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Martin Hernandez, Xinyan Qing, Mo Zhou, Yuhua Zhu · 2026-10-20
Continuous-time reinforcement learning seeks an optimal policy under unknown dynamics driven by stochastic differential equations using observations collected at discrete times. We develop a policy gradient framework that combines rigorous convergence analysis with learning from …
Ma ZhenYao, Yue Liang, Jian-Qiao Zhu · 2026-10-20
Many scientific phenomena are best understood as outcomes of underlying optimization problems, yet automated scientific discovery has largely focused on recovering equations that describe observed input-output patterns. We introduce OptScientist, a novel automated framework for d…
Gabin Maxime Nguegnang, Bubacarr Bah, Holger Rauhut, Ulrich Terstiege · 2026-10-20
Stochastic gradient descent (SGD) is the cornerstone of modern deep learning, yet its theoretical convergence properties remain poorly understood in non-convex settings. To address this gap, we study SGD dynamics in deep linear neural networks - simplified models that retain key …
Andrew J. Ochoa, Martin J. A. Schuetz, Helmut G. Katzgraber · 2026-10-20
We demonstrate a hybrid quantum-classical approach for exploring ground-state manifolds of maximum independent set problems, in which quantum hardware supplies the initial solutions and an entirely classical post-processing algorithm expands them, increasing the solution diversit…
Wei Jiang, Dingzhi Yu, Zechao Li · 2026-10-20
We study variance reduction for non-convex optimization when gradient evaluations return with a delay. The server can update the parameter while earlier evaluations remain unfinished. We first analyze an ordered recursive momentum estimator for stochastic optimization. Under aver…
Jan Quan, Panagiotis Patrinos · 2026-10-20
We provide two closed, convex sets with nonempty intersection and an initial point for which the Douglas-Rachford algorithm converges weakly but not strongly. This resolves an open question as noted earlier by Aragón Artacho, Borwein and Tam (2014, Remark 2.2). Our construction i…
Yunus Emre Demirci, Somnath Pradhan, Serdar Yüksel · 2026-10-20
We study continuous-time stochastic control problems under partial information. Our main contributions are the following: (i) We show near optimality, under finite horizon as well as discounted infinite horizon cost criteria, of piece-wise constant control policies obtained via s…
Thierno Thioune, Babacar Mbaye Ndiaye · 2026-10-20
A related paper (arXiv:2610.06967) developed a stochastic optimization framework in which football performance combines GDP/population-based potential with a latent mean-reverting efficiency process. The framework was applied to a cross-section of the 24 national teams participat…
Galina Sidorenko, Johan Thunberg · 2026-10-20
We study discrete-time consensus on the Euclidean unit sphere, where weighted combinations of neighboring states are normalized to unit length. For symmetric weights on connected undirected graphs and ambient dimension $d\ge3$, earlier results establish instability of non-consens…
Elisabetta Carlini, Valentina Coscetti, Francisco J. Silva · 2026-10-20
We introduce and analyze a numerical framework for a class of first-order, non-local Mean Field Game (MFG) systems with two sources of low regularity: the time-dependent data are merely measurable, and the Hamiltonian is only of class $C^{1,1}$ with respect to the momentum variab…
Karthik Prakhya, Zimeng Wang, Alp Yurtsever · 2026-10-20
We propose adaptive primal-dual subgradient methods for constrained convex optimization. Our first method applies an AdaGrad-style step-sizes to the dual problem and recovers primal solutions by averaging the associated Fenchel-type oracle outputs. It achieves $\widetilde{\mathca…
Ivan Ilin, Peter Richtárik · 2026-10-20
Teams of large language model (LLM) agents are increasingly applied to complex tasks, but their collaboration protocols are mostly designed empirically, without convergence guarantees. We formalize collaborative problem solving as block optimization: each agent improves one part …
Daisuke Inoue, Kazuhiro Sato · 2026-10-20
We define finite-time controllability allocation scores (CASs) as optimal solutions to two convex optimization problems that allocate a fixed actuation budget among prescribed input functions of linear infinite-dimensional continuum systems with selected target outputs. The objec…
Keyi Wang, Robert Mieth, Ahmed Aziz Ezzat · 2026-10-20
The reliable and cost-effective integration of large-scale offshore wind farms into power systems is largely influenced by maintenance operations. To date, power producers primarily rely on farm-level information (e.g., health signals, power generation, weather conditions) for ma…
Zhen Peng, Bin Gao · 2026-10-20
We study the set $\mathrm{Gq}(P,Q)$ of real $n\times p$ matrices $X$ satisfying $X^\top Q X = P$, where the nonsingular matrices $P$ and $Q$ are both symmetric or both skew-symmetric and the set is nonempty. Special choices of $P$ and $Q$ yield the Stiefel, generalized Stiefel, i…
Ruben Hoeksma, Jesse van Rhijn, Marc Uetz, Wick Wijnholds · 2026-10-20
This paper shows that a mixed integer PDE-constrained design optimization problem can be made amenable to be solved to optimality using standard mixed-integer programming solvers. The concrete problem that we consider is the optimal design of the topology of an antenna, a problem…
Alyona Nekrasova, Makar Sidorov, Savelii Chezhegov, Alexander Gasnikov, Margarita Preobrazhenskaia and others · 2026-10-20
Gradient clipping is a key tool for obtaining high-probability convergence guarantees for stochastic first-order methods under heavy-tailed noise. Existing analyses typically assume a bounded central moment of order $α\in(1,2]$, which excludes distributions with tails of order $u…
Alexandra Suvroikova, Darina Dvinskikh, Yuriy Dorn, Alexander Gasnikov · 2026-10-20
Polyak--Ruppert averaging gives SGD and momentum methods the same asymptotic covariance. We characterize how fast finite runs reach it and how far they can be parallelized. For strongly convex quadratics with additive noise, we prove an online--offline bridge: the empirical risk …
Zhaobo Liu · 2026-10-20
We study the complexity of minimal positive realization for discrete-time systems. We prove that, given a strictly proper transfer matrix with rational coefficients and an order bound encoded in unary, deciding whether a positive realization exists within that bound is complete f…
Eghbal Hosseini · 2026-10-20
Worst-case instances show where optimization algorithms fail: the Klee-Minty cube for the simplex method, ill-conditioned and rippled bowls for gradient descent, degenerate minima for Newton's method, redundant Klee-Minty cubes for interior-point methods, unprunable trees for bra…
Pratik Jawanpuria, Bhabatosh Garai, Bamdev Mishra · 2026-10-20
Muon and related optimizers update a weight matrix with a spectrally transformed gradient. In this work, we study such spectral optimizers with a constant step size on strongly convex matrix quadratics, which isolate the effect of the update from the confounds of nonconvexity, no…
Hayato Watanabe, Takami Sato, Kazuhide Nakata, Ken Kobayashi · 2026-10-20
We study two relaxations for bilinear terms in box-constrained variables: the reformulation-linearization technique (RLT) relaxation and the SDP-RLT relaxation, which combines RLT with semidefinite programming (SDP). We represent the pattern of bilinear terms by an undirected gra…
Zhipeng Cao, Taoran Wu, Weiru Cui, Luke Ong, Bai Xue · 2026-10-20
Learned barrier certificates provide a principled mechanism for establishing safety of stochastic systems, but their validity may deteriorate during deployment when the underlying dynamics differ from those used for training. We propose an anytime-valid runtime monitor that audit…
Rikiya Okazaki, Shotaro Yagishita, Hideitsu Hino · 2026-10-20
We propose a parameter-free and efficient gradient descent algorithm for $(L_0,L_1)$-smooth optimization. This notion of smoothness, introduced by Zhang et al. (2020), allows the smoothness bound to grow with the gradient norm. Similar to cutting-plane localization, our method us…
Lei Zhang, Xiuting Li · 2026-10-20
In this paper, we study global exact controllability of semilinear Schrödinger equations by localized internal additive controls. For every globally Lipschitz nonlinearity in arbitrary dimensions, we prove that any two $L^2$ states can be connected in any prescribed positive time…
Ubaldo Ruiz · 2026-10-20
We study minimum-time escape of an omnidirectional evader from the forward conic field of view of a Reeds-Shepp pursuer with minimum turning radius $r$. For speed ratio $ν$ and cone half-angle $0<α<π/2$, we prove a global escape/holding classification: straight reversal hol…
Vaishnavi Sharma, Vaibhav Katewa · 2026-10-20
The open-loop minimum-energy control (MEC) problem asks for control inputs that minimize the control energy while ensuring the terminal state reaches a desired value. In this paper, we study the open-loop MEC problem for stochastic linear time-invariant systems. We consider a var…
Hongwei Mei · 2026-10-20
The existing theory of stochastic linear-quadratic (LQ) optimal control problems focuses on open-loop and closed-loop solvability. For finite horizon problems, it is widely accepted that those two types of solvability are not equivalent in general, as demonstrated by explicit cou…
Hongkun Xia, Dacheng Yao · 2026-10-20
We study an infinite-horizon discounted optimal switching problem for an Ornstein--Uhlenbeck process whose mean-reversion level can be switched between two values. Switching incurs positive, potentially asymmetric fixed costs, and the mode with the higher mean-reversion level ent…
Alan Lujan · 2026-10-20
Many economic problems have several controls per period, whose joint choice is subject to the curse of dimensionality. Solving them in stages is computationally cheaper, but no general result says when staging is exact. I develop a separability theory, discrete choices and non-co…
Baturhan Bayraktar, Merve Bodur, Martin Grunow, Rainer Kolisch · 2026-10-19
Matrix assembly layouts provide manufacturing flexibility under product variety and demand volatility through locally reconfigurable production stations. Periodic redesign exploits this flexibility, yet existing models allow only annual revisions. Finer calendars expose a flexibi…
Sanyou Mei · 2026-10-19
We study turn-based deterministic zero-sum games with discounted and long-run average costs. For discounted costs, we establish exponential and superpolynomial iteration lower bounds for the simple strategy-iteration method with Dantzig's rule under unrestricted costs and unit we…
David E. Bernal Neira · 2026-10-19
Quantum and physics-inspired solvers provide specialized sampling interfaces for Ising and quadratic unconstrained binary optimization models, but constrained optimization requires broader coordination and certification. This survey uses classical decomposition to analyze how suc…
Peter E. Caines, Minyi Huang · 2026-10-19
This paper analyzes graphexon mean field games (GXMFG) on large network limits. By considering edge distributions of a sequence of finite graphs, we define the empirical graphexon measures and study their subsequential weak limits in a graphexon space consisting of all symmetric …
Victoria Grushkovskaya, Sameh Eisa · 2026-10-19
In this paper, we leverage the recently developed general higher-order Lie bracket approximation theory and framework for control-affine systems to show that we can design extremum seeking (ES) systems that combine flows based on: (i) first-order Lie bracket approximation, which …
Ihsan Topaloglu · 2026-10-19
We study the shape optimization problem introduced by Mazzoleni, Muratov, and Ruffini as a model for a superconducting charge qubit, in which the first Dirichlet eigenvalue of a set of prescribed volume competes with the Coulomb self-energy of the ground state. We prove that, for…
Raul Jimenez, Pablo Tejerina-Pérez, Leonid Sarieddine, Pedro Tarancón-Álvarez, Marisol Traforetti and others · 2026-10-19
Physics-informed neural networks (PINNs) and other residual-trained solvers judge a candidate solution by the size of its sampled PDE residual. For first-order Hamilton-Jacobi equations this is not sufficient: the same equation and boundary data admit Lipschitz almost-everywhere …
Thomas Berger, Hannes Gernandt, Pushya Mitra · 2026-10-19
We analyze explicit and implicit Euler discretizations of the continuous-time closed-loop dynamics generated by a funnel controller for a fully actuated nonlinear full-state system of relative degree one with scalar positive input gain. A quantitative continuous-time funnel margi…
Sahiba Arora, Alexander A. Wierzba · 2026-10-19
The study of bounded-input bounded-output (BIBO) stability of infinite-dimensional systems gives rise to difficulties that do not occur in the classical finite-dimensional setting. In this paper, we resolve several questions concerning the definition and characterisation of BIBO …
Xiajie Huang, Cristina Álvarez Yuste, Nikita Guseynov, Nana Liu, Javier González-Conde · 2026-10-19
We develop quantum algorithms for optimal control over a prescribed finite time interval (finite horizon), focusing on continuous-time linear-quadratic regulation (LQR). This foundational control problem often requires solving a nonlinear matrix Riccati equation, which can be cos…
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