-strongly-concave objectives.
New method tackles composite optimization with error feedback.
problem Challenges in distributed machine learning training and message compression.
method Combines Dual Averaging with EControl for composite optimization.
result First strong convergence analysis for composite optimization with error feedback.
We compute the rational cohomology of the universal family of smooth cubic surfaces using Vassiliev's method of simplicial resolution. Modulo embedding, the universal family has cohomology isomorphic to that of P2. A consequence of our theorem is that over the finite field Fq, away from finitely…
This dissertation advances the theoretical foundation of local optimization methods in Federated Learning.
problem Theoretical understanding of local optimization methods in Federated Learning is lacking.
method The dissertation proposes and analyzes new methods to improve convergence rates and communication efficiency in Federated Learning.
result Sharp bounds and convergence rates for FedAvg are established, and new methods like FedAc and Federated Dual Averaging are proposed.
In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and the non-smooth part is equipped with a simple proximal mapping. We propose a pr…
Stochastic approximation is one of the effective approach to deal with the large-scale machine learning problems and the recent research has focused on reduction of variance, caused by the noisy approximations of the gradients. In this paper, we have proposed novel variants of SAAG-I and II (Stochastic Average Adjusted…
New method improves certified robustness for classifier confidence.
problem Certifying confidence in classifier predictions.
method Randomized smoothing with modified Neyman-Pearson lemma.
result Certified radii for prediction confidence improved.
FedAc accelerates Federated Averaging for distributed optimization.
problem Efficiently optimizing distributed machine learning models.
method Federated Accelerated Stochastic Gradient Descent (FedAc) using a potential-based perturbed iterate analysis.
result FedAc achieves faster convergence and lower communication costs than previous methods.
Smoothed SGD improves quantile estimation without crossing curves.
problem Estimating quantiles without crossing estimated curves.
method Smoothed SGD algorithm with Bahadur representation and Gaussian approximation.
result Smoothed SGD provides non-asymptotic tail probability bounds and a Gaussian approximation for quantile estimates.
New algorithms optimize without knowing problem parameters.
problem Optimizing large-scale problems without knowing key parameters.
method Combining mirror descent with dual averaging techniques.
result Converges without prior knowledge of problem parameters.
We prove that the expected value of the ratio between the smooth four-genus and the Seifert genus of two-bridge knots tends to zero as the crossing number tends to infinity.
We consider stochastic gradient descent algorithms for minimizing a non-smooth, strongly-convex function. Several forms of this algorithm, including suffix averaging, are known to achieve the optimal O(1/T) convergence rate in expectation. We consider a simple, non-uniform averaging strategy of Lacoste-Julien et al. …
Paper analyzes complexity of solving nonconvex-strongly-concave problems.
problem Finding approximate stationary points of nonconvex-strongly-concave minimax problems.
method Introduces a generic acceleration scheme to solve crafted subproblems.
result Algorithm nearly matches lower complexity bounds in general setting.
Consider a random smooth Gaussian field G(x):F→R, where F is a compact in Rd. We derive a formula for average area of a surface generated by the equation G(x)=0 and give some applications. As an auxiliary result we obtain an integral expression for area of a surface induced by zeros of a \e…
New method reduces communication in distributed learning, improving privacy and utility.
problem Distributed learning with minimal communication and privacy protection.
method Non-interactive blind model averaging (BlindAvg) with output perturbation.
result BlindAvg converges to centralized learning with strong L2-regularization and SoftmaxReg for better privacy-utility tradeoff.
Exponential smoothers are a simple and memory efficient way to compute running averages of time series. Here we define and describe practical properties of exponential smoothers for signals observed at constant and variable intervals.
This paper is devoted to the geometric analysis of the incompressible averaged Euler equations on compact Riemannian manifolds with boundary. The equation also coincides with the model for a second-grade non-Newtonian fluid. We study the analytical and geometrical properties of the Lagrangian flow map. We prove existen…
This paper shows that the time t map of the averaged Euler equations, with Dirichlet, Neumann, and mixed boundary conditions is canonical relative to a Lie-Poisson bracket constructed via a non-smooth reduction for the corresponding diffeomorphism groups. It is also shown that the geodesic spray for Neumann and mixed…
This paper advances FL algorithms for composite optimization and statistical recovery.
problem Federated learning optimization and statistical recovery in composite settings.
method Proposes Fast Federated Dual Averaging for strongly convex and smooth loss, and Multi-stage Federated Dual Averaging for restricted strongly convex and smooth loss.
result Establishes state-of-the-art iteration and communication complexity, and high probability complexity bound with linear speedup.
TT-DAC-PS: A deterministic actor-critic approach for optimal trade execution
problem Optimal execution of large stock sell programs
method Twin-Target Deterministic Actor-Critic with Policy Smoothing
result Reduces mean implementation shortfall percentage
In this paper, we study a class of stochastic optimization problems, referred to as the \emph{Conditional Stochastic Optimization} (CSO), in the form of $\min_{x \in \mathcal{X}} \EE_ξf_ξ\Big({\EE_{η|ξ}[g_η(x,ξ)]}\Big)$, which finds a wide spectrum of applications including portfolio selection, reinforcement learning, …
This paper analyzes stability and generalization of Markov chain stochastic gradient methods.
problem Analyzing stability and generalization of Markov chain stochastic gradient methods.
method Algorithmic stability in statistical learning theory.
result Established optimal generalization bounds for both smooth and non-smooth cases.
Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant Lasso address this dependence by jointly estimating the noise level and the regressi…
Sharp bounds established for Federated Averaging (FedAvg), improving convergence rates.
problem Undetermined convergence rate of Federated Averaging (FedAvg) in Federated Learning.
method Developed novel iterate bias concept and proved sharp bounds on it, leading to improved convergence results.
result Lower bounds for FedAvg match existing upper bounds, showing no improvable capacity.
This paper solves aggregation of Pareto optimal models by using Bayesian priors and weighted averaging.
problem How to rationally aggregate Pareto optimal models while preserving Pareto efficiency.
method Four logical steps: 1) Bayesian models, 2) Prior as preference ranking, 3) Consistent aggregation, 4) Weighted average of priors.
result All rational/consistent aggregation rules follow a generalized hierarchical Bayesian model.
We explore the performance of sample average approximation in comparison with several other methods for stochastic optimization when there is information available on the underlying true probability distribution. The methods we evaluate are (a) bagging; (b) kernel smoothing; (c) maximum likelihood estimation (MLE); and…
A novel online framework for analyzing multidimensional functional data.
problem Analysis of multidimensional functional data streams poses significant challenges.
method Online functional principal component analysis using tensor product splines on a Stiefel manifold with Riemannian stochastic gradient descent.
result Efficient and scalable modeling of multidimensional functional data.