New algorithms for sampling in constrained domains without learning rates.
problem Sampling in constrained domains with fairness constraints and post-selection inference.
method Coin betting ideas from convex optimisation and a unifying framework for constrained sampling.
result Our algorithms achieve competitive performance without hyperparameter tuning.
In-BO optimizes complex constrained domains using SIn-GP surrogate models.
problem Optimizing in complex constrained domains with irregular shapes.
method Sparse Intrinsic Gaussian Processes (SIn-GP) on manifolds with heat kernel estimation.
result In-BO outperforms traditional BO in complex constrained domains.
New method for constrained sampling using gradient flows.
problem Sampling from constrained domains.
method Introducing a boundary condition for gradient flow to confine particles within the domain.
result Provable continuous-time convergence in total variation for constrained sampling.
Deep learning struggles with out-of-distribution data, so this paper tackles domain generalization.
problem Deep learning models fail with out-of-distribution data.
method Formulates domain generalization as a constrained statistical learning problem, then uses nonconvex duality theory to develop an algorithm with convergence guarantees.
result Improves domain generalization by up to 30 percentage points on various benchmarks.
Extends Langevin dynamics for constrained domains.
problem Optimization of constrained probability measures.
method Mirror mean-field Langevin dynamics (MMFLD).
result Linear convergence guarantees and propagation of chaos results.
Proposes r2SGLD for efficient constrained exploration in non-convex learning.
problem Stagnation in high-temperature chains of reSGLD in distribution tails.
method r2SGLD: replica exchange with reflection steps in a bounded domain.
result Reflection steps enhance mixing rates with quadratic improvement in domain diameter.
The paper tackles gradual domain adaptation with manifold-constrained DRO, showing error bounds across distributions.
problem Gradual domain adaptation challenge with manifold-constrained data distributions.
method Distributionally Robust Optimization (DRO) with an adaptive Wasserstein radius.
result Theoretical bounds on classification error across distributions, demonstrating error propagation dynamics.
We propose a class of intrinsic Gaussian processes (in-GPs) for interpolation, regression and classification on manifolds with a primary focus on complex constrained domains or irregular shaped spaces arising as subsets or submanifolds of R, R2, R3 and beyond. For example, in-GPs can accommodate spatial domains arising…
DE-PSGLD samples from constrained distributions in a decentralized manner.
problem Sampling from log-concave distributions with constraints.
method Decentralized Proximal Stochastic Gradient Langevin Dynamics with proximal regularization.
result DE-PSGLD converges to a regularized Gibbs distribution and maintains posterior concentration.
We use a locally constrained mean curvature flow to prove the isoperimetric inequality for spacelike domains in generalized Robertson-Walker spaces satisfying the null convergence condition.
Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA). Bayesian inference involving probability distributions confined to constrained d…
New samplers minimize KL divergence for constrained and non-Euclidean geometries.
problem Efficient sampling from constrained and non-Euclidean distributions.
method Stein Variational Mirror Descent and Mirrored Stein Variational Gradient Descent.
result New samplers converge more rapidly and accurately than prior methods.
Paper tackles constrained learning with non-convex losses, overcoming challenges with new approach.
problem Challenges in learning with non-convex losses and statistical constraints.
method Learning in the empirical dual domain, bounding empirical duality gap.
result Established a constrained counterpart to classical learning theory.
The area of constrained clustering has been extensively explored by researchers and used by practitioners. Constrained clustering formulations exist for popular algorithms such as k-means, mixture models, and spectral clustering but have several limitations. A fundamental strength of deep learning is its flexibility, a…
Paper proposes risk-averse reinforcement learning algorithms.
problem Managing model uncertainty in reinforcement learning.
method Entropic risk constrained policy gradient and actor-critic algorithms.
result Demonstrates usefulness of risk-averse algorithms on various domains.
New diffusion models handle constrained domains, improving generative tasks.
problem Diffusion models struggle with manifolds defined by inequality constraints.
method Developed two noising processes: logarithmic barrier metric and reflected Brownian motion.
result Demonstrated practical utility on synthetic and real-world tasks.
Gaussian processes (GPs) provide a powerful framework for extrapolation, interpolation, and noise removal in regression and classification. This paper considers constraining GPs to arbitrarily-shaped domains with boundary conditions. We solve a Fourier-like generalised harmonic feature representation of the GP prior in…
Geometric inequalities for static convex domains in hyperbolic space proved.
problem Proving geometric inequalities for static convex domains in hyperbolic space.
method Using static convexity of flow hypersurfaces, new inequalities are derived.
result New family of geometric inequalities for static convex domains in hyperbolic space.
Algorithm mitigates performance loss in constrained reinforcement learning with model misspecification.
problem Performance loss in reinforcement learning policies due to model misspecification in constrained control systems.
method Proposes an algorithm to handle constrained model misspecification in continuous control systems.
result Algorithm successfully mitigates performance loss in real-world reinforcement learning tasks.
New algorithm enhances generative modeling for bounded domains.
problem Ad-hoc thresholding techniques for boundary enforcement in diffusion models.
method Reflected Schrödinger Bridge algorithm for entropy-regularized optimal transport.
result Generative modeling in diverse bounded domains with optimal transport properties.
New method improves generative modeling on convex domains using regularized mirror maps and Student-t priors.
problem Challenges in generative modeling on convex domains with heavy-tailed targets.
method Mirror Flow Matching with regularized mirror maps and Student-t priors.
result Empirically outperforms baselines and achieves competitive sample quality.
RFM improves CNFs by adding a boundary constraint term and matching velocity fields.
problem Flow matching on constrained domains leads to unnatural samples.
method RFM adds a boundary constraint term and matches velocity fields in a simulation-free manner.
result RFM achieves comparable or better results on standard image benchmarks and produces high-quality samples.
Develops a theory to make learning solutions fair and safe.
problem Ensuring learning solutions are unbiased and safe in critical applications.
method Generates a generalization theory based on PAC learning framework, introduces constrained learning algorithm.
result Proves that constrained learning is as learnable as unconstrained learning, provides practical algorithm.
New conditions ensure Dantzig-Wolfe relaxation matches rank-constrained optimization problems.
problem Rank-constrained optimization problems with linear matrix inequalities.
method Investigates Dantzig-Wolfe relaxation and develops conditions for exactness.
result Conditions for extreme point, convex hull, and objective exactness.
Machine-learning models for security-critical applications such as bot, malware, or spam detection, operate in constrained discrete domains. These applications would benefit from having provable guarantees against adversarial examples. The existing literature on provable adversarial robustness of models, however, exclu…
Adaptive algorithm AMSGrad converges for weakly convex constrained optimization problems.
problem Solving constrained stochastic optimization problems with weakly convex objectives.
method Analysis of AMSGrad algorithm for a specific class of problems.
result AMSGrad achieves a convergence rate of ildeO(t−1/4) for the norm of the gradient of the Moreau envelope. We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the feasible set of densities and propose a general recipe for such problems. We apply …
New method for sampling on constrained domains using orthogonal-space gradient flow.
problem Sampling on manifolds defined by constraints is challenging.
method Orthogonal-Space Variational Gradient Descent (O-Gradient)
result O-Gradient converges to the target constrained distribution efficiently.
MAGI-X learns unknown dynamics from data without numerical integration.
problem Difficult to propose ODEs in closed-form for complex systems.
method MAGI-X uses neural networks within a manifold-constrained Gaussian process framework.
result MAGI-X achieves competitive accuracy in fitting and forecasting with reduced computational time.
Proposes a new method for constrained generative modeling using Langevin dynamics.
problem Challenges in satisfying underlying constraints with score-based generative models.
method Uses kinetic Langevin dynamics with specular reflection to model constraints.
result Demonstrates efficient numerical samplers with optimal convergence rates.
Valid certifies LLMs' domain adherence, bounding out-of-domain behavior.
problem Adversarial susceptibility of LLMs to generate out-of-domain outputs.
method VALID approach providing adversarial bounds as a certificate.
result Validates LLMs' domain adherence with meaningful certificates.
This article studies the sensitivity of the power utility maximization problem with respect to the investor's relative risk aversion, the statistical probability measure, the investment constraints and the market price of risk. We extend previous descriptions of the dual domain then exploit the link between the constra…
The paper shows how Lagrangian duality improves deep learning for constrained problems.
problem Learning optimization problems with complex constraints in science and engineering.
method Lagrangian duality applied to deep learning models.
result Lagrangian duality brings significant benefits for constrained learning tasks.
ADMM solves constrained CASH problems by breaking them into smaller, manageable pieces.
problem Handling black-box constraints in CASH problems.
method Leverages ADMM optimization framework to decompose CASH problems.
result ADMM facilitates incorporation of black-box constraints.
New model generates data on constrained sets without losing tractability.
problem Generating data on constrained sets without losing tractability.
method Mirror Diffusion Models (MDM) learn diffusion processes in a dual space constructed from a mirror map.
result MDM generates data on convex constrained sets without losing tractability.
State-constrained offline RL expands RL's learning scope.
problem Batch-constrained offline RL limits policies to seen actions.
method Introduces state-constrained offline RL focusing on state distribution.
result Policy can take high-quality out-of-distribution actions.
New method constrains CNN filter frequencies to improve robustness.
problem CNN bias towards low frequency components, leading to poor performance in scenario transformations.
method Frequency domain regularization by constraining filter spectra, training valid frequency range end-to-end.
result Demonstrated effectiveness in defending adversarial perturbations, reducing generalization gap, and improving transfer learning.
The paper tackles MAP inference over non-convex constraints in safety-critical settings.
problem Efficiently computing MAP predictions subject to non-convex constraints is challenging.
method The paper investigates conditions for exact and efficient MAP inference over continuous variables and devises scalable algorithms for both tractable and general cases.
result The proposed methods outperform constraint-agnostic baselines and scale to complex densities.
A new method solves diagonally constrained SDPs quickly and accurately.
problem Solving large-scale diagonally constrained SDPs efficiently.
method Combines momentum from convex optimization with coordinate descent and matrix factorization.
result Local linear convergence and first-order critical point convergence proved.
A new method uncovers intrinsic data structures for unsupervised domain adaptation.
problem Learning domain-aligned features can damage intrinsic target discrimination.
method Structurally Regularized Deep Clustering (H-SRDC) integrating structural source regularization.
result H-SRDC outperforms existing methods in image classification and semantic segmentation.
The paper studies continuous submodular functions and their optimization.
problem Maximizing continuous submodular functions in poly. time.
method Characterization of continuous submodularity, operations preserving it, and algorithms for constrained maximization.
result Continuous submodularity is equivalent to a weak DR property, leading to continuous DR-submodular functions with the full DR property.
New flow for capillary surfaces converges to spherical caps.
problem Optimizing capillary surfaces in space forms.
method Constrained mean curvature flow.
result Flow converges to spherical caps globally.
Active learning agents typically employ a query selection algorithm which solely considers the agent's learning objectives. However, this may be insufficient in more realistic human domains. This work uses imitation learning to enable an agent in a constrained environment to concurrently reason about both its internal …
Physics-informed neural networks struggle with stiffness leading to gradient imbalance.
problem Gradient pathologies in physics-informed neural networks.
method Learning rate annealing and novel neural network architecture.
result Significant improvement in predictive accuracy (50-100x) across various physics problems.
Learning domain-invariant representation is a dominant approach for domain generalization (DG), where we need to build a classifier that is robust toward domain shifts. However, previous domain-invariance-based methods overlooked the underlying dependency of classes on domains, which is responsible for the trade-off be…
We prove symplectic hypersurfaces in Weinstein domains and give obstructions for manifold boundaries.
problem Obstructions for 3-manifolds to bound Weinstein domains in certain symplectic 4-manifolds.
method Symplectic embedding and deformation techniques.
result Obstructions for 3-manifolds to bound Weinstein domains in rational surfaces.
Domain adaptation framework identifies latent variables for target distribution identifiability.
problem Unsupervised domain adaptation without identifiable joint distribution of features and labels.
method Formulated latent variable model with invariant and changing components, constrained domain shift to influence only changing components.
result Joint distribution of data and labels in target domain is identifiable under mild conditions.
Adapts Bayesian optimization for mixed constraints in aircraft design.
problem Optimizing expensive black box functions with mixed constraints.
method Super efficient global optimization with upper trust bound for constraints, Gaussian process uncertainty, refinement procedure.
result Superior performance on aircraft design problem compared to state-of-the-art solvers.