arXiv research

Deviation inequalities for stochastic approximation methods.

New method assesses financial and cyber risks under uncertainty.

Paper develops bounds for stochastic approximation with averaging.

This work analyzes nonexpansive stochastic approximations with Markovian noise, proving convergence in reinforcement learning.

Optimal algorithms for Riemannian optimization with reduced complexity.

Paper uses averaging from many particle filters to approximate posterior predictive distributions.

The paper develops time-uniform inference methods for stochastic approximation parameters.

Study on stochastic approximation with Polyak-Ruppert averaging for linear systems.

Paper analyzes normal approximation for two-timescale stochastic algorithms, revealing interaction between fast and slow timescales.

Paper approximates risk measures using SGD with Langevin dynamics.

Paper improves confidence intervals for LSA with multiplier bootstrap.

Novel approach simplifies VI problems with faster performance.

Improved stochastic Halpern iteration for fixed-point approximation in normed spaces.

New streaming methods improve convergence rates for optimization problems.

Stochastic algo learns from evolving data, achieving optimal performance.

Improved stochastic optimization outperforms standard methods.

Paper improves CLT and bootstrap approximations for LSA with decreasing step size.

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…

Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a Markov chain with a stationary distribution. With this perspective, we derive several new results. (1) We show that constant SGD can be used as an approximate Bayesian posterior inference algorithm. Specifically, we show how to adjust …

The paper offers precise bounds for averaged LSA iterates in linear systems.

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, …

We propose an explicit recursive method to approximate a power-law with a finite sum of weighted exponentials. Applications to moving averages with long memory are discussed in relationship with stochastic volatility models.

Study improves accuracy of risk measures using advanced algorithms.

We propose Stochastic Weight Averaging in Parallel (SWAP), an algorithm to accelerate DNN training. Our algorithm uses large mini-batches to compute an approximate solution quickly and then refines it by averaging the weights of multiple models computed independently and in parallel. The resulting models generalize equ…

Study on bias of constant-step stochastic approximation with Markovian noise.

This work characterizes the benefits of averaging schemes widely used in conjunction with stochastic gradient descent (SGD). In particular, this work provides a sharp analysis of: (1) mini-batching, a method of averaging many samples of a stochastic gradient to both reduce the variance of the stochastic gradient estima…

Study on SA with heavy-tailed and LRD noise, establishing finite-time bounds.

We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion is given by an averaged ordinary differential equation. We then demonstrate that…

Study integrates machine learning with SAA for optimizing decisions based on uncertain parameters and covariates.

In the machine learning and optimization community, there are two main approaches for the convex risk minimization problem, namely, the Stochastic Approximation (SA) and the Sample Average Approximation (SAA). In terms of oracle complexity (required number of stochastic gradient evaluations), both approaches are consid…

Two-Tailed Averaging improves generalization by optimizing the number of leading iterates to ignore.

Averaged SGD achieves optimal convergence rate for neural networks in the NTK regime.

The paper studies efficient simulation methods for financial firm values under fast mean-reverting volatility.

A new TS-SA method alleviates non-stationarity in TS algorithms for bandits.

Develops first-order methods for average-reward MDPs with strong guarantees.

This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their applicability remains limited when the problem dimension is large and the projecti…

Improving optimization for iterate-averaged language models

Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient descent, using Monte Carlo approximation for the gradients. This enables variatio…

Paper derives convergence rates and confidence intervals for LSA with Markovian noise.

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…

Study optimal and instance-dependent guarantees for solving linear equations with Markovian data.

GACTGAN synthesizes tabular data better with less computational overhead.

We highlight a pitfall when applying stochastic variational inference to general Bayesian networks. For global random variables approximated by an exponential family distribution, natural gradient steps, commonly starting from a unit length step size, are averaged to convergence. This useful insight into the scaling of…

DASA speeds up SA with delayed agents, achieving N-fold speedup.

The study examines how averaging data improves model performance.

Derives error bounds for stochastic iterative algorithms using Stein's method.

Distributed data-parallel algorithms aim to accelerate the training of deep neural networks by parallelizing the computation of large mini-batch gradient updates across multiple nodes. Approaches that synchronize nodes using exact distributed averaging (e.g., via AllReduce) are sensitive to stragglers and communication…

New method reduces sample complexity for robust reinforcement learning.