LMO Methods

LMO: Linear Minimization Oracle

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Latest papers

13 papers6 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

Geometry-Aware Multi-Objective Optimization: Norm-Constrained Oracles with Entropic Weight Updates
Oct 9, 2026El Mahdi Chayti, Alireza Mirrokni, Martin JaggiLMO Methods Multi-Objective Optimization
Machine Learning and Optimization Laboratory (MLO), EPFL
Lower Bounds for Randomized Linear-Oracle Optimization over Strongly Convex Sets
Oct 9, 2026Sebastian PokuttaLMO Methods Oracle Complexity
Zuse Institute Berlin and TU Berlin
Optimizing Large Language Models with Chained LMOs
Oct 7, 2026Sungyoon Kim, Kaan Ozkara, Youngsuk ParkLMO Methods Deep Learning Optimization
Department of Electrical Engineering, Stanford University · Amazon Annapurna Labs
Lower Bounds for Linear-Oracle Online Learning
Sep 29, 2026Mohit SinhaOnline Convex Optimization Information-Theoretic Lower Bounds
Local LMO is Secretly a Projection Method!
Sep 27, 2026Peter Richtárik, Ammar MahranLMO Methods Constrained Optimization
King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
Sharp Oracle-Regret Tradeoffs for Projection-Free Online Convex Optimization
Sep 23, 2026Vaneet AggarwalOnline Convex Optimization LMO Methods
Purdue University West Lafayette, Indiana, USA
OmniOpt: Taxonomy, Geometry, and Benchmarking of Modern Optimizers
Jul 4, 2026Siyuan Li, Jiabao Pan, Yumou Liu +9LMO Methods Deep Learning Optimization
Shanghai Artificial Intelligence Laboratory · Westlake University · Shanghai University +4
From SGD to Muon: Adaptive Optimization via Schatten-p Norms
May 19, 2026Thomas Massena, Corentin Friedrich, Mathieu SerrurierLMO Methods Neural Network Optimization
DTIPG - SNCF, IRIT · IRIT
Ringmaster LMO: Asynchronous Linear Minimization Oracle Momentum Method
May 18, 2026Abdurakhmon Sadiev, Artavazd Maranjyan, Ivan Ilin +1LMO Methods Momentum Methods
KAUST
Accelerating LMO-Based Optimization via Implicit Gradient Transport
May 7, 2026Won-Jun Jang, Si-Hyeon LeeLMO Methods Muon Optimizer
School of Electrical Engineering · Korea Advanced Institute of Science and Technology (KAIST) · Daejeon, South Korea
Deriving Hyperparameter Scaling Laws via Modern Optimization Theory
Mar 16, 2026Egor Shulgin, Dimitri von Rütte, Tianyue H. Zhang +3LMO Methods Scaling Laws
King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia · ETH Zürich, Zürich, Switzerland · Mila, Quebec AI Institute & Université de Montréal, Quebec, Canada +1
Ky Fan Norms and Beyond: Dual Norms and Combinations for Matrix Optimization
Dec 10, 2025Alexey Kravatskiy, Ivan Kozyrev, Nikolai Kozlov +3LMO Methods Deep Learning Optimization
MIRIAI · Russia · MIPT, INM RAS +3
Accelerated Frank-Wolfe Algorithms: Complementarity Conditions and Sparsity
Nov 4, 2025Dan GarberConstrained Optimization Frank-Wolfe Algorithms
Faculty of Data and Decision Sciences Technion - Israel Institute of Technology

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Geometry-Aware Multi-Objective Optimization: Norm-Constrained Oracles with Entropic Weight Updates

El Mahdi Chayti, Alireza Mirrokni, Martin Jaggi

Machine Learning and Optimization Laboratory (MLO), EPFL

LMO Methods Multi-Objective Optimization Multi-Task Optimization Gradient Descent Stochastic Optimization

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Multiple-gradient descent is typically formulated in Euclidean geometry, whereas matrix-aware optimizers use directions induced by other norms. We analyze a single-loop multi-objective method combining a norm-constrained linear minimization oracle with entropic updates of task weights. For any finite-dimensional norm pair, we establish an

O(T^{-1/2})

ergodic stationarity rate in the deterministic setting, deriving the required trajectory gradient bound from smoothness and lower-boundedness in the unregularized case. With stochastic gradients and a bounded-gradient assumption, one persistent blended-gradient momentum buffer yields an

O(T^{-1/4})

rate whose leading term has no explicit dependence on the number of tasks. We also establish static regret for the inner weighting objective on arbitrary bounded gradient sequences and, with entropy regularization and a weight floor, iteration-wise inner-gap control after burn-in while retaining ergodic stationarity, conditional on a trajectory gradient bound. The optimal blended gradient can be nonunique in spectral and sign geometries, motivating a selection-independent inner gap. Our analysis extends the spectral construction studied by concurrent MOON to general norms. Experiments compare the method with existing multi-task optimizers and examine its oracle, weighting, and momentum choices.