The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation, where the step size is adapted measuring the length of a so-called cumulative path. The cumulative path is a combination of the previous steps realized by the algorithm, where the importance of each step decreases with time. This article studies …
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48 results for “Step Functions”
This paper provides a block coordinate descent algorithm to solve unconstrained optimization problems. In our algorithm, computation of function values or gradients is not required. Instead, pairwise comparison of function values is used. Our algorithm consists of two steps; one is the direction estimate step and the o…
Signature functions of knotsmath.GT
Knot signature function defined and conditions for its existence are given.
problem Defining and characterizing the signature function of knots.
method Presentation of necessary and sufficient conditions for a function to be a knot signature function.
result Conditions for a function to be the signature function of a knot are established.
Characterizes functions in Carnot groups of step 2.
problem Understanding intrinsic Lipschitz functions in Carnot groups.
method Characterization via intrinsic distributional gradients.
result Characterization of locally intrinsic Lipschitz functions in Carnot groups of step 2.
Researchers describe Casimir functions for 3- and 4-step nilpotent Lie groups.
problem Understanding Casimir functions for free nilpotent Lie groups of steps 3 and 4.
method Construction of Casimir functions for free nilpotent Lie groups of steps 3 and 4.
result For 3-step groups, coadjoint orbits are fully described as affine subspaces or direct products of quadrics.
Random Function Descentmath.OC
Random Function Descent improves optimization in high dimensions.
problem Lack of effective optimization methods in high-dimensional spaces.
method Introducing a 'random function' framework to optimize classical optimization problems.
result Random Function Descent (RFD) is a scalable optimization method that bridges Bayesian and classical optimization.
Paper develops an online learning algorithm for functional data models.
problem Recovering slope functions or predictors in functional data models.
method Online regularized learning algorithm in reproducing kernel Hilbert spaces with polynomially decaying step-size.
result Established fast convergence rates for estimation error without capacity assumption.
Paper develops a constant step stochastic Douglas-Rachford algorithm for convex minimization.
problem Finding solutions to convex minimization problems with random functions.
method Stochastic Douglas-Rachford algorithm with constant step size.
result Iterates stay close to the solution set with high probability.
Polyak step size GD reaches final radius of convergence after log iterations.
problem Statistical and computational complexities of Polyak step size GD.
method Generalized smoothness and Lojasiewicz conditions, stability of gradients.
result Polyak step size GD reaches final statistical radius of convergence after logarithmic number of iterations.
FHBI enhances generalization in Bayesian inference with iterative steps in functional spaces.
problem Improving generalization in Bayesian inference models.
method Iterative two-step procedure with adversarial and functional descent steps in a reproducing kernel Hilbert space.
result FHBI consistently outperforms nine baseline methods on the VTAB-1K benchmark.
A multi-step model reduces compounding errors in reinforcement learning.
problem Compounding errors in one-step models lead to inaccurate predictions in reinforcement learning.
method Introduced a multi-step model that directly outputs the outcome of a sequence of actions.
result The multi-step model yields better action selection and more accurate value-function estimation.
Exchangeable graphs arise via a sampling procedure from measurable functions known as graphons. A natural estimation problem is how well we can recover a graphon given a single graph sampled from it. One general framework for estimating a graphon uses step-functions obtained by partitioning the nodes of the graph accor…
New framework guarantees convergence of multi-step MAML.
problem Convergence of multi-step MAML in nonconvex settings.
method Developed a theoretical framework for two types of MAML objective functions.
result Guaranteed convergence rate and computational complexity for multi-step MAML.
Adaptive step sizes improve optimization for convex and nonconvex problems.
problem Optimizing functions that are not strongly convex.
method Bridge nonconvex and strongly convex problems via regularization, then apply Barzilai-Borwein step sizes with SARAH.
result Regularized SARAH methods achieve better complexity in nonconvex problems.
Efficiently optimizes expensive functions with multi-step lookahead using one-shot optimization.
problem Optimizing expensive functions with long-term impacts using myopic approaches.
method Formulated as nested optimization problems within a multi-step scenario tree, optimized in one-shot fashion.
result Multi-step expected improvement is computationally tractable and outperforms existing methods.
A new machine learning method for Bayesian inverse problems in function spaces.
problem Bayesian inverse problems in function spaces with incompatibility of white noise sources.
method One-step generative transport with amortized neural operator and prior-aligned Gaussian random field.
result Generative operator trained on prior samples and noisy observations generates posterior samples efficiently.
Proposes an exponentially increasing step-size for faster parameter estimation in statistical models.
problem Slow convergence of gradient descent in locally convex loss functions.
method Exponentially increasing step-size in gradient descent algorithm.
result Converges linearly to optimal solution under homogeneous assumptions.
The paper analyzes and validates two step size schedules for SGD: exponential and cosine, proving their adaptivity and performance.
problem The variability of SGD performance due to step size choice.
method Analysis and empirical evaluation of exponential and cosine step sizes.
result Exponential and cosine step sizes are adaptive to noise and achieve optimal performance without tuning hyperparameters.
New RL method learns K-step lookahead Q-functions for fixed-horizon MDPs.
problem Challenges in online reinforcement learning for non-episodic, finite-horizon MDPs.
method Introduces a K-step lookahead Q-function with a time-varying threshold for selecting actions.
result Achieves minimax optimal constant regret for K=1 and regret for K ≥ 2.
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.
A new Bayesian method optimizes time-dependent expensive functions with lookahead.
problem Maximizing a time-dependent, expensive oracle with limited evaluations.
method Recursive, two-step lookahead expected payoff (r2LEY) acquisition function.
result r2LEY outperforms myopic methods in synthetic and real-world datasets.
We propose a mini-batching scheme for improving the theoretical complexity and practical performance of semi-stochastic gradient descent applied to the problem of minimizing a strongly convex composite function represented as the sum of an average of a large number of smooth convex functions, and simple nonsmooth conve…
The purpose of this paper is to present the first continuous families of Riemannian manifolds isospectral on functions but not on 1-forms, and simultaneously, the first continuous families of Riemannian manifolds with the same marked length spectrum but not the same 1-form spectrum. The examples presented here are Riem…
A Multi-step Loss Function for Robust Learning of the Dynamics in Model-based Reinforcement Learningcs.LG
The paper introduces a multi-step loss function to improve model-based reinforcement learning.
problem Compounding of one-step prediction errors in long trajectories.
method A multi-step objective function combining MSE losses at various future horizons.
result Models trained with the multi-step loss achieve significant improvement in future prediction.
Geometric step decay schedules improve stochastic algorithms' convergence on sharp nonconvex problems.
problem Convergence of stochastic algorithms on sharp nonconvex problems.
method Geometric step decay schedule applied to stochastic algorithms.
result Geometric step decay schedules lead to local linear convergence rates for sharp nonconvex problems.
The paper tackles noisy combinations of continuous and step functions, providing conditions for their identification.
problem Recovering noisy observations as a combination of continuous and step functions.
method Topological and local properties of the functions are used to determine conditions for identification. A practical estimation algorithm is provided.
result Conditions for the identification of continuous and step functions based on their global and local properties.
This paper introduces MOCM for better fMRI analysis stability.
problem Stable performance of MVP models on new fMRI datasets.
method Integrated objective function and multi-objective optimization approach.
result Superior performance compared to other techniques.
Speed learning on the flymath.OC
Adaptive step size improves online learning performance.
problem Tedious tuning of step size in online learning algorithms.
method Adapt step size by gradient descent on the step size itself.
result Online adaptation reduces performance variability.
Convergence Analysis of a Momentum Algorithm with Adaptive Step Size for Non Convex Optimizationmath.OC
New convergence analysis for ADAM algorithm in non-convex optimization with adaptive step size.
problem Convergence issues in ADAM algorithm for non-convex optimization.
method Study of ADAM algorithm under bounded adaptive step size assumption, providing safe step sizes.
result Novel first order convergence rate result in deterministic and stochastic contexts.
Learning the Step-size Policy for the Limited-Memory Broyden-Fletcher-Goldfarb-Shanno Algorithmcs.LG
Proposes a neural network for learning step-size policies for L-BFGS optimization.
problem Optimizing step sizes for L-BFGS in large-scale problems.
method Neural network architecture using local iterate information, trained via stochastic optimization.
result Outperforms existing step size selection methods in training classifiers.
Method learns graphons from graphs via Gromov-Wasserstein barycenters.
problem Learning nonparametric graph models from finite graphs.
method Approximate graphons with step functions, use Gromov-Wasserstein distance, learn barycenters.
result Proposed method outperforms state-of-the-art on synthetic and real-world data.
W-Flow generates images in one step, faster and better than multi-step methods.
problem Efficiently generating images from a simple reference distribution to a target data distribution.
method W-Flow uses Wasserstein gradient flows to transform the reference distribution to the target distribution in a single step, trained with Sinkhorn divergence.
result W-Flow achieves state-of-the-art results in ImageNet 256256 generation with improved mode coverage and faster sampling.
Paper uses RL to optimize daily step distribution for better health biomarkers.
problem Lack of personalized PA distribution recommendations for health biomarkers.
method Developed an offline reinforcement learning algorithm to learn optimal PA distributions.
result Learned optimal policy suggests more consistent daily steps and tailored recommendations.
New tests for VaR and ES forecast encompassing using flexible link functions.
problem Testing forecast encompassing for Value at Risk and Expected Shortfall.
method Flexible link functions for testing convex forecast combinations and nonstandard asymptotic theory for boundary parameters.
result Tests based on new link functions outperform unrestricted linear link functions for one-step and multi-step forecasts.
Deep Portfolio Theoryq-fin.PM
Develops an automated portfolio selection process using deep learning.
problem Risk-return trade-off in portfolio selection.
method Four-step routine: encode, calibrate, validate, verify.
result Automated and general portfolio selection process.
Automatic, Dynamic, and Nearly Optimal Learning Rate Specification by Local Quadratic Approximationstat.ML
A new method automatically and dynamically sets learning rates in deep learning.
problem Determining the appropriate learning rate in deep learning tasks is challenging and often subjective.
method Local Quadratic Approximation (LQA) to automatically and dynamically set learning rates.
result The proposed method leads to nearly optimal learning rates in a computationally efficient way.
Proposes SD-KDE for density estimation using debiased kernel density with score-based adjustments.
problem Density estimation with bias in kernel density estimation.
method Adjusts data points by taking a step along the estimated score function, then applies standard KDE with modified bandwidth.
result Significantly reduces mean integrated squared error compared to standard Silverman KDE, especially with noisy score function estimates.
The paper extends risk measures to two-step approximations and studies log-concave distributions.
problem Extending classical risk measures to two-step approximations.
method Optimization problem for determining optimal regime thresholds and values for log-concave distributions.
result Conditions for the uniqueness of regime changing in log-concave distributions.
Method learns neural network to overestimate reference function with guarantees.
problem Learning a neural network to overestimate a reference function on a given domain.
method Two-step process: constructing Majoring Points and optimizing a neural network.
result The learned neural network overestimates the reference function on the domain.
We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step procedure of first, doing inference over the function space and second, finding th…
Introduces a new length functional for Ricci flow to detect steady solitons.
problem Detecting steady solitons in Ricci flow.
method Develops a modified length functional and shows it satisfies differential inequalities.
result The length functional generates a distance function that saturates on steady soliton manifolds.
New -step policy gradient method avoids local optima in restricted policy classes.
problem Suboptimal local optima in policy gradient methods for restricted policy classes.
method Proposes a -step policy gradient method to escape myopic local optima.
result The method converges to near optimal solutions exponentially close to the optimal deterministic policy.
mS2GD improves S2GD for large-scale convex optimization.
problem Minimizing a strongly convex function with a large sum of smooth convex functions and a simple nonsmooth convex regularizer.
method mS2GD combines deterministic and stochastic gradient steps with mini-batching.
result mS2GD achieves faster convergence and parallelizable implementation.
The paper develops methods for causal function estimation and inference with multiway clustered data.
problem Estimation and inference for causal functions under multiway clustering.
method Two-step procedure using machine learning for nuisance parameters and projection onto basis functions.
result Rejects the null hypothesis of uniformly zero effects and reveals heterogeneous treatment effects.
Blended Matching Pursuitmath.OC
New algorithm combines gradient and coordinate descent steps for faster convergence.
problem Optimizing smooth convex functions over atom-spans.
method Blended matching pursuit combining coordinate descent and gradient descent.
result Derives linear convergence rates for non-strongly convex functions.
Introduces GOLS-I for automatically determining step sizes in neural networks without surrogates.
problem Determining step sizes in neural network training using predetermined rules or expensive global optimization strategies.
method Gradient-Only Line Searches (GOLS-I) that are Inexact.
result GOLS-I is a competitive strategy for reliably determining step sizes in stochastic loss functions.
Three-hidden-layer neural networks can approximate Hölder continuous functions uniformly with exponential rate.
problem Approximating Hölder continuous functions with neural networks.
method Introduced Floor-Exponential-Step (FLES) networks with three hidden layers.
result Uniform approximation of Hölder continuous functions with an exponential rate.
New method detects communities in hypergraphs, achieving optimal statistical limit.
problem Community detection in hypergraphs under stochastic block model.
method Two-step algorithm: spectral clustering followed by local refinement.
result Achieves optimal statistical limit for community detection in hypergraphs.