Improved online prediction with guaranteed coverage.
problem Creating reliable online predictions for arbitrary sequences.
method Online conformal prediction with decaying step sizes.
result Substantially improved practical properties, including close coverage at every time point.
Applying standard Markov chain Monte Carlo (MCMC) algorithms to large data sets is computationally expensive. Both the calculation of the acceptance probability and the creation of informed proposals usually require an iteration through the whole data set. The recently proposed stochastic gradient Langevin dynamics (SG…
Paper analyzes convergence of OMD algorithms with geometric conditions.
problem Analyzing convergence of online mirror descent algorithms.
method Presented necessary and sufficient conditions for convergence of OMD with step size sequences.
result Established conditions for convergence and linear convergence under specific variances.
New SVRG and SARAH schemes reduce tuning effort for variance reduction.
problem Optimal performance of SVRG and SARAH requires tuning of parameters.
method Introduces Barzilai-Borwein step sizes, averaging, and adaptive inner loop length.
result Improves SVRG, SARAH, and BB variants' convergence rates and performance.
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.
We introduce a new neural architecture to learn the conditional probability of an output sequence with elements that are discrete tokens corresponding to positions in an input sequence. Such problems cannot be trivially addressed by existent approaches such as sequence-to-sequence and Neural Turing Machines, because th…
The paper interprets learned step sizes in deep-unfolded gradient descent.
problem Intuitive interpretation of learned non-constant step sizes in deep-unfolded gradient descent.
method Theoretical analysis and optimization of spectral radius.
result Chebyshev steps achieve the lower bound of convergence rate for first-order methods.
SGD converges almost surely in non-convex problems, avoiding saddle points and accelerating convergence.
problem Understanding convergence of SGD in non-convex optimization problems.
method Analysis of SGD trajectories, focusing on boundedness, convergence to strict saddle points, and rate of convergence.
result SGD converges almost surely to a minimizer in non-convex problems, avoiding strict saddle points.
New SARAH variant MB-SARAH-RBB accelerates mini-batch optimization.
problem Improving the performance of SARAH in mini-batch settings.
method Introduced MB-SARAH-RBB, a variant of SARAH using RBB step size calculation.
result MB-SARAH-RBB converges linearly for strongly convex objectives and outperforms existing methods.
Applying standard Markov chain Monte Carlo (MCMC) algorithms to large data sets is computationally infeasible. The recently proposed stochastic gradient Langevin dynamics (SGLD) method circumvents this problem in three ways: it generates proposed moves using only a subset of the data, it skips the Metropolis-Hastings a…
The paper explores properties of projections and gradient methods in hyperbolic space forms.
problem Optimization problems in hyperbolic space forms.
method Intrinsic κ-projection and gradient projection methods.
result Every accumulation point of the sequence generated by the gradient projection method is a stationary point.
We establish decoupled functional CLTs for two-time-scale stochastic approximation.
problem Understanding the asymptotic behavior of two-time-scale stochastic approximation.
method Martingale problem approach and auxiliary sequence.
result The limiting dynamics of two-time-scale SA are independent of each other.
Improved privacy analysis for stochastic gradient descent.
problem Analyzing privacy leakage in noisy stochastic gradient descent.
method Modeling Rényi divergence dynamics with Langevin diffusions, proving exponential privacy loss convergence for smooth and strongly convex objectives.
result Privacy loss converges exponentially fast for smooth and strongly convex objectives under constant step size.
Self-attention optimizers converge to optimal weights, revealing bias patterns.
problem Understanding the implicit bias in self-attention mechanisms.
method Analysis of gradient-based optimization in self-attention layers.
result Adaptive step-size strategies can accelerate convergence to optimal weights.
New approach reduces malware detection memory requirements and speeds up training.
problem Efficiently classifying long sequences of malware detection data.
method Developed a new temporal max pooling method and global channel gating design.
result 116x more memory efficient and 25.8x faster training on original dataset.
Gradient equilibrium improves online learning performance without requiring sublinear regret.
problem Achieving sublinear regret in online learning.
method Gradient equilibrium: average of gradients converges to zero.
result Gradient equilibrium can be achieved by standard online learning methods.
We adapt the Douglas-Rachford (DR) splitting method to solve nonconvex feasibility problems by studying this method for a class of nonconvex optimization problem. While the convergence properties of the method for convex problems have been well studied, far less is known in the nonconvex setting. In this paper, for the…
New method tackles blind demixing from noisy bilinear measurements.
problem Blind demixing of source signals from noisy bilinear measurements.
method Provably nonconvex demixing via Wirtinger flow, similar to vanilla gradient descent.
result Aggressive step size and computational optimality guarantees without regularization.
We provide non-asymptotic bounds for the well-known temporal difference learning algorithm TD(0) with linear function approximators. These include high-probability bounds as well as bounds in expectation. Our analysis suggests that a step-size inversely proportional to the number of iterations cannot guarantee optimal …
Implicit Q-learning and SARSA adjust step-sizes automatically, improving stability and performance.
problem Numerical instability and slow progress in Q-learning and SARSA due to step-size calibration.
method Reformulate iterative updates as fixed-point equations, scaling step-sizes inversely with feature norms.
result Implicit methods maintain stability over broader step-size ranges and achieve comparable convergence rates.
Proposes a semi-implicit back propagation method for neural networks.
problem Challenges in training neural networks, especially gradient vanishing and small step sizes.
method Proposes a semi-implicit back propagation method using error back propagation and proximal methods.
result The proposed method leads to better performance in terms of loss decreasing and training/validation accuracy compared to SGD and ProxBP.
Introduces Spectral Attention for better long-range time series forecasting.
problem Challenges in capturing long-range dependencies in time series forecasting.
method Spectral Attention mechanism that preserves temporal correlations and long-range dependencies.
result Achieves state-of-the-art results on 11 real-world time series datasets.
Differentiable sampling corrects alignment issues in neural machine translation.
problem Incorrect alignment of reference words and sampled output in scheduled sampling.
method Optimizes alignment probability based on model's soft alignment prediction.
result Improves BLEU score compared to maximum likelihood and scheduled sampling.
TIDBD adapts TD step-sizes for better performance.
problem Finding optimal step-sizes for TD learning.
method Generalizes IDBD to TD learning, adapting step-sizes per feature.
result TIDBD outperforms other TD methods in various tasks.
The paper analyzes fixed step-size SA schemes on Riemannian manifolds.
problem Developing efficient algorithms for optimization on curved spaces.
method Fixed step-size stochastic approximation schemes in a Riemannian framework.
result The schemes converge to the solution as the step-size approaches zero.
Set-Sequence model learns cross-sectional dynamics directly from time series data.
problem Predicting large cross-sections of time series data with latent cross-sectional dynamics.
method A model that learns cross-sectional structure directly, enhancing expressivity and eliminating manual feature engineering.
result Significantly outperforms strong baselines in equity portfolio optimization and loan risk prediction.
A two-step approach efficiently selects hyperparameters for FCMs.
problem Efficiently selecting hyperparameters for FCMs in a computationally expensive process.
method Two-step sequential approach: first estimate context length k, then estimate α.
result The proposed method achieves comparable compression performance to exhaustive search but with reduced computational cost.
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.
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 …
New algorithm improves stability of optimization algorithms by adapting step-size.
problem Optimization algorithms' effectiveness is sensitive to step-size hyperparameters.
method Adapts NGN step-size method with momentum to enhance stability.
result Achieves convergence rate of O(1/√K) without restrictive assumptions.
AutoStep MCMC adapts step size locally for better sampling efficiency.
problem Challenging step size selection for complex, multiscale targets.
method AutoStep MCMC uses a locally adaptive step size for involutive proposals.
result AutoStep MCMC is π-invariant, irreducible, and aperiodic.
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.
This paper optimizes step sizes for faster convergence in sparse coding.
problem Improving convergence rate of ISTA for sparse coding.
method Learning step sizes for ISTA using neural networks.
result A simple step size strategy can improve convergence rate of ISTA.
New findings show convergence in SA without square summable step sizes.
problem Finding optimal step sizes for stochastic approximation algorithms.
method Analyzed step-size sequences of the form αn=α0n−ρ with ρ∈(0,1), and derived convergence and rate results. result Convergence of parameter estimates with probability one and in Lp for any p≥1; MSE rate of convergence is O(αn), improved to O(max{αn2,1/n}) with averaging. 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.
We analyze constant step-size and iterate averaging in linear stochastic approximation algorithms.
problem Policy evaluation in reinforcement learning using temporal difference algorithms.
method Constant step-size and Polyak-Ruppert averaging of iterates.
result MSE decays as O(1/t) for a range of constant step-sizes under certain conditions.
Time-aware neural models improve system identification from unevenly sampled data.
problem Improving system identification from continuous variables with unevenly sampled time data.
method Introduced a time-aware and stationary extension of recurrent neural networks.
result Demonstrated improved performance on industrial input/output processes.
Adaptive step-size improves optimization in complex geometries.
problem Optimizing functions with non-Euclidean geometries.
method Adaptive step-size strategy for optimization algorithms.
result Guaranteed convergence for Adaptive Conditional Gradient Descent.
Negative step sizes improve second-order methods for neural networks.
problem Second-order methods discard negative curvature, limiting their effectiveness.
method Introduce negative step sizes in second-order methods combined with Wolfe line search.
result Negative step sizes lead to global convergence and improved performance.
New convergence results for NGVI with various step sizes and sample sizes.
problem Understanding convergence of stochastic NGVI for various schedules.
method Projected stochastic NGVI for exponential family variational distributions.
result Geometric convergence and $\mathcal{O}\left(\frac{1}{T^ρ}
ight)$ rates for different schedules.
New optimal step sizes and mini-batch sizes for SAGA.
problem Finding optimal step sizes and mini-batch sizes for SAGA.
method Provided closed-form expressions for expected smoothness constant and suggested new step sizes and mini-batch sizes.
result Total complexity of SAGA decreases linearly with mini-batch size up to an optimal value.
Maximal concentration bounds for stochastic approximation with heavy-tailed noise.
problem Analyzing the convergence of stochastic approximation algorithms under heavy-tailed Markovian noise.
method Novel Lyapunov function and black-box truncation argument.
result Tail behavior of the error can be sub-Gaussian, sub-Weibull, or lighter than any Pareto but heavier than any Weibull.
SGD converges to an invariant distribution with sub-Gaussian or sub-exponential properties.
problem Optimizing smooth and strongly convex objectives using SGD.
method Analysis through Markov chains, focusing on convergence and concentration properties.
result SGD iterates and their invariant limit distribution inherit sub-Gaussian or sub-exponential concentration properties.
Adaptive step-size method improves compressed SGD performance in machine learning.
problem Communication bottleneck in distributed and decentralized optimization.
method Developed an adaptive step-size method for compressed SGD.
result Order-optimal convergence rates for various objective functions.
StepGAN improves conditional sequence generation with less computation.
problem Stabilizing training of sequence generative adversarial networks (SeqGAN).
method Modified discriminator assigns scores at each generation step.
result StepGAN outperforms previous methods on synthetic and chit-chat tasks.
The practical performance of online stochastic gradient descent algorithms is highly dependent on the chosen step size, which must be tediously hand-tuned in many applications. The same is true for more advanced variants of stochastic gradients, such as SAGA, SVRG, or AdaGrad. Here we propose to adapt the step size by …
Paper analyzes symbolic-dynamics inspired Markov modeling for time-series data.
problem Capturing temporal patterns in sequential data for statistical learning.
method Two-step process: discretization of continuous attributes and estimation of temporal memory.
result Effective Markov modeling depends on accurate discretization and memory estimation.
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.