StochAstic Recursive grAdient algoritHm (SARAH), originally proposed for convex optimization and also proven to be effective for general nonconvex optimization, has received great attention due to its simple recursive framework for updating stochastic gradient estimates. The performance of SARAH significantly depends o…
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48 results for “SARAH algorithm”
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 functions over a network.
method Stochastic first-order gradient method with SARAH variance reduction and gradient tracking.
result Achieves -accurate first-order stationary point with improved gradient complexity.
The main theme of this work is a unifying algorithm, \textbf{L}oop\textbf{L}ess \textbf{S}ARAH (L2S) for problems formulated as summation of individual loss functions. L2S broadens a recently developed variance reduction method known as SARAH. To find an -accurate solution, L2S enjoys a complexity of ${\cal O}\b…
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 has been proven to be at least for $n \leq …
The variance reduction class of algorithms including the representative ones, SVRG and SARAH, have well documented merits for empirical risk minimization problems. However, they require grid search to tune parameters (step size and the number of iterations per inner loop) for optimal performance. This work introduces `…
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.
Adaptivity is an important yet under-studied property in modern optimization theory. The gap between the state-of-the-art theory and the current practice is striking in that algorithms with desirable theoretical guarantees typically involve drastically different settings of hyperparameters, such as step-size schemes an…
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…
The main goal of this work is equipping convex and nonconvex problems with Barzilai-Borwein (BB) step size. With the adaptivity of BB step sizes granted, they can fail when the objective function is not strongly convex. To overcome this challenge, the key idea here is to bridge (non)convex problems and strongly convex …
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.
There is growing interest in large-scale machine learning and optimization over decentralized networks, e.g. in the context of multi-agent learning and federated learning. Due to the imminent need to alleviate the communication burden, the investigation of communication-efficient distributed optimization algorithms - p…
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 sample complexity, matching best-known rate.
Variance-reduced algorithms, although achieve great theoretical performance, can run slowly in practice due to the periodic gradient estimation with a large batch of data. Batch-size adaptation thus arises as a promising approach to accelerate such algorithms. However, existing schemes either apply prescribed batch-siz…
We develop two new stochastic Gauss-Newton algorithms for solving a class of non-convex stochastic compositional optimization problems frequently arising in practice. We consider both the expectation and finite-sum settings under standard assumptions, and use both classical stochastic and SARAH estimators for approxima…
We introduce a hybrid stochastic estimator to design stochastic gradient algorithms for solving stochastic optimization problems. Such a hybrid estimator is a convex combination of two existing biased and unbiased estimators and leads to some useful property on its variance. We limit our consideration to a hybrid SARAH…
Stochastic Recursive Variance Reduction for Efficient Smooth Non-Convex Compositional Optimizationstat.ML
Stochastic compositional optimization arises in many important machine learning tasks such as value function evaluation in reinforcement learning and portfolio management. The objective function is the composition of two expectations of stochastic functions, and is more challenging to optimize than vanilla stochastic o…
Sarah Frank-Wolfe: Methods for Constrained Optimization with Best Rates and Practical Featuresmath.OC
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.
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.
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…
ProxSARAH: An Efficient Algorithmic Framework for Stochastic Composite Nonconvex Optimizationmath.OC
We propose a new stochastic first-order algorithmic framework to solve stochastic composite nonconvex optimization problems that covers both finite-sum and expectation settings. Our algorithms rely on the SARAH estimator introduced in (Nguyen et al, 2017) and consist of two steps: a proximal gradient and an averaging s…
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.
Two types of zeroth-order stochastic algorithms have recently been designed for nonconvex optimization respectively based on the first-order techniques SVRG and SARAH/SPIDER. This paper addresses several important issues that are still open in these methods. First, all existing SVRG-type zeroth-order algorithms suffer …
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 -approximate local minima within evaluations.
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.
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 convergence rates, improving upon non-accelerated counterparts.
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 and convergence rates on the expected squared norm of the FBS residual.
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 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 for -stationary solutions.
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.
Examines algorithmic modeling across three cultures.
problem Tackles algorithmic modeling in different cultural contexts.
method Uses parametric regressions, interpretable algorithms, and complex algorithms.
result Extension of Leo Breiman's thesis to include cultural differences.
Playing repeated matrix games (RMG) while maximizing the cumulative returns is a basic method to evaluate multi-agent learning (MAL) algorithms. Previous work has shown that , , or algorithms have good behaviours on average in RMG. Besides, hedging algorithms have been shown to be effective on predi…
Meta-algorithm selection aims to choose the best algorithm selector for a given problem instance.
problem Selecting the best algorithm selector for a specific problem instance.
method Apply algorithm selection to the selection of other algorithms (meta-algorithm selection).
result Meta-algorithm selection can be beneficial in some cases but faces challenges in solving the meta-level problem.
Proposes CLRS benchmark to evaluate algorithmic reasoning.
problem Difficulty in transferring results across publications due to targeted algorithmic data.
method Develops a comprehensive benchmark covering various algorithmic tasks.
result Demonstrates performance of algorithmic reasoning baselines on the CLRS benchmark.
Combines multiple bandit algorithms to create a nearly optimal single algorithm.
problem Designing a single bandit algorithm that performs nearly as well as the best individual algorithm in a stochastic environment.
method Develops two general corralling algorithms that achieve favorable regret guarantees.
result The regret of the corralling algorithms is no worse than the best individual algorithm's performance.
Accelerated Randomized Coordinate Descent Algorithms for Stochastic Optimization and Online Learningcs.LG
We propose accelerated randomized coordinate descent algorithms for stochastic optimization and online learning. Our algorithms have significantly less per-iteration complexity than the known accelerated gradient algorithms. The proposed algorithms for online learning have better regret performance than the known rando…
The exchange algorithm is studied for its convergence and asymptotic variance.
problem Theoretical limitations of the exchange algorithm in sampling from doubly-intractable distributions.
method Theoretical analysis of the exchange algorithm's convergence speed and asymptotic variance.
result The exchange algorithm converges at a geometric rate and satisfies a Central Limit Theorem.
Bayesian networks (BN) are used in a big range of applications but they have one issue concerning parameter learning. In real application, training data are always incomplete or some nodes are hidden. To deal with this problem many learning parameter algorithms are suggested foreground EM, Gibbs sampling and RBE algori…
No algorithm outperforms uniform sampling in A/B testing.
problem Identifying the best arm in A/B testing with fixed budget.
method Introducing consistent and stable algorithms, deriving lower bounds, and proving optimality of uniform sampling.
result No algorithm performs better than uniform sampling in A/B testing.
This review article surveys data augmentation MCMC algorithms.
problem Sampling from intractable probability distributions.
method Comprehensive study of DA MCMC algorithms, their convergence properties, and acceleration strategies.
result Synthesizes recent developments and provides insights for researchers.
The Bayesian Learning Rulestat.ML
Bayesian learning rule unifies and generalizes various machine learning algorithms.
problem Machine learning algorithms are diverse and not always understood.
method Bayesian principles and natural gradients are used to derive algorithms.
result Derives a wide range of algorithms including classical and modern ones.
Learning to Optimizecs.LG
Algorithm design is a laborious process and often requires many iterations of ideation and validation. In this paper, we explore automating algorithm design and present a method to learn an optimization algorithm, which we believe to be the first method that can automatically discover a better algorithm. We approach th…
This review summarizes five Lasso optimization algorithms.
problem Optimizing the Lasso objective function.
method Five representative algorithms: ISTA, FISTA, CGDA, SLA, PFA.
result Comparison of convergence rates and strengths/weaknesses.
Neural networks mimic algorithms to solve complex problems.
problem Current machine learning methods struggle with generalisation and efficiency.
method Representing algorithms in a continuous space and adapting them to real-world problems.
result Neural networks can execute classical algorithms more efficiently.
Paper proposes a reinforcement learning framework for efficient hyper-parameter tuning of stochastic optimization algorithms.
problem Efficient tuning of hyper-parameters for stochastic optimization algorithms.
method Modeling hyper-parameter tuning as a Markov decision process and using policy gradient algorithms.
result The proposed framework significantly reduces the time required for hyper-parameter tuning compared to Bayesian optimization.
In this paper, we propose a convergent parallel best-response algorithm with the exact line search for the nondifferentiable nonconvex sparsity-regularized rank minimization problem. On the one hand, it exhibits a faster convergence than subgradient algorithms and block coordinate descent algorithms. On the other hand,…