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Tag: optimal

  • Near-Optimal Sample Complexity for Online Constrained MDPs

    Near-Optimal Sample Complexity for Online Constrained MDPs arXiv:2602.15076v1 Announce Type: cross Abstract: Safety is a fundamental challenge in reinforcement learning (RL), particularly in real-world applications such as autonomous driving, robotics, and healthcare. To address this, Constrained Markov Decision Processes (CMDPs) are commonly used to enforce safety constraints while optimizing performance. However, existing methods often suffer…

  • First Provably Optimal Asynchronous SGD for Homogeneous and Heterogeneous Data

    First Provably Optimal Asynchronous SGD for Homogeneous and Heterogeneous Data arXiv:2601.02523v1 Announce Type: cross Abstract: Artificial intelligence has advanced rapidly through large neural networks trained on massive datasets using thousands of GPUs or TPUs. Such training can occupy entire data centers for weeks and requires enormous computational and energy resources. Yet the optimization algorithms behind…

  • Sharp Structure-Agnostic Lower Bounds for General Functional Estimation

    Sharp Structure-Agnostic Lower Bounds for General Functional Estimation arXiv:2512.17341v1 Announce Type: new Abstract: The design of efficient nonparametric estimators has long been a central problem in statistics, machine learning, and decision making. Classical optimal procedures often rely on strong structural assumptions, which can be misspecified in practice and complicate deployment. This limitation has sparked growing…

  • Estimation of Stochastic Optimal Transport Maps

    Estimation of Stochastic Optimal Transport Maps arXiv:2512.09499v1 Announce Type: new Abstract: The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing statistical theory for OT map estimation is quite restricted, hinging on Brenier’s theorem (quadratic cost,…

  • On the Equivalence of Optimal Transport Problem and Action Matching with Optimal Vector Fields

    On the Equivalence of Optimal Transport Problem and Action Matching with Optimal Vector Fields arXiv:2510.27385v1 Announce Type: new Abstract: Flow Matching (FM) method in generative modeling maps arbitrary probability distributions by constructing an interpolation between them and then learning the vector field that defines ODE for this interpolation. Recently, it was shown that FM can…

  • Multimodal Bandits: Regret Lower Bounds and Optimal Algorithms

    Multimodal Bandits: Regret Lower Bounds and Optimal Algorithms arXiv:2510.25811v1 Announce Type: new Abstract: We consider a stochastic multi-armed bandit problem with i.i.d. rewards where the expected reward function is multimodal with at most m modes. We propose the first known computationally tractable algorithm for computing the solution to the Graves-Lai optimization problem, which in turn…

  • Simplifying Optimal Transport through Schatten-$p$ Regularization

    Simplifying Optimal Transport through Schatten-$p$ Regularization arXiv:2510.11910v1 Announce Type: new Abstract: We propose a new general framework for recovering low-rank structure in optimal transport using Schatten-$p$ norm regularization. Our approach extends existing methods that promote sparse and interpretable transport maps or plans, while providing a unified and principled family of convex programs that encourage low-dimensional…

  • Near-Optimal Experiment Design in Linear non-Gaussian Cyclic Models

    Near-Optimal Experiment Design in Linear non-Gaussian Cyclic Models arXiv:2509.21423v1 Announce Type: new Abstract: We study the problem of causal structure learning from a combination of observational and interventional data generated by a linear non-Gaussian structural equation model that might contain cycles. Recent results show that using mere observational data identifies the causal graph only up…

  • An Introduction to Sliced Optimal Transport

    An Introduction to Sliced Optimal Transport arXiv:2508.12519v1 Announce Type: new Abstract: Sliced Optimal Transport (SOT) is a rapidly developing branch of optimal transport (OT) that exploits the tractability of one-dimensional OT problems. By combining tools from OT, integral geometry, and computational statistics, SOT enables fast and scalable computation of distances, barycenters, and kernels for probability…

  • When 50/50 Isn’t Optimal: Debunking Even Rebalancing

    When 50/50 Isn’t Optimal: Debunking Even Rebalancing A new theory of class imbalance demonstrates that the optimal training imbalance in a binary problem is not 50% The post When 50/50 Isn’t Optimal: Debunking Even Rebalancing appeared first on Towards Data Science. Marco Baity-Jesi Go to original source

  • Optimal and Practical Batched Linear Bandit Algorithm

    Optimal and Practical Batched Linear Bandit Algorithm arXiv:2507.08438v1 Announce Type: new Abstract: We study the linear bandit problem under limited adaptivity, known as the batched linear bandit. While existing approaches can achieve near-optimal regret in theory, they are often computationally prohibitive or underperform in practice. We propose texttt{BLAE}, a novel batched algorithm that integrates arm…

  • Optimal Convergence Rates of Deep Neural Network Classifiers

    Optimal Convergence Rates of Deep Neural Network Classifiers arXiv:2506.14899v1 Announce Type: new Abstract: In this paper, we study the binary classification problem on $[0,1]^d$ under the Tsybakov noise condition (with exponent $s in [0,infty]$) and the compositional assumption. This assumption requires the conditional class probability function of the data distribution to be the composition of…

  • Optimal Transport with Heterogeneously Missing Data

    Optimal Transport with Heterogeneously Missing Data arXiv:2505.17291v1 Announce Type: new Abstract: We consider the problem of solving the optimal transport problem between two empirical distributions with missing values. Our main assumption is that the data is missing completely at random (MCAR), but we allow for heterogeneous missingness probabilities across features and across the two distributions.…

  • Optimal Transport-Based Domain Adaptation for Rotated Linear Regression

    Optimal Transport-Based Domain Adaptation for Rotated Linear Regression arXiv:2505.09229v1 Announce Type: new Abstract: Optimal Transport (OT) has proven effective for domain adaptation (DA) by aligning distributions across domains with differing statistical properties. Building on the approach of Courty et al. (2016), who mapped source data to the target domain for improved model transfer, we focus…

  • Optimal Transport for Machine Learners

    Optimal Transport for Machine Learners arXiv:2505.06589v1 Announce Type: new Abstract: Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important tool in machine learning, especially for designing and evaluating generative models. These course notes cover…

  • Bayesian learning of the optimal action-value function in a Markov decision process

    Bayesian learning of the optimal action-value function in a Markov decision process arXiv:2505.01859v1 Announce Type: new Abstract: The Markov Decision Process (MDP) is a popular framework for sequential decision-making problems, and uncertainty quantification is an essential component of it to learn optimal decision-making strategies. In particular, a Bayesian framework is used to maintain beliefs about…

  • Optimal Scheduling of Dynamic Transport

    Optimal Scheduling of Dynamic Transport arXiv:2504.14425v1 Announce Type: new Abstract: Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable design freedom, and a central question is how to exploit this…

  • Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition

    Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition arXiv:2502.09047v1 Announce Type: new Abstract: A common pursuit in modern statistical learning is to attain satisfactory generalization out of the source data distribution (OOD). In theory, the challenge remains unsolved even under the canonical setting of covariate shift for the linear model.…

  • Optimal Transport-based Conformal Prediction

    Optimal Transport-based Conformal Prediction arXiv:2501.18991v1 Announce Type: new Abstract: Conformal Prediction (CP) is a principled framework for quantifying uncertainty in blackbox learning models, by constructing prediction sets with finite-sample coverage guarantees. Traditional approaches rely on scalar nonconformity scores, which fail to fully exploit the geometric structure of multivariate outputs, such as in multi-output regression or…

  • Optimal Survey Design for Private Mean Estimation

    Optimal Survey Design for Private Mean Estimation arXiv:2501.18121v1 Announce Type: new Abstract: This work identifies the first privacy-aware stratified sampling scheme that minimizes the variance for general private mean estimation under the Laplace, Discrete Laplace (DLap) and Truncated-Uniform-Laplace (TuLap) mechanisms within the framework of differential privacy (DP). We view stratified sampling as a subsampling operation,…

  • Near-Optimal Algorithms for Omniprediction

    Near-Optimal Algorithms for Omniprediction arXiv:2501.17205v1 Announce Type: new Abstract: Omnipredictors are simple prediction functions that encode loss-minimizing predictions with respect to a hypothesis class $H$, simultaneously for every loss function within a class of losses $L$. In this work, we give near-optimal learning algorithms for omniprediction, in both the online and offline settings. To begin,…

  • Optimal Transport Barycenter via Nonconvex-Concave Minimax Optimization

    Optimal Transport Barycenter via Nonconvex-Concave Minimax Optimization arXiv:2501.14635v1 Announce Type: new Abstract: The optimal transport barycenter (a.k.a. Wasserstein barycenter) is a fundamental notion of averaging that extends from the Euclidean space to the Wasserstein space of probability distributions. Computation of the unregularized barycenter for discretized probability distributions on point clouds is a challenging task when…