Tootfinder

Physics-informed learning under mixing: How physical knowledge speeds up learning
Anna Scampicchio, Leonardo F. Toso, Rahel Rickenbach, James Anderson, Melanie N. Zeilinger
https://arxiv.org/abs/2509.24801

Physics-informed learning under mixing: How physical knowledge speeds up learning
A major challenge in physics-informed machine learning is to understand how the incorporation of prior domain knowledge affects learning rates when data are dependent. Focusing on empirical risk minimization with physics-informed regularization, we derive complexity-dependent bounds on the excess risk in probability and in expectation. We prove that, when the physical prior information is aligned, the learning rate improves from the (slow) Sobolev minimax rate to the (fast) optimal i.i.d. one w…

Event-Driven Control via Sparsity-Promoting Regularization: A Rollout Approach with Performance Guarantees
Shumpei Nishida, Kunihisa Okano
https://arxiv.org/abs/2509.24799 https…

Event-Driven Control via Sparsity-Promoting Regularization: A Rollout Approach with Performance Guarantees
This paper presents a controller design method aiming to balance control performance and actuation frequency. In this framework, actuation timings are determined in an event-driven manner, resulting in intermittent control actions. Control performance is measured by an infinite-horizon average cost, and input sparsity is promoted through actuation-rate regularization. Since the formulated optimal control problem has a combinatorial nature, we employ a rollout algorithm to find a suboptimal solu…

General Divergence Regularized Optimal Transport: Sample Complexity and Central Limit Theorems
Jiaping Yang, Yunxin Zhang
https://arxiv.org/abs/2510.02489 https://

General Divergence Regularized Optimal Transport: Sample Complexity and Central Limit Theorems
Optimal transport has emerged as a fundamental methodology with applications spanning multiple research areas in recent years. However, the convergence rate of the empirical estimator to its population counterpart suffers from the curse of dimensionality, which prevents its application in high-dimensional spaces. While entropic regularization has been proven to effectively mitigate the curse of dimensionality and achieve a parametric convergence rate under mild conditions, these statistical gua…

Convergence Rate of Generalized Nash Equilibrium Learning in Strongly Monotone Games with Linear Constraints
Tatiana Tatarenko, Maryam Kamgarpour
https://arxiv.org/abs/2507.12112 …

Convergence Rate of Generalized Nash Equilibrium Learning in Strongly Monotone Games with Linear Constraints
We consider payoff-based learning of a generalized Nash equilibrium (GNE) in multi-agent systems. Our focus is on games with jointly convex constraints of a linear structure and strongly monotone pseudo-gradients. We present a convergent procedure based on a partial regularization technique and establish the convergence rate of its iterates under one- and two-point payoff-based feedback. To the best of our knowledge, this work is the first one characterizing the convergence speed of iterates to…

Dynamic mode decomposition for detecting transient activity via sparsity and smoothness regularization
Yutaro Tanaka, Hiroya Nakao
https://arxiv.org/abs/2508.10266 https://

Dynamic mode decomposition for detecting transient activity via sparsity and smoothness regularization
Dynamic Mode Decomposition (DMD) is a data-driven modal decomposition technique that extracts coherent spatio-temporal structures from high-dimensional time-series data. By decomposing the dynamics into a set of modes, each associated with a single frequency and a growth rate, DMD enables a natural modal decomposition and dimensionality reduction of complex dynamical systems. However, when DMD is applied to transient dynamics, even if a large number of modes are used, it remains difficult to in…

Generalization Analysis for Classification on Korobov Space
Yuqing Liu
https://arxiv.org/abs/2509.22748 https://arxiv.org/pdf/2509.22748

Generalization Analysis for Classification on Korobov Space
In this paper, the classification algorithm arising from Tikhonov regularization is discussed. The main intention is to derive learning rates for the excess misclassification error according to the convex $η$-norm loss function $ϕ(v)=(1 - v)_{+}^η$, $η\geq1$. Following the argument, the estimation of error under Tsybakov noise conditions is studied. In addition, we propose the rate of $L_p$ approximation of functions from Korobov space $X^{2, p}([-1,1]^{d})$, $1\leq p \leq \infty$, by the s…