We call a Morse function on a closed manifold -constrained if neither nor has critical points of indefinite Morse index . In this paper we study bordism groups of -constrained Morse functions, and thus interpolate between the case of bordism groups of Morse functions (computed by Ikegami…
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48 results for “functionally constrained”
New method tackles constrained optimization in multi-fidelity Bayesian optimization.
problem Efficiently identifying feasible regions in constrained optimization problems.
method Proposes CMFBO method with novel acquisition functions.
result Demonstrates effectiveness on synthetic problems and real-world ICF and joint design problems.
The paper develops methods for time-varying constrained online convex optimization.
problem Time-varying loss and constraint functions in online convex optimization.
method Model-based augmented Lagrangian methods (MALM) for time-varying and delayed feedback.
result Sublinear regret and constraint violation for both time-varying and delayed feedback scenarios.
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.
Double Duality: Variational Primal-Dual Policy Optimization for Constrained Reinforcement Learningcs.LG
Algorithm optimizes constrained reinforcement learning with dual variables.
problem Minimizing convex functional subject to convex constraint in large state spaces.
method VPDPO algorithm using Lagrangian and Fenchel duality.
result Achieves sublinear regret and constraint violation, globally optimal policy.
A new method for optimizing non-decomposable metrics with constraints.
problem Optimizing complex machine learning objectives with thresholded constraints.
method Formulate rate-constrained optimization using the Implicit Function theorem and solve with gradient-based methods.
result Demonstrated effectiveness over existing methods on benchmark datasets.
Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy under compactly supported infinitesimal conformal variations. Examples include all constant mean curvature surfaces in space forms. In this paper we investigate more generally the crit…
Self-distillation improves constrained language generation by aligning models with target distributions.
problem Sparse and uninformative reward signals in constrained generation settings.
method Iteratively refining the base model through self-distillation, incorporating learned twist functions and proposals.
result Substantial gains in generation quality through improved model alignment with target distributions.
New method optimizes processes under constraints using bivariate Gaussian models.
problem Optimizing processes with constraints using traditional methods.
method Developed a constrained expected improvement acquisition function using bivariate Gaussian process models.
result Demonstrated improved performance in a manufacturing cure process optimization.
The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice. While these relaxations can be solved globally optimally, they are often too loos…
New adaptive methods for constrained convex optimization and variational inequalities.
problem Optimization of constrained convex problems and variational inequalities.
method AdaACSA and AdaAGD+ are accelerated methods that achieve nearly-optimal convergence rates for smooth and non-smooth functions.
result Achieve nearly-optimal convergence rates for both smooth and non-smooth functions, even with stochastic gradients.
New algorithm solves complex optimization problems efficiently.
problem Minimizing convex upper-level functions over optimal lower-level solutions.
method Reformulates bilevel problems into functionally constrained problems, achieving near-optimal rates.
result Achieves near-optimal rates for both smooth and nonsmooth problems.
Proposes Constrained Q-learning for reinforcement learning with constraints.
problem Optimizing multiple objectives while adhering to constraints in reinforcement learning.
method Directly restricts the action space in Q-update to learn optimal Q-function for constrained MDP.
result Improves safety and optimality in high-level decision making for autonomous driving.
Paper tackles multivariate shape-constrained convex regression problems.
problem Fitting a convex function to data with component-wise monotonicity and uniform Lipschitz continuity.
method Least squares estimator via solving a constrained convex quadratic programming problem. Efficient algorithms designed: sGS-ADMM and pALM.
result Both proposed algorithms outperform state-of-the-art methods in numerical experiments.
PDCA algorithm learns policies for RL with constraints using a primal-dual approach.
problem Offline constrained reinforcement learning with general function approximation.
method Primal-Dual-Critic Algorithm (PDCA) using a primal-dual approach.
result PDCA finds a near saddle point of the Lagrangian, nearly optimal for constrained RL.
Koopman Regularizationmath.DS
Koopman Regularization learns governing equations from sparse data.
problem Learning governing equations from sparse and corrupted data.
method Constrained optimization using Koopman Eigenfunctions.
result Restores dynamics precisely with minimal assumptions.
Develops methods for estimating constrained function-valued parameters in infinite-dimensional models.
problem Estimating function-valued parameters with structural constraints in complex models.
method Characterizes constrained solutions as minimizers of penalized population risk, using a Lagrange-type formulation and path through unconstrained space.
result Proposes estimators that achieve optimal risk and constraint satisfaction, applicable across various statistical learning approaches.
Training neural networks under a strict Lipschitz constraint is useful for provable adversarial robustness, generalization bounds, interpretable gradients, and Wasserstein distance estimation. By the composition property of Lipschitz functions, it suffices to ensure that each individual affine transformation or nonline…
We give an overview of the constrained Willmore problem and address some conjectures arising from partial results and numerical experiments. Ramifications of these conjectures would lead to a deeper understanding of the Willmore functional over conformal immersions from compact surfaces.
Bayesian optimization (BO) is a model-based approach to sequentially optimize expensive black-box functions, such as the validation error of a deep neural network with respect to its hyperparameters. In many real-world scenarios, the optimization is further subject to a priori unknown constraints. For example, training…
Paper tackles non-convex constrained DRO with a stochastic algorithm for large-scale applications.
problem Training robust models against data distribution shifts with non-convex loss functions.
method Developed a stochastic algorithm for non-convex constrained DRO with a complexity independent of dataset size.
result Algorithm finds ε-stationary points with computational complexity of O(ε^(-3k_*-5)) for general Cressie-Read divergence.
A new method for optimizing black-box problems with constraints.
problem Optimizing black-box systems with multiple performance criteria and constraints.
method Developed a novel constrained Bayesian optimization approach based on the knowledge gradient method.
result A new acquisition function that balances optimality and feasibility.
This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of…
Efficiently optimizes constrained problems with two-step lookahead BO.
problem Optimizing constrained problems with limited computational resources.
method Two-step lookahead Bayesian optimization with inequality constraints, using a novel unbiased gradient estimator.
result Significantly improves query efficiency over previous methods.
New method improves robustness of neural network-based debiasing.
problem Improving robustness of neural network-based debiasing.
method Moment-constrained learning for neural networks.
result Improved performance compared to state-of-the-art benchmarks.
Constrained Willmore surfaces are critical points of the Willmore functional under conformal variations. As shown in [5] one can associate to any conformally immersed constrained Willmore torus f a compact Riemann surface Σ, such that f can be reconstructed in terms of algebraic data on Σ. Particularly interesting exam…
Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained optimization from theoretical, algorithmic, and application aspects in the context of spars…
Solves VaR-constrained portfolio optimization in markets with stochastic volatility.
problem Optimizing portfolio in markets with stochastic volatility under VaR constraints.
method Dynamic programming approach to Heston's stochastic volatility model.
result Optimal investment strategy linked to unconstrained problem via a vega-neutral derivative.
We investigate the Hawking energy of small surfaces in space times without symmetry assumptions by introducing the notion of Hawking type functionals. In particular, we find that Hawking type functionals are generalized Willmore functionals which allows us to find area constrained, minimizing, immersed, haunted bubble …
The paper optimizes policies constrained to Schur stabilizing controllers using a Newton-type algorithm.
problem Optimizing policies under linear constraints in control systems.
method Newton-type algorithm on a manifold of Schur stabilizing controllers with a Riemannian metric.
result Local convergence guarantees for the Newton-type algorithm without relying on exponential mapping or retractions.
Novel method for efficient optimization of noisy, expensive hybrid models.
problem Efficient optimization of hybrid models with noisy observations and constraints.
method Constrained Upper Quantile Bound (CUQB) method exploiting composite structure.
result Significantly improved sampling efficiency and theoretical guarantees.
Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networksphysics.geo-ph
Unified framework for Bayesian PDE-constrained inversion using physics-informed neural networks.
problem Incorporating prior distributions in function space into Bayesian PINN-based inversion.
method Functional-prior-based approaches (fpBPINN) to Bayesian PDE-constrained inversion using physics-informed neural networks (PINNs). Two complementary approaches: FPI-BPINN and fParVI-PINN.
result Accurate estimation of posterior distributions in seismic traveltime tomography and Darcy-flow permeability inversion.
In this paper we consider two special classes of constrained Willmore tori in the 3-sphere. The first class is given by the rotation of closed elastic curves in the upper half plane - viewed as the hyperbolic plane - around the x-axis. The second is given as the preimage of closed constrained elastic curves, i.e., elas…
Minimalist softmax attention learns constrained Boolean functions with supervision.
problem Learning -bit Boolean functions, especially AND and OR.
method Minimalist single-head softmax-attention mechanism with teacher forcing.
result Minimalist attention can solve Boolean tasks with supervision, but not without.
A new method trains physics-constrained neural networks more efficiently.
problem Training machine learning tools with limited data and physical constraints.
method Dual-Dimer method for searching saddle points in nonconvex-nonconcave functions.
result The Dual-Dimer method improves training efficiency and convergence speed.
New method solves complex constrained optimization problems.
problem Constrained nonconvex-nonconcave minimax optimization problems.
method Inexact proximal gradient method using sequential convex programming.
result Established complexity guarantees for approximate stationary points.
Functional BART with Shape Priors: A Bayesian Tree Approach to Constrained Functional Regressionstat.ME
Functional BART adds shape priors to Bayesian tree regression for better curve fitting.
problem Regression with function-on-scalar data and shape constraints.
method Bayesian tree structure with spline representations, customized Bayesian backfitting algorithm, shape priors.
result Improved estimation and prediction accuracy with shape priors.
CEI achieves convergence rates for constrained Bayesian optimization.
problem Constrained Bayesian optimization with theoretical convergence rates.
method Analyzing simple regret upper bound for CEI in RKHS and Gaussian process settings.
result CEI achieves convergence rates of and for squared exponential and Matérn kernels, respectively.
We study the safe reinforcement learning problem with nonlinear function approximation, where policy optimization is formulated as a constrained optimization problem with both the objective and the constraint being nonconvex functions. For such a problem, we construct a sequence of surrogate convex constrained optimiza…
Oracle-efficient algorithm for offline RL with partial data coverage.
problem Offline reinforcement learning with partial data coverage and constraints.
method PDOCRL, a primal-dual algorithm with decomposed linear-programming formulation.
result Near-optimal, near-feasible policy with \(\widetilde{\mathcal O}(ε^{-2})\) sample guarantee.
Novel evolutionary strategy solves stochastic constrained optimization problems.
problem Optimizing objective functions with stochastic constraints in reinforcement learning.
method Design of a novel optimization algorithm with a sufficient decrease mechanism for stochastic constrained problems.
result Demonstrated convergence of the algorithm on control tasks and constrained optimization problems.
Shielded LMC samples from non-convex spaces with repulsive drift.
problem Sampling from non-convex spaces with convex holes.
method Combining adaptive temperature and repulsive drift.
result Advantages over unconstrained sampling in constrained spaces.
Method reformulates constrained optimization as latent space inference.
problem Optimizing black-box functions with hard constraints.
method Posterior inference in latent space using flow-based models and diffusion models.
result Method achieves superior performance across various tasks.
The tori , where , are constrained Willmore surfaces, i.e. critical points of the Willmore functional among tori of the same conformal type. We compute which of the are stable critical points.
New RL algorithm achieves sublinear regret and constraint violation without simulators.
problem Maximizing reward under utility constraints in large-scale systems.
method Model-free, simulator-free algorithm using LSVI-UCB with primal-dual optimization and soft-max policy.
result Achieves regret and constraint violation bounds.
Proposes ConstraintMatch for semi-supervised clustering with unconstrained data.
problem Leveraging unconstrained data alongside constraints for clustering models.
method Semi-supervised context with pseudo-constraining and pseudo-labeling mechanisms.
result Demonstrates effectiveness of ConstraintMatch over baselines.
We propose and analyze a constrained level-set method for semi-automatic image segmentation. Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the segmented objects. Such a-priori information can be expressed in terms of upper a…
Understanding Machine-learned Density Functionalsphysics.chem-ph
Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and highly accurate energies are achieved. Accurate {\em constrained optimal densitie…