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arXiv Machine Learning

Non-Parametric Optimization for Scalable Learning in Stochastic Decision Problems

The paper introduces a stochastic variational framework using Malliavin calculus to derive non‑parametric optimality conditions for time‑varying stochastic optimization problems. It proposes the Stochastic Path Follower (SPF), a deep‑learning algorithm that remains scalable regardless of parameter‑space dimensionality. Experiments on least‑squares recovery and logistic regression under distribution drift demonstrate that SPF outperforms existing learning‑based and gradient‑based methods in both performance and scalability.

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arXiv Statistics ML
Sep 11

Learning-Based Surrogate Method for Stochastic Optimization under Decision-Dependent Uncertainty with Adaptive Random Designs

The paper introduces a learning-based surrogate approach for stochastic optimization problems where uncertainty depends on the decision, modeled via a nonparametric regression. It constructs a surrogate that embeds iteratively updated Jacobian estimates, using an adaptive random design that focuses sampling near the current iterate to achieve dimension‑independent convergence of the Jacobian estimates. The resulting learning‑based stochastic prox‑linear (L‑SPL) algorithm demonstrates nonasymptotic convergence rates and outperforms existing methods in sample efficiency and objective value in numerical experiments.

By Boyang Shen, Junyi Liu
ragbenchmarks
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arXiv Machine Learning
Jun 2

Safeguarded Stochastic Polyak Step Sizes for Non-smooth Optimization: Robust Performance Without Small (Sub)Gradients

arXiv:2512. 02342v3 Announce Type: replace-cross Abstract: The stochastic Polyak step size (SPS) has proven to be a promising choice for stochastic gradient descent (SGD), delivering competitive performance relative to state-of-the-art methods on smooth convex and non-convex optimization problems, including deep neural network training.

By Dimitris Oikonomou, Nicolas Loizou
benchmarks
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arXiv Machine Learning
Jul 7

Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses

arXiv:2406. 14340v2 Announce Type: replace-cross Abstract: The standard stochastic gradient descent (SGD) optimization method, as well as adaptive methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (particularly, in the situation of constant learning rates).

By Steffen Dereich, Arnulf Jentzen, Adrian Riekert
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arXiv Machine Learning
Jul 22

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise

arXiv:2607. 19173v1 Announce Type: new Abstract: Neural stochastic differential equations (SDEs) have emerged as powerful tools for learning noisy or stochastic dynamics directly from data; however, existing approaches largely assume uncoupled and continuous noise, limiting their applicability to realistic stochastic drivers, and often scale poorly in time, requiring expensive autoregressive training.

By Arthur Bizzi, Olga Fink
benchmarks
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arXiv Machine Learning
Sep 15

Stochastic Gradient Descent over P2

The paper develops a diffusion approximation for stochastic gradient descent (SGD) when the optimization target is a functional on the Wasserstein space ℝ2. By lifting the problem to a Hilbert space via Lions differentiability, the authors construct a Gaussian random-field approximation whose velocity field matches the mean and covariance of the original stochastic gradient. They prove that this Gaussian approximation achieves second‑order weak accuracy, providing a rigorous basis for replacing sample‑driven randomness with analytically tractable Gaussian fluctuations in stochastic optimization over probability measures.

By Maria Oprea, Qin Li, Yunan Yang
diffusion
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