arXiv research

VISA improves inference efficiency for complex models.

SAA method solves insurance portfolio optimization with CVaR constraints.

Novel approach simplifies VI problems with faster performance.

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

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…

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, …

Optimal algorithms for Riemannian optimization with reduced complexity.

New method approximates CVaR with less data for heavy-tailed risks.

The paper improves Monte Carlo methods for optimization problems.

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

Improved stochastic optimization outperforms standard methods.

New method reduces sample complexity for robust reinforcement learning.

In this work, we propose a smart idea to couple importance sampling and Multilevel Monte Carlo (MLMC). We advocate a per level approach with as many importance sampling parameters as the number of levels, which enables us to compute the different levels independently. The search for parameters is carried out using samp…

Paper improves TD(0) convergence rate with LFA, i.i.d. samples, and averaging.

We show that the sets in a family with finite VC dimension can be uniformly approximated within a given error by a finite partition. Immediate corollaries include the fact that VC classes have finite bracketing numbers, satisfy uniform laws of averages under strong dependence, and exhibit uniform mixing. Our results ar…

The paper studies the convergence of SAA for systemic risk measures.

Paper introduces DOO models to outperform SAA out-of-sample.

New methods optimize functions faster with less gradient accuracy needed.

This article revisits an analysis on inaccuracies of time series averaging under dynamic time warping conducted by \cite{Niennattrakul2007}. The authors presented a correctness-criterion and introduced drift-outs of averages from clusters. They claimed that averages are inaccurate if they are incorrect or drift-outs. F…

New Q-learning method achieves optimal sample complexity for average-reward problems.

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

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

The paper improves error bounds for Bayesian quadrature in noisy settings.

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

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…

Learning latent variable models with stochastic variational inference is challenging when the approximate posterior is far from the true posterior, due to high variance in the gradient estimates. We propose a novel rejection sampling step that discards samples from the variational posterior which are assigned low likel…

New algorithm LOOP learns infinite-horizon AMDPs efficiently with function approximation.

Improved predictive posterior density estimation through optimized importance sampling.

Deviation inequalities for stochastic approximation methods.

Develops a method for learning proposals in nested importance samplers.

MCRapper efficiently computes patterns in data using Monte-Carlo Rademacher Averages.

Let F be a family of Borel measurable functions on a complete separable metric space. The gap (or fat-shattering) dimension of F is a combinatorial quantity that measures the extent to which functions f in F can separate finite sets of points at a predefined resolution gamma > 0. We establish a connection between the g…

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…

The paper analyzes risk estimation methods and derives bounds for OCE risk.

Adaptive importance sampling techniques are widely known for the Gaussian setting of Brownian driven diffusions. In this work, we want to extend them to jump processes. Our approach relies on a change of the jump intensity combined with the standard exponential tilting for the Brownian motion. The free parameters of ou…

While it's always possible to compute a variational approximation to a posterior distribution, it can be difficult to discover problems with this approximation. We propose two diagnostic algorithms to alleviate this problem. The Pareto-smoothed importance sampling (PSIS) diagnostic gives a goodness of fit measurement f…

This paper introduces time-uniform CLT-based confidence intervals for statistical inference.

Hierarchical GANs reduce anomaly detection costs.

SIFT reduces training time by selecting samples with approximate losses.

In this paper, we propose a novel policy iteration method, called dynamic policy programming (DPP), to estimate the optimal policy in the infinite-horizon Markov decision processes. We prove the finite-iteration and asymptotic l\infty-norm performance-loss bounds for DPP in the presence of approximation/estimation erro…

We propose SWA-Gaussian (SWAG), a simple, scalable, and general purpose approach for uncertainty representation and calibration in deep learning. Stochastic Weight Averaging (SWA), which computes the first moment of stochastic gradient descent (SGD) iterates with a modified learning rate schedule, has recently been sho…

New sampling method guarantees approximate first-order stationary points for non-convex functions.

Paper analyzes NAC with neural networks for efficient policy optimization.

A new method for exponentially weighted moving models using approximations.

Paper develops bounds for stochastic approximation with averaging.

The paper sets lower bounds for sampling non-log-concave distributions using Fisher information.

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 …

Taking advantage of the recent litterature on exact simulation algorithms (Beskos, Papaspiliopoulos and Roberts) and unbiased estimation of the expectation of certain fonctional integrals (Wagner, Beskos et al. and Fearnhead et al.), we apply an exact simulation based technique for pricing continuous arithmetic average…