Combines Bayesian and Lipschitz optimization for better global function optimization.
problem Optimizing black-box functions with improved global performance.
method Proposes Lipschitz Bayesian optimization (LBO) by integrating Lipschitz continuity within traditional Bayesian optimization.
result Proves that LBO can yield the same or better regret bound compared to pure Bayesian optimization, and shows substantial performance improvements in some cases.
ECP optimizes expensive functions without knowing Lipschitz constant.
problem Optimizing expensive, non-convex functions with unknown Lipschitz constants.
method ECP minimizes evaluations by focusing on potentially optimal regions, eliminating Lipschitz constant estimation.
result Guaranteed no-regret performance and minimax-optimal regret bounds.
LiPopt uses polynomial optimization to estimate neural network Lipschitz constants efficiently.
problem Estimating the Lipschitz constant of neural networks efficiently.
method Sparse polynomial optimization, leveraging network connectivity to reduce complexity.
result Superior estimates of the ℓ ∞ \ell_\infty ℓ ∞ -Lipschitz constant compared to existing methods. This paper bounds the Lipschitz constants of neural networks and their gradients.
problem Estimating the Lipschitz constant of complex models like neural networks.
method Local upper and lower bounds on Lipschitz constants computed with respect to network parameters.
result It is impossible to derive global upper bounds for the Lipschitz constants of neural networks.
Efficient algorithm for global optimization of multivariate Lipschitz functions.
problem Global optimization of multivariate Lipschitz continuous functions.
method Proposes an efficient minimax optimal algorithm using a predetermined query creation rule.
result Achieves an average regret bound of O ( L n T − 1 n ) O(L\sqrt{n}T^{-\frac{1}{n}}) O ( L n T − n 1 ) , minimax optimal. The Piyavskii-Shubert algorithm is analyzed for global optimization of Lipschitz functions.
problem Maximizing a non-concave Lipschitz function over a compact domain.
method Sequential function evaluations using a bandit-optimization approach.
result New bounds on the number of evaluations needed for optimization accuracy.
New methods solve non-Lipschitz smooth problems with guaranteed convergence.
problem Non-Lipschitz smooth problems in machine learning and signal processing.
method Bregman-divergence based algorithms for relatively smooth problems.
result Guaranteed convergence to second-order stationary points for any relatively smooth problem.
Sharp Lipschitz bounds for flow-matching and diffusion models with optimal sampling rates.
problem Establishing optimal Lipschitz regularity for flow-matching and diffusion models.
method Sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores.
result Achieves optimal sampling rate of d / N \sqrt{d}/N d / N for Euler-type samplers in dimension d d d . Improved DP SO with large Lipschitz parameters, handling outliers and heavy-tailed data.
problem Differential privacy in stochastic optimization with large Lipschitz parameters.
method Assumes bounded k-th order moments, provides linear-time algorithms for smooth convex and non-smooth convex losses.
result Improved risk bounds scaling with k-th moment, not uniform Lipschitz parameter.
New parameterization of neural networks with Lipschitz bounds for robustness.
problem Developing robust neural networks with Lipschitz bounds.
method Introducing a new parameterization that admits a Lipschitz bound during training without requiring projections or barrier functions.
result The new parameterization improves robustness to adversarial attacks in image classification.
New method for differentially private optimization with general Lipschitz conditions.
problem Differentially private optimization under general Lipschitz conditions.
method Generalized Lipschitz condition for per-sample gradients, tuning clip norm based on minimum per-sample Lipschitz constant.
result Efficacy of the recommended clip norm tuning method verified on 8 datasets.
Efficient binary sampling method for global optimization of univariate functions with low regret.
problem Global optimization of univariate loss functions.
method Binary sampling approach to circumvent hard-to-determine query points in traditional methods.
result At most L log ( 3 T ) L\log (3T) L log ( 3 T ) and 2.25 H 2.25H 2.25 H regret for L L L -Lipschitz continuous and H H H -Lipschitz smooth functions respectively. Paper presents adaptive Lipschitz bandit framework for efficient optimization.
problem Optimizing rewards and minimizing regret in stochastic Lipschitz bandit problems.
method Adaptive learning of partitions in context- and arm-space using hierarchical Bayesian models.
result Achieves state-of-the-art performance in real-world tasks like neural network hyperparameter tuning.
Paper introduces a neural network for consistent estimation of optimal transport maps.
problem Statistically consistent estimation of optimal transport maps between probability distributions.
method Lipschitz-constrained GAN penalized by quadratic transportation cost.
result The generator converges uniformly to the optimal transport map as sample size increases.
New method improves optimization algorithms without Lipschitz smoothness.
problem Improving optimization algorithms in the absence of Lipschitz smoothness.
method Dual kernel conditioning (DKC) to provide dual Lipschitz continuity.
result First complexity bounds and iterate convergence for random reshuffling mirror descent.
Study invariant Lipschitz bandits, improving regret bounds.
problem Optimizing decisions under symmetry in online settings.
method Integrates side observations using group orbits into UniformMesh algorithm.
result Improved regret bound for invariant Lipschitz bandit class.
ECPv2 optimizes Lipschitz functions efficiently and scalably.
problem Global optimization of Lipschitz-continuous functions with unknown Lipschitz constants.
method Adapting the Every Call is Precious (ECP) framework, ECPv2 introduces adaptive lower bounds, Worst-m memory, and random projections to reduce computational cost and improve acceptance regions.
result ECPv2 retains ECP's no-regret guarantees with optimal finite-time bounds and expands the acceptance region with high probability.
We determine the asymptotic behavior of the optimal Lipschitz constant for the systole map from Teichmuller space to the curve complex.
Optimizes privacy-preserving optimization for heavy-tailed data.
problem Privacy-preserving optimization with heavy-tailed gradients.
method Pure ε-differential privacy framework for Lipschitz extensions.
result Minimax optimal excess-risk rate for pure ε-DP heavy-tailed SCO.
The study provides optimal estimates for surfaces close to constant mean curvature.
problem Optimizing estimates for surfaces near constant mean curvature.
method Bi-Lipschitz and W 2 , 2 W^{2,2} W 2 , 2 parametrization for surfaces with density close to one and small Willmore energy. result Quantitative rigidity for L 2 L^2 L 2 -almost CMC surfaces. The paper proposes a method to train NNs with a small Lipschitz constant to improve robustness.
problem Neural networks' susceptibility to adversarial perturbations in safety-critical applications.
method The paper introduces a framework to train multi-layer NNs by minimizing their Lipschitz constant, using an optimization scheme based on the Alternating Direction Method of Multipliers.
result The proposed training procedure successfully increases the robustness of neural networks.
This paper tackles safe global optimization of noisy functions with a Lipschitz condition.
problem Safe global maximization of expensive, noisy, Lipschitz functions.
method Develops a δ-Lipschitz framework and two algorithms to ensure safety constraints are met.
result The proposed methods ensure safety constraints are met before evaluating noisy functions.
Paper presents an efficient algorithm for estimating Lipschitz functions from noisy data.
problem Estimating unknown Lipschitz functions from noisy observations.
method Extends max-affine methods to Lipschitz setting using nonlinear feature expansion and adaptive partitioning.
result Achieves minimax convergence rate with respect to intrinsic dimension, up to logarithmic factors.
GD-trained shallow ReLU nets learn Lipschitz functions with noise.
problem Learning Lipschitz functions with additive noise in overparameterized neural networks.
method Gradient Descent (GD) with early stopping, focusing on the Neural Tangent Kernel (NTK).
result Early-stopped GD achieves minimax optimal rates for learning Lipschitz functions.
Lipschitz GANs solve gradient uninformativeness in GANs.
problem Gradient uninformativeness in GANs.
method Introduce Lipschitz constraint on the discriminative function space.
result Lipschitz GANs eliminate gradient uninformativeness and generate better quality samples.
Optimizes Lipschitz estimates for partitions of unity and characterizes spaces with Assouad-Nagata dimension.
problem Understanding the properties of partitions of unity and their Lipschitz bounds.
method Analyzes the standard partition of unity and its ℓ p \ell^p ℓ p -generalizations, using the approximate midpoint property and Lebesgue number. result Optimal Lipschitz bounds for partitions of unity and characterizes metric spaces with Assouad-Nagata dimension.
Improved algorithm for Lipschitz bandit optimization with reduced complexity.
problem Efficiently solving the Lipschitz bandit optimization problem.
method Tree UCB-Hoeffding algorithm with adaptive partitions and tree-based search strategy.
result Achieves the regret lower bound up to a logarithmic factor with O ( T log T ) \mathcal{O}(T\log T) O ( T log T ) computational cost. HALO uses local Lipschitz constants to optimize functions efficiently.
problem Efficiently solving global optimization problems with complex objective functions.
method Hybrid Adaptive Lipschizian Optimization (HALO) algorithm that estimates local Lipschitz constants and balances global and local information.
result HALO outperforms other global optimization algorithms on numerous test functions.
We model how Lipschitz continuity changes during neural network training.
problem Understanding how Lipschitz continuity evolves during training.
method We use a system of stochastic differential equations to capture the dynamics of Lipschitz continuity under SGD.
result We identify three factors driving the evolution of Lipschitz continuity: gradient flow projection, gradient noise, and Hessian projection.
The goal of the paper is to design sequential strategies which lead to efficient optimization of an unknown function under the only assumption that it has a finite Lipschitz constant. We first identify sufficient conditions for the consistency of generic sequential algorithms and formulate the expected minimax rate for…
New method for RL tasks transfer using Lipschitz continuity.
problem Knowledge transfer in RL tasks over time.
method Established Lipschitz continuity between MDPs and applied it to RL.
result Improved convergence rate and no negative transfer with high probability.
The paper studies optimal maps between hyperbolic surfaces, focusing on their rigidity and obstructions.
problem Finding optimal Lipschitz maps between hyperbolic surfaces and understanding their rigidity and obstructions.
method Introducing deflations, optimal maps to trees that obstruct optimal maps between surfaces, and using a smooth orthogeodesic foliation.
result Deflations are the main obstructions to optimal maps between hyperbolic surfaces, and they are essentially the only ones.
BLiE optimizes hyperparameters with theoretical guarantees and superior performance.
problem Hyperparameter optimization in machine learning.
method Lipschitz bandit approach exploiting Lipschitz continuity.
result BLiE finds ε-optimal hyperparameters with theoretical complexity.
Paper presents a method to accurately estimate Lipschitz constants for DNNs.
problem Estimating Lipschitz constants for deep neural networks is crucial for robustness and stability analysis.
method Convex optimization framework using quadratic constraints to solve SDP for accurate and efficient estimation.
result Our method provides the most accurate Lipschitz bounds compared to existing methods.
New algorithm tackles delayed feedback in Lipschitz bandits with sublinear regret.
problem Delayed feedback in Lipschitz bandits.
method Design of algorithms for bounded and unbounded stochastic delays.
result Sublinear regret guarantees for both bounded and unbounded delays.
Study risk-sensitive reinforcement learning with Lipschitz dynamic risk measures, establishing regret bounds.
problem Risk-sensitive reinforcement learning in Markov decision processes.
method Two model-based algorithms for Lipschitz dynamic risk measures, focusing on regret bounds.
result Upper bounds demonstrate optimal dependencies on actions and episodes, reflecting risk sensitivity vs. sample complexity trade-off.
The problem of optimizing unknown costly-to-evaluate functions has been studied for a long time in the context of Bayesian Optimization. Algorithms in this field aim to find the optimizer of the function by asking only a few function evaluations at locations carefully selected based on a posterior model. In this paper,…
Optimistic method adapted for faster convex-concave min-max problems.
problem Solving convex-concave min-max optimization problems efficiently.
method Adaptive, line search-free second-order methods combining optimistic updates and second-order information.
result Achieves optimal convergence rate without line search or backtracking.
New algorithm tracks changes in infinite action space rewards.
problem Non-stationary Lipschitz bandits with infinite actions.
method Adaptive tracking of significant shifts using hierarchical discretization.
result Achieves minimax-optimal dynamic regret bound of O ~ ( i l d e L 1 / 3 T 2 / 3 ) \mathcal{\widetilde{O}}( ilde{L}^{1/3}T^{2/3}) O ( i l d e L 1/3 T 2/3 ) . New methods for convex optimization with locally Lipschitz gradient, achieving faster convergence.
problem Optimization problems with locally Lipschitz continuous gradient.
method Accelerated proximal gradient (APG) methods and proximal augmented Lagrangian method.
result Achieved faster convergence rates for convex optimization problems with locally Lipschitz gradient.
New algorithms sample from log concave distributions without gradient Lipschitz continuity.
problem Sampling from log concave distributions without gradient Lipschitz continuity.
method Two algorithms based on monotone polygonal (tamed) Euler schemes.
result Non-asymptotic 2-Wasserstein distance bounds between the process and target measure.
New method balances multivariate model fitting for mixed likelihoods.
problem Multivariate models often fit only a subset of observed variables.
method Lipschitz standardization for data preprocessing.
result Lipschitz standardization leads to more accurate multivariate models.
OTAD uses optimal transport to create robust models against adversarial attacks.
problem Vulnerability of deep neural networks to adversarial perturbations.
method OTAD combines optimal transport and Lipschitz networks to create a robust model.
result OTAD outperforms other robust models on diverse datasets.
New framework enhances neural network robustness against adversarial attacks.
problem Vulnerability of deep neural networks to small perturbations.
method Integrates Lipschitz constraint using optimal transport and hinge regularization.
result Proposes a new loss function that certifies adversarial robustness.
Adaptive sampling improves convergence in heterogeneous distributed optimization.
problem Poor performance of classical SGD and SVRG in heterogeneous distributed settings.
method Adaptive sampling of machines with an adaptive estimate of local Lipschitz constants.
result Significantly accelerates convergence rate from maximum to average Lipschitz constant.
This paper analyzes challenges and solutions in deep learning optimization.
problem Gradient vanishing and exploding issues in deep learning.
method Improvement of gradient flow and constraints on Lipschitz constant.
result Enhanced understanding of Jacobian matrices and Lipschitz constants in deep learning modules.
New algorithms for online learning without boundedness or Lipschitz loss assumptions.
problem Online learning with unbounded domains and non-Lipschitz losses.
method Developed an algorithm with a specific regret bound and used it for saddle-point optimization.
result First algorithm achieving non-trivial dynamic regret in an unbounded domain for non-Lipschitz losses.
Study identifies three quantization regimes for ReLU networks.
problem Approximation of Lipschitz functions by ReLU networks with finite-precision weights.
method Established through nonasymptotic tight lower and upper bounds on minimax approximation error.
result Memory-optimality achieved in proper quantization regime for deep networks.