A revised arXiv paper studies stochastic gradient descent for learning operators between general Hilbert spaces. It defines weak and strong regularity conditions on the target operator to describe its structure and complexity, and derives convergence rates along with minimax lower bounds.
A new arXiv preprint shows that the stochastic optimal control and path space formulations of the Schrodinger bridge problem are equivalent for the kinematic equation on compact connected Lie groups. The proof relies on geometric tools such as the horizontal lift. The result connects control-theoretic and measure-theoretic views of this class of optimal transport problems.
A new arXiv paper proposes cleaning up predicted edge costs via eigenvalue decomposition before solving shortest-path problems, rather than feeding raw predictions straight into the optimizer. The approach is positioned as a substitute for predict-then-optimize pipelines like SPO+, which learn a mapping from contextual features to unknown costs and then optimize on those predictions. The authors argue this denoising step can improve outcomes on combinatorial problems where prediction error propagates into the final solution.
A new arXiv paper proposes jointly optimizing federated learning and wireless transmission to counter client drift caused by heterogeneous data and multiple local updates. The approach also aims to handle unreliable wireless links, where transmission errors can invalidate model updates.
A new arXiv paper introduces an approach for deriving strong yet compact action-selection policies in Markov Decision Processes whose value functions are submodular. The method builds on a linear-programming formulation of submodular orienteering, a problem where an agent must reach a set of targets under a budget. The authors argue this yields policies that are both effective and compact, relevant to reinforcement learning and operations research settings where repeated action choice is required.
A new arXiv paper studies an online learning problem where a system must repeatedly choose k paths through a network to keep the slowest path's transmission time as low as possible. The authors formalize this as a stochastic semi-bandit problem, where feedback is observed only for the paths actually selected. They propose and analyze algorithms for minimizing the longest path length under uncertainty.
A new arXiv paper proposes an unsupervised graph neural network approach to the Minimum Dominating Set problem, an NP-hard combinatorial task. The method is aimed at applications such as influence maximization in social networks, viral marketing, and public health interventions. The work frames dominating set selection as a learning problem that does not require labeled optimal solutions.
A new arXiv paper develops projection-free algorithms for stochastic optimization problems whose objectives are nested compositions of smooth functions over a closed convex decision set. The work targets the multi-level compositional setting, where gradients must be estimated through several layers of functions. It aims to avoid costly projection steps while still handling constraints.
A new arXiv paper studies distributionally robust optimization problems framed as minimax games over a Euclidean space paired with a Riemannian manifold. The authors propose a Riemannian ascent-descent method and show it converges to basin saddle points in these nonconvex, nonconcave landscapes. The work connects geometric optimization theory with practical robust statistical risk modeling.
A research paper analyzes allocating indivisible goods among agents who share identical additive valuations, combining envy-freeness up to one good (EF1) with Nash social welfare (NSW). The authors study computational complexity, derive approximation guarantees, and run experiments. They note that under additive valuations every maximum-NSW allocation already satisfies EF1.
A new arXiv preprint examines how different optimization algorithms perform when used to solve inverse problems inside differentiable physics simulators. The work argues that such simulators combine the physical fidelity of numerical solvers with gradient-based learning, which could benefit scientific discovery and engineering design. The study benchmarks optimizer choices to identify which ones work best in this setting.
A new arXiv paper examines constrained online convex optimization where both constraint values and gradients are observed with noise. The authors introduce an algorithm called LEDGER, which they show achieves O(√T) expected regret and constraint violation under standard feasibility assumptions. The work targets settings with adversarial constraints and conditionally unbiased, finite-variance observations.
A new arXiv paper argues that fine-tuning instruction-tuned models can improve target tasks while causing unwanted behavioral drift away from the reference model, which may erode existing abilities. The authors propose a drift-constrained optimization approach in which the direction of parameter updates, rather than their size, is what governs this divergence. Treating drift as a controlled constraint instead of an incidental byproduct of training is the paper's central framing.
A new arXiv paper presents a deterministic algorithm for online inverse linear optimization that attains O(d) regret, a bound that holds uniformly across the time horizon. Each round requires O(d^2) computation time. The result matches a recent bound by Dewasurendra and addresses an open question raised by Gollapudi and colleagues.
Researchers propose a cloud-edge framework for collaborative large language model training and deployment. The approach accelerates personalized bilevel optimization to reconcile globally consistent models with locally adapted ones. It targets the difficulty existing cloud-edge systems have in balancing those two goals.
A new arXiv paper proves that logconcave probability measures lying along the Gaussian cooling path satisfy a thin-shell stability property, extending the classical thin-shell theorem. This stability result translates into better complexity bounds for the core task of drawing samples from an arbitrary logconcave distribution, including when the process begins from a cold start rather than a warm one. The work sits in the theory of Markov chain Monte Carlo and sampling algorithm analysis.
A revised arXiv preprint argues that neural combinatorial optimization has largely been limited to policies that work on a single candidate solution, whether by building one from scratch or refining it step by step. The authors propose shifting toward population-based architectures that evaluate and evolve multiple solutions together. The work appears in the cs.LG category as a replacement submission.
A new arXiv paper studies a single-loop, single-call stochastic algorithm that uses Halpern anchoring to solve constrained convex-concave problems and monotone variational inequalities. The method draws one unbiased sample of the gradient operator per iteration. The authors report improved last-iterate convergence guarantees for this anytime setting.
A new arXiv paper proposes SAILOR, an interactive approach in which a language model turns natural-language optimization problems into solver-ready code. Because such descriptions often omit or leave vague the numerical values a solver needs, the method draws on solver feedback to recover missing costs, capacities, demands, bounds and penalties. The work targets the gap between fluent problem descriptions and the complete, precise inputs that optimization software requires.
The paper compares two federated learning setups: parallel training, where clients work simultaneously, and sequential training, where clients update the model one after another. It derives convergence guarantees for the sequential approach when client data distributions differ, a setting where parallel methods often struggle. The analysis aims to clarify when sequential federated learning offers theoretical advantages over its parallel counterpart.
A new arXiv preprint proposes the Universe of Universes framework, which models the collection of major large language models as a structured corpus that can be queried rather than as isolated systems. The authors describe a compositional architecture combining automated reasoning and machine learning, and introduce concepts such as benefit yield functions, implosion thresholds, and infrastructure-aware optimization for coordinating multiple LLMs.
A new arXiv preprint addresses the difficulty of calibrating agent-based models, whose objective landscapes are stochastic, rugged, and expensive to evaluate through simulation. The authors adapt inner-loop surrogate-assisted evolutionary computation, combining genetic algorithms and particle swarm optimization to reduce the number of costly black-box evaluations. The work sits at the intersection of machine learning and simulation-based modeling.
Researchers released cvxgenrust, an open-source tool that produces tailored Rust code for solving families of parameterized convex optimization problems written in CVXPY. The system canonicalizes a problem family and derives affine mappings onto Clarabel cone programs. The paper targets use cases where a solver must be recompiled for many related parameter values rather than solved from scratch each time.
A preprint examines the use of diffusion approximations, which substitute Gaussian noise for the randomness of stochastic gradients, as a way to analyze how stochastic gradient descent behaves over time. The authors probe the conditions under which such approximations remain valid for describing the algorithm's long-run dynamics.
A new arXiv preprint examines how learning rate schedules can be optimized within the functional scaling law framework, which separates training dynamics into signal learning and noise forgetting. The authors analyze power-law kernel regression to characterize these two components, comparing schedules such as power decay and warmup-stable-decay. The work offers theoretical guidance on choosing learning rate schedules for model training.
A new arXiv paper proposes a pullback-corrected scalar auxiliary variable (PB-SAV) optimizer that adds momentum and adaptive mobility. The method is aimed at scientific machine learning objectives that combine several loss terms, such as the residual, boundary, initial, and data losses used in physics-informed neural networks. The abstract frames the work as addressing optimization challenges specific to these composite objectives.
A new arXiv paper introduces upper-linearizable (and quadratizable) functions, a class generalizing concavity and DR-submodularity across monotone and non-monotone settings. The authors present a meta-algorithm that converts algorithms for linearizable problems into ones for this broader class. It is applied to stationary and non-stationary DR-submodular optimization.
A new arXiv paper studies finite-sum optimization under individual smoothness assumptions, where the best achievable incremental first-order oracle complexity has remained unresolved. It proposes a "dense weak hiding" approach that tightens the gap between existing algorithms, which need roughly n plus sqrt(n) times a smoothness-scaled term, and previously known lower bounds. The results cover both general nonconvex objectives and those satisfying the Polyak-Lojasiewicz condition.
A new arXiv paper reframes hyperparameter optimization as a numerical optimization problem rather than a sequence of independent trials. The authors propose a multi-objective, damped Gauss-Newton search method that estimates a finite-difference-based model of the objective landscape. The work is a replacement cross-list submission on arXiv's machine learning section.
A new arXiv paper presents a technique for exactly removing spins from Ising optimization problems while permitting more complex interactions. Since Ising hardware has a limited spin budget, the approach lets larger problems fit within the same device capacity than standard quadratization, which adds auxiliary spins to reduce higher-order terms to pairwise ones.
A newly posted paper builds explicit counterexamples to Rockafellar's sum conjecture, showing pairs of maximally monotone operators that meet the interior-domain qualification yet whose sum fails maximal monotonicity. One example is constructed on the Banach space c0 and another on l1. The results settle a long-standing open question in convex analysis and optimization theory.
A new arXiv preprint examines ways to improve the ACTS software suite's handling of configuration parameters used in track seeding for charged-particle reconstruction. Because those settings strongly influence both reconstruction quality and computing cost, they are typically adjusted by hand through expert judgement and repeated testing. The work proposes new directions for reducing that manual tuning burden.
A new arXiv preprint introduces a variance reduction technique for finite-sum coupled compositional optimization, a setting where existing single-function estimators such as SPIDER, SARAH and STORM do not directly apply. The authors propose a multi-block, single-probe estimator intended to improve convergence rates in this coupled setting. The work is a theoretical optimization contribution.
A new arXiv paper introduces a three-term spectral modification of the Hestenes-Stiefel conjugate gradient method, derived using least-squares approximations of a modified quasi-Newton update. The approach aims to retain the algorithm's resistance to jamming while guaranteeing sufficient descent. The authors apply it to a revised robust binary classification model.
A new arXiv preprint examines constant-stepsize stochastic approximation, where iterates settle into a stationary distribution that varies with the chosen stepsize. The work focuses on steady-state convergence, meaning the behavior of the rescaled stationary law as the stepsize shrinks toward zero. It is a theoretical contribution to the analysis of stochastic optimization algorithms rather than a released model or tool.
The paper proposes a set of elementary inequalities as a general tool for analyzing first-order iterative optimization methods, aiming to unify how implicit and explicit regularization are understood. Building on existing comparison inequalities, the authors show how this framework can be used to study statistical risk. It is a revised cross-list submission to arXiv's machine learning category.
A new study examines how augmented primal-dual methods behave when constraint values are estimated from samples rather than known exactly. The authors show that unbiased constraint estimates can still yield a biased augmented multiplier signal, which moves the equilibrium point of the mean dynamics. The paper analyzes stability and convergence properties under this sampling-induced shift.
The paper studies nonsmooth contractive stochastic approximation with a constant step size, motivated by Q-learning. It examines both additive-noise dynamics and synchronous as well as asynchronous variants, establishing steady-state convergence through a prelimit coupling method. The work is an updated arXiv submission.
Researchers propose ACR-PINN, a physics-informed neural network framework that pairs layer-wise dynamic adaptation of coordinate representations with a method for resolving conflicts among gradients coming from heterogeneous physical constraints. The work frames architecture and optimization as a joint design problem, aiming to improve training when competing constraints pull the model in different directions.
A new arXiv paper applies genetic programming to dynamic multi-mode resource-constrained project scheduling, where tasks face precedence rules, limited resources, several execution modes, and uncertain durations. The authors add surrogate assistance and phenotypic characterisation to guide the evolutionary search toward promising schedules. The work sits at the intersection of evolutionary computation and operations research rather than commercial AI products.