New technique reduces bias in CSO problems, improving sample complexity.
problem Reducing bias in conditional stochastic optimization problems.
method Introducing a stochastic extrapolation technique combined with variance reduction.
result Achieved significantly better sample complexity for nonconvex smooth objectives.
Estimates proportions of LLM-generated text in mixed documents.
problem Estimating the proportion of text generated by a pre-specified LLM in mixed documents.
method Developed estimators for two observation regimes: full observation and pivotal reduction, and established sample complexity bounds.
result Full observation estimators require fewer samples than pivotal reduction estimators.
Study on estimating Gumbel--Max watermark proportions in edited documents.
problem Estimating the proportion of a document generated from a watermarked LLM.
method Comparison of full observation and pivotal reduction observation regimes; development of estimators and information-theoretic lower bounds.
result Full observation yields a substantially smaller sample complexity compared to pivotal reduction.
Improved sample complexity for actor-critic algorithms in MDPs.
problem Achieving optimal policies with limited data in reinforcement learning.
method Single-timescale actor-critic with STORM (STOchastic Recursive Momentum) and a sample buffer.
result Optimal sample complexity of O(ε−2) for ε-optimal policies. New method reduces variance in stochastic optimization with high confidence.
problem Achieving high-probability guarantees in stochastic optimization with weaker noise assumptions.
method Stochastic proximal point method combining proximal subproblem solver and probability booster.
result Demonstrates convergence with low sample complexity under bounded variance assumptions.
VRCQ algorithm reduces variance in Q-learning for MDPs, achieving optimal sample complexity.
problem Estimating the optimal Q-function in MDPs with synchronous sampling.
method VRCQ combines direct variance reduction and Cascade Q-learning.
result VRCQ is minimax optimal and instance optimal for single-action problems.
Study finds that only a fraction of data is needed for accurate patient-level prediction models.
problem Developing predictive models for patient-level outcomes using large observational data.
method Empirical assessment of sample size effects on model performance and complexity using learning curves.
result A median reduction of 9.5% to 78.5% in the number of observations and 8.6% to 68.3% in the number of predictors can be achieved with adequate sample size.
VRER selectively reuses samples to improve policy optimization in complex systems.
problem Lack of effective reuse of historical samples in reinforcement learning.
method Variance reduction based experience replay (VRER) framework.
result VRER accelerates policy optimization and enhances performance.
Many machine learning problems, especially multi-modal learning problems, have two sets of distinct features (e.g., image and text features in news story classification, or neuroimaging data and neurocognitive data in cognitive science research). This paper addresses the joint dimensionality reduction of two feature ve…
This thesis explores fast algorithms for large matrices and data augmentation to improve model efficiency.
problem Efficient handling of large models and data in scientific computing and machine learning.
method Randomized low-rank decomposition algorithms and data augmentation techniques.
result Improved sample efficiency and generalization of machine learning models.
Asynchronous Q-learning achieves optimal Q-function estimation with reduced sample complexity.
problem Learning the optimal Q-function in asynchronous Q-learning with limited samples.
method Demonstrates sample complexity bound with variance reduction for γ-discounted MDPs. result Sample complexity improved by a factor of ∣S∣∣A∣ and tmix∣S∣∣A∣. New RL algorithm reduces sample complexity for optimal learning.
problem Achieving optimal learning with minimal samples in RL.
method Early-settled variance reduction method with Q-learning sequences.
result Near-optimal regret achieved with sample size SApoly(H). New algorithm reduces offline RL data requirements significantly.
problem Optimizing policies using only historical data in reinforcement learning.
method Off-Policy Double Variance Reduction (OPDVR) algorithm.
result OPDVR achieves optimal sample complexity with O(H2/dmε2) episodes. Sparse random projection (RP) is a popular tool for dimensionality reduction that shows promising performance with low computational complexity. However, in the existing sparse RP matrices, the positions of non-zero entries are usually randomly selected. Although they adopt uniform sampling with replacement, due to lar…
SPCA improves PCA by learning from simple to complex samples.
problem Noise and outliers in complex data.
method Self-paced Principal Component Analysis (SPCA) that integrates samples from simple to more complex.
result SPCA improves state-of-the-art results on popular datasets.
A/B testing improves marketing decisions by selecting effective stratification variables.
problem Improving the sensitivity of A/B testing through stratified sampling.
method Designing an algorithm to select a subset of stratification variables for variance reduction.
result The subset selection method outperforms other variance reduction techniques in A/B testing.
Efficiently reduces rank of non-negative matrices with quadratic time complexity.
problem Efficiently reducing the rank of non-negative matrices.
method Formulated rank reduction as a mean-field approximation using a log-linear model.
result Optimal solution for minimizing KL divergence can be computed in closed form.
Variance reduction is a simple and effective technique that accelerates convex (or non-convex) stochastic optimization. Among existing variance reduction methods, SVRG and SAGA adopt unbiased gradient estimators and are the most popular variance reduction methods in recent years. Although various accelerated variants o…
SPREV simplifies visualization of complex labeled datasets.
problem Challenges of reducing dimensions and visualizing labeled datasets with small class size, high dimensionality, and low sample size.
method SPREV uses a novel dimensionality reduction technique integrating geometric principles.
result SPREV effectively visualizes hidden patterns in complex labeled datasets.
Pessimistic Q-learning improves sample efficiency in offline reinforcement learning.
problem Insufficient coverage and sample scarcity in offline reinforcement learning datasets.
method Pessimistic Q-learning algorithm for offline reinforcement learning, focusing on variance reduction.
result Near-optimal sample complexity achieved with the proposed algorithm.
New method reduces sample complexity for learning Ising model dynamics exponentially.
problem Learning binary graphical models from correlated samples produced by a dynamical process.
method Two estimators based on interaction screening objective and conditional likelihood loss.
result Sample complexity reduces exponentially for samples from a dynamical process far from equilibrium.
ULA estimates covariance of log-concave distributions efficiently.
problem Estimating covariance matrices of log-concave distributions efficiently.
method Unadjusted Langevin algorithm (ULA) for sampling and covariance estimation.
result Sample complexity of single-chain ULA is smaller than that of parallel ULA by a logarithmic factor.
In this work we present novel differentially private identity (goodness-of-fit) testers for natural and widely studied classes of multivariate product distributions: Gaussians in Rd with known covariance and product distributions over {±1}d. Our testers have improved sample complexity compared to …
Derivative-free optimization has become an important technique used in machine learning for optimizing black-box models. To conduct updates without explicitly computing gradient, most current approaches iteratively sample a random search direction from Gaussian distribution and compute the estimated gradient along that…
Stochastic particle-optimization sampling (SPOS) is a recently-developed scalable Bayesian sampling framework that unifies stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) algorithms based on Wasserstein gradient flows. With a rigorous non-asymptotic convergence theory developed recently…
Study shows sample complexity for multicalibration is Θ(ε^-3) with polylogarithmic factors.
problem Minimizing Expected Calibration Error (ECE) for predictors with respect to a family of groups.
method Proved necessary and sufficient sample complexity of Θ(ε^-3) for multicalibration, using online-to-batch reduction and lower bounds.
result Sample complexity of multicalibration is Θ(ε^-3) with polylogarithmic factors, distinguishing it from marginal calibration.
In the Best-k-Arm problem, we are given n stochastic bandit arms, each associated with an unknown reward distribution. We are required to identify the k arms with the largest means by taking as few samples as possible. In this paper, we make progress towards a complete characterization of the instance-wise sample…
The principal support vector machines method (Li et al., 2011) is a powerful tool for sufficient dimension reduction that replaces original predictors with their low-dimensional linear combinations without loss of information. However, the computational burden of the principal support vector machines method constrains …
A new method for reducing model complexity using neural active manifolds.
problem Uncertainty quantification in computationally expensive models.
method Autoencoders and surrogate models to discover a neural active manifold.
result Neural active manifolds reduce model variance in multifidelity sampling.
This paper bridges offline and online RL by studying policy finetuning with a reference policy.
problem Sample-efficient reinforcement learning in online and offline settings.
method Design of policy finetuning algorithms and analysis of sample complexity.
result Theoretical analysis shows that the optimal policy finetuning algorithm is either offline reduction or purely online RL.
Adapts DR objectives for both sample and feature size reduction.
problem Simultaneously reduce sample and feature sizes.
method Semi-relaxed Gromov-Wasserstein optimal transport.
result OT plan delivers competitive hard clustering.
We propose a new yet natural algorithm for learning the graph structure of general discrete graphical models (a.k.a. Markov random fields) from samples. Our algorithm finds the neighborhood of a node by sequentially adding nodes that produce the largest reduction in empirical conditional entropy; it is greedy in the se…
Improved diffusion models for generative tasks without dimensionality constraints.
problem Sample complexity bounds for learning score functions in diffusion models.
method Dimension-free sample complexity bounds, martingale-based error decomposition, variance reduction technique (Bootstrapped Score Matching).
result Achieved a double exponential improvement in sample complexity over prior results.
GenSDR tackles SDR by leveraging generative models to fully recover lower-dimensional structures.
problem Challenges in identifying low-dimensional sufficient structures in nonlinear SDR.
method Proposes GenSDR, a method that uses modern generative models to fully recover information in the central σ-field.
result Establishes consistency of GenSDR estimator for sample-level data and extends its applicability to non-Euclidean responses.
We consider multi-level composite optimization problems where each mapping in the composition is the expectation over a family of random smooth mappings or the sum of some finite number of smooth mappings. We present a normalized proximal approximate gradient (NPAG) method where the approximate gradients are obtained v…
New algorithms reduce complexity for solving nonconvex optimization problems with stochastic objectives and constraints.
problem Solving nonconvex optimization problems with stochastic objectives and constraints.
method Single-loop quadratic penalty and augmented Lagrangian algorithms with variance reduction techniques.
result Achieved best-known complexity guarantees for solving nonconvex optimization problems with stochastic objectives and constraints.
Temporal difference (TD) learning is a popular algorithm for policy evaluation in reinforcement learning, but the vanilla TD can substantially suffer from the inherent optimization variance. A variance reduced TD (VRTD) algorithm was proposed by Korda and La (2015), which applies the variance reduction technique direct…
Cubic regularization (CR) is an optimization method with emerging popularity due to its capability to escape saddle points and converge to second-order stationary solutions for nonconvex optimization. However, CR encounters a high sample complexity issue for finite-sum problems with a large data size. %Various inexact …
This work simplifies Gaussian process regression for multiple outputs.
problem Exponential computational complexity in Gaussian process regression.
method Approximating the covariance kernel using eigenvalues and functions.
result Significant reduction in training and regression complexity.
Through the lens of information-theoretic reductions, we examine a reductions approach to fair optimization and learning where a black-box optimizer is used to learn a fair model for classification or regression. Quantifying the complexity, both statistically and computationally, of making such models satisfy the rigor…
New algorithms learn robust policies from shifted distributions.
problem Learning robust policies in environments with distributional shifts.
method Two novel model-free algorithms: distributionally robust Q-learning and variance-reduced distributionally robust Q-learning.
result Achieves minimax sample complexity upper bound of ildeO(∣S∣∣A∣(1−γ)−4ε−2). New framework allows reinforcement learning with polynomial sample complexity.
problem Generalization in reinforcement learning with function approximation.
method Introduces Bilinear Classes, a structural framework for RL.
result Polynomial sample complexity for Bilinear Classes, matching best known bounds.
Reduced sample complexity for group-invariant distributions.
problem Improving sample complexity for estimating divergences of group-invariant distributions.
method Quantified reduction in sample complexity for Wasserstein-1 metric and Lipschitz-regularized α-divergences under finite and infinite groups.
result Sample complexity reduction proportional to group size for finite groups, and convergence rate depends on intrinsic dimension for infinite groups.
Paper proposes a method to estimate variance reduction in DNN training using importance sampling.
problem Challenges in assessing variance reduction during DNN training using importance sampling.
method Proposes a method for estimating variance reduction using minibatches sampled under importance sampling.
result Demonstrates consistent reduction in variance, improved training efficiency, and enhanced model accuracy.
Spectral dimensionality reduction methods enable linear separations of complex data with high-dimensional features in a reduced space. However, these methods do not always give the desired results due to irregularities or uncertainties of the data. Thus, we consider aggressively modifying the scales of the features to …
Improved stochastic optimization outperforms standard methods.
problem Optimizing smooth, strongly convex functions with noisy data.
method Variance reduction strategy called VISOR.
result VISOR achieves optimal sample complexity and oracle complexity.
Reduces identity testing of reversible Markov chains to simpler symmetric chain tests.
problem Testing identity of reversible Markov chains from a single trajectory.
method Using lumping-congruent Markov embeddings, the problem is simplified to testing symmetric chains over a larger state space.
result Achieves state-of-the-art sample complexity for identity testing.
We propose a sample efficient stochastic variance-reduced cubic regularization (Lite-SVRC) algorithm for finding the local minimum efficiently in nonconvex optimization. The proposed algorithm achieves a lower sample complexity of Hessian matrix computation than existing cubic regularization based methods. At the heart…