L2S unifies SARAH for sum of losses with improved convergence.
problem Finding accurate solutions to problems with multiple loss functions.
method Loop-less SARAH (L2S) for sum of losses, with improved complexity and step sizes.
result L2S achieves better generalization properties and faster convergence in neural networks.
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.
In this paper, we propose a StochAstic Recursive grAdient algoritHm (SARAH), as well as its practical variant SARAH+, as a novel approach to the finite-sum minimization problems. Different from the vanilla SGD and other modern stochastic methods such as SVRG, S2GD, SAG and SAGA, SARAH admits a simple recursive framewor…
Paper develops probabilistic bounds for a stochastic gradient algorithm in non-convex problems.
problem Stochastic optimization in non-convex finite sum problems.
method Develops a new dimension-free Azuma-Hoeffding type bound for a martingale difference sequence.
result Empirical results show superior probabilistic performance of Prob-SARAH compared to other algorithms.
GT-SARAH optimizes decentralized non-convex problems with recursive variance reduction.
problem Decentralized non-convex optimization of N N N functions over a network. method Stochastic first-order gradient method with SARAH variance reduction and gradient tracking.
result Achieves ε ε ε -accurate first-order stationary point with improved gradient complexity. 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.
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.
New algorithm adapts to optimize non-convex problems efficiently.
problem Inefficient hyperparameter tuning in existing optimization methods.
method Combining geometrization and SARAH algorithms.
result Achieves adaptivity to both accuracy and PL constant.
The total complexity (measured as the total number of gradient computations) of a stochastic first-order optimization algorithm that finds a first-order stationary point of a finite-sum smooth nonconvex objective function F ( w ) = 1 n ∑ i = 1 n f i ( w ) F(w)=\frac{1}{n} \sum_{i=1}^n f_i(w) F ( w ) = n 1 ∑ i = 1 n f i ( w ) has been proven to be at least Ω ( n / ε ) Ω(\sqrt{n}/ε) Ω ( n / ε ) for $n \leq …
A new hybrid algorithm reduces stochastic gradient evaluations for nonconvex optimization.
problem Solving stochastic composite nonconvex optimization problems efficiently.
method Proposes a new hybrid variance-reduced proximal gradient method with a stochastic gradient estimator.
result Achieves optimal stochastic oracle complexity bound with one less gradient evaluation.
Optimizes bilevel empirical risk minimization with improved oracle calls.
problem Optimizing bilevel empirical risk minimization problems.
method Proposes a bilevel extension of the SARAH algorithm.
result Demonstrates improved oracle calls to achieve stationarity.
New algorithm reduces complexity for optimizing complex machine learning tasks.
problem Optimizing complex machine learning objectives like reinforcement learning and portfolio management.
method Developed SARAH-Compositional algorithm using Stochastic Recursive Gradient Descent.
result Achieved optimal IFO complexity bounds for stochastic compositional optimization.
New scheme adapts batch size for faster variance-reduced algorithms.
problem Slowness of variance-reduced algorithms due to large batch size.
method Eliminates backtracking line search, adapts batch size via history stochastic gradients.
result Significantly reduces overall complexity for SVRG and SARAH/SPIDER.
In this paper, we study and analyze the mini-batch version of StochAstic Recursive grAdient algoritHm (SARAH), a method employing the stochastic recursive gradient, for solving empirical loss minimization for the case of nonconvex losses. We provide a sublinear convergence rate (to stationary points) for general noncon…
A new algorithm SRG-DQN reduces variance in deep Q-learning.
problem Inaccurate estimation of anchor points in SVRG for deep Q-learning.
method Introduces recursive gradient variance reduction for stochastic gradient updates.
result Demonstrates improved efficiency and effectiveness of SRG-DQN on reinforcement learning tasks.
New algorithm framework solves stochastic composite nonconvex optimization problems efficiently.
problem Solving stochastic composite nonconvex optimization problems.
method ProxSARAH framework using SARAH estimator with proximal gradient and averaging steps.
result Achieves best-known complexity bounds with constant and adaptive step-sizes.
This paper develops efficient decentralized optimization methods for large-scale machine learning.
problem Efficient distributed optimization over networks with reduced communication.
method Develops communication-efficient approximate Newton-type methods for decentralized optimization.
result Establishes linear convergence for various optimization problems.
STORM-PG uses momentum for faster policy gradient updates.
problem Improving policy gradient methods for reinforcement learning.
method Introduces STORM-PG, a SARAH-based algorithm with exponential moving average.
result Achieves O ( 1 / ε 3 ) O(1/ε^3) O ( 1/ ε 3 ) sample complexity, matching best-known rate. New algorithms solve non-convex optimization problems efficiently.
problem Non-convex stochastic compositional optimization problems.
method Developed two stochastic Gauss-Newton algorithms.
result Established global oracle complexity for stochastic Gauss-Newton methods.
Paper proposes faster method to find local minima in nonconvex optimization.
problem Escaping saddle points and finding local minima in nonconvex optimization.
method LENA (Last stEp shriNkAge) framework for faster perturbed stochastic gradient methods.
result LENA finds ( ε , ε H ) (ε, ε_{H}) ( ε , ε H ) -approximate local minima within i l d e O ( ε − 3 + ε H − 6 ) ilde O(ε^{-3} + ε_{H}^{-6}) i l d e O ( ε − 3 + ε H − 6 ) evaluations. Two new Frank-Wolfe algorithms improve convergence for constrained optimization.
problem Solving optimization problems with structured constraints in machine learning.
method Two new variants of the Frank-Wolfe (FW) method for stochastic finite-sum minimization.
result Best convergence guarantees for convex and non-convex objective functions.
The paper models financial correlation matrices using permutation invariant Gaussian models and predicts market anomalies.
problem Modeling and predicting financial correlation matrices from high-frequency data.
method Constructing permutation invariant Gaussian matrix models with 4 parameters, using graph theory and polynomial functions.
result The permutation invariant Gaussian matrix model predicts the expectation values of cubic and quartic polynomials with strong evidence of fit.
SARAH and SPIDER are two recently developed stochastic variance-reduced algorithms, and SPIDER has been shown to achieve a near-optimal first-order oracle complexity in smooth nonconvex optimization. However, SPIDER uses an accuracy-dependent stepsize that slows down the convergence in practice, and cannot handle objec…
SRG improves optimization efficiency with reduced memory and computation overhead.
problem Limited applicability of variance-reduced optimization algorithms.
method SRG (stochastic reweighted gradient) using importance sampling.
result SRG outperforms SGD and provably improves convergence in strongly-convex cases.
LaPSRL achieves optimal regret for isoperimetric RL distributions.
problem Designing RL algorithms with sublinear regret for non-log-concave distributions.
method Posterior Sampling (PSRL) and Langevin sampling (LaPSRL) for isoperimetric distributions.
result LaPSRL achieves order-optimal regret and subquadratic complexity.
New lower bounds for gradient methods in strongly convex finite-sum optimization.
problem Developing tight lower bounds for randomized gradient methods in finite-sum optimization.
method Deriving tight lower complexity bounds for SAG, SAGA, SVRG, SARAH, and related methods.
result Tight matches between lower bounds and upper bounds for various methods under specific conditions.
New hybrid SGD algorithms improve stochastic nonconvex optimization complexity.
problem Solving stochastic nonconvex optimization problems efficiently.
method Hybrid SARAH-SGD algorithm combining biased and unbiased estimators.
result Achieves better complexity bound for ε \varepsilon ε -stationary points. Develops an accelerated algorithm for solving nonmonotone generalized equations.
problem Solving nonmonotone generalized equations with possibly non-accelerated schemes.
method Combines Nesterov's acceleration and variance-reduction techniques for a class of generalized equations.
result Achieves O ( 1 / k 2 ) \mathcal{O}(1/k^2) O ( 1/ k 2 ) convergence rates, improving upon non-accelerated counterparts. New HMC framework reduces variance for sampling from log-concave distributions.
problem Efficient sampling from log-concave distributions with high precision.
method Unified formulation of biased and unbiased variance reduction methods for HMC.
result Unbiased and biased gradient estimators achieve different gradient complexities and accuracy.
Improved zeroth-order algorithms for nonconvex optimization with reduced complexity and improved performance.
problem Designing efficient zeroth-order algorithms for nonconvex optimization with reduced function query complexities and improved convergence rates.
method Proposed new algorithms ZO-SVRG-Coord-Rand and ZO-SPIDER-Coord, developed new analyses, and addressed issues of function query complexities and stepsize generation.
result New algorithms outperform existing methods in terms of function query complexities and convergence rates.
Improved optimization technique reduces training complexity for non-convex problems.
problem Training non-convex optimization problems with exploding gradients.
method Employed variance reduction technique (SPIDER) with carefully designed learning rate.
result Improved stochastic gradient complexity to O ( ε − 3 ) O(ε^{-3}) O ( ε − 3 ) for ε ε ε -stationary solutions. Develops variance-reduced methods for solving generalized equations.
problem Solving a class of generalized equations, including minimization, minimax, and variational inequalities.
method Integrates accelerated operator splitting, fixed-point methods, and variance reduction techniques.
result Achieves both O ( 1 / k 2 ) \mathcal{O}(1/k^2) O ( 1/ k 2 ) and o ( 1 / k 2 ) o(1/k^2) o ( 1/ k 2 ) convergence rates on the expected squared norm of the FBS residual. New variance-reduction methods solve stochastic composite inclusions.
problem Solving nonmonotone stochastic composite inclusions.
method Developed unbiased and biased variance-reduced estimators for FRBS method.
result Achieved best oracle complexities for finite-sum and expectation settings.