Optimal L2 extension theorem for holomorphic vector bundles with singular metrics.
problem Establishing conditions for optimal L2 extension in complex geometry.
method Analyzing singular Nakano positivity and applying L2 extension theorem.
result Necessary condition for equality in optimal L2 extension theorem.
Optimal L2 extension of sections from subvarieties in Kähler manifolds.
problem Extending holomorphic sections from subvarieties in weakly pseudoconvex manifolds.
method Using optimal L2 extension for holomorphic sections of a holomorphic vector bundle. result Achieved optimal L2 extension of sections from subvarieties in weakly pseudoconvex Kähler manifolds. Study optimal holomorphic extensions on complex manifolds with transitivity property.
problem Optimal holomorphic extensions on complex manifolds with transitivity property.
method Use Toeplitz operators and transitivity property for optimal holomorphic extensions.
result Transitivity property of optimal holomorphic extensions with small defect.
A new machine learning approach for generating high-quality chordal extensions.
problem Defining the definitive relation between chordal extension and optimization algorithm performance.
method On-policy imitation learning scheme mimicking the minimum degree rule to generate high-quality chordal extensions.
result On-policy imitation learning approach effectively learns the minimum degree policy and produces graphs with desirable fill-in characteristics.
Jensen simplifies machine learning and optimization with an extensible toolkit.
problem Complex machine learning and optimization tasks in production environments.
method Develops a framework for convex functions and optimization algorithms, enabling easy deployment and extension.
result Jensen allows for quick model deployment and extension with minimal code, making machine learning accessible.
The paper solves conjectures related to strong openness and optimal L2 extension.
problem Strong openness of multiplier ideal sheaves and optimal L2 extension. method Solution of conjectures related to Demailly's strong openness and related conjectures.
result Optimal L2 extension implies Berndtsson's positivity of vector bundles. Study optimal holomorphic extensions for jets along submanifolds as tensor powers increase.
problem Optimal holomorphic extensions of jets along submanifolds for high tensor powers.
method Careful study of Schwartz kernels and Bergman projectors for asymptotic analysis.
result Explicit asymptotic formula for the extension operator as tensor power tends to infinity.
Optimizes submodular extensions for efficient marginal estimation.
problem Efficiently compute approximate marginals for submodular energy functions.
method Equivalence between submodular extensions and LP relaxations for MAP estimation; worst-case optimality established.
result Worst-case optimal submodular extension for various models.
The paper characterizes positivity of holomorphic vector bundles via Lp-estimates and extensions.
problem Characterizing positivity of holomorphic vector bundles using Lp-estimates and extensions. method Introducing four conditions for Hermitian (or Finsler) vector bundles and characterizing Nakano and Griffiths positivity.
result Characterization of Nakano and Griffiths positivity via specific Lp-conditions. Solves portfolio optimization with cardinality constraints using column generation.
problem Portfolio optimization with cardinality constraints.
method Column generation method applied to a subset of assets in a master convex quadratic problem, using dual information to propose new assets.
result Solves portfolio optimization problems efficiently with cardinality constraints.
We consider the optimization of active extension portfolios. For this purpose, the optimization problem is rewritten as a stochastic programming model and solved using a clever multi-start local search heuristic, which turns out to provide stable solutions. The heuristic solutions are compared to optimization results o…
In this paper, we solve the optimal constant problem in the setting of Ohsawa's generalized L2 extension theorem. As applications, we prove a conjecture of Ohsawa and the extended Suita conjecture, we also establish some relations between Bergman kernel and logarithmic capacity on compact and open Riemann surfaces…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast…
We consider the problem of extending functions φ:\to S^n to functions u:B^{n+1}\to S^n for n=2,3. We assume φto belong to the critical space W^{1,n} and we construct a W^{1,(n+1,\infty)}-controlled extension u. The Lorentz-Sobolev space W^{1,(n+1,\infty)} is optimal for such controlled extension. Then we use such resul…
Bayesian optimization adapted for dynamic problems with improved efficiency.
problem Optimizing functions that change over time.
method Spatiotemporal Gaussian process priors and adaptive evaluation strategy.
result Improves efficiency in tracking and optimizing dynamic functions.
RPO uses past and future state-action info for better policy optimization.
problem Sample inefficiency in on-policy reinforcement learning methods.
method Reflective Policy Optimization (RPO) integrates past and future state-action info for policy improvement.
result RPO improves policy performance and contracts the solution space, leading to faster convergence.
In this paper we discuss an extension of Perelman's comparison for quadrangles. Among applications of this new comparison theorem, we study the equidistance evolution of hypersurfaces in Alexandrov spaces with non-negative curvature. We show that, in certain cases, the equidistance evolution of hypersurfaces become tot…
Paper proposes efficient optimizers for large language models with fast convergence and low memory usage.
problem Designing efficient optimizers for large language models with low-memory requirements and fast convergence.
method Structured Fisher information matrix approximation and low-rank extension framework.
result New optimizers (RACS and Alice) achieve better convergence and lower memory usage than existing methods.
Solves convex optimization with many constraints in a distributed system.
problem Solving convex optimization problems with many convex constraints in a distributed setting.
method Extension of ADMM to handle arbitrary inequality constraints.
result Inherits convergence guarantees of ADMM and Augmented Lagrangian method.
In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least squares problem, highlight special structure, and show that the classic filtering an…
A simple model for unbalanced optimal transport captures key features.
problem Capturing the main features of unbalanced optimal transport.
method Introducing a metric on the conical extension of diffeomorphisms and studying its properties.
result Total mass evolves with constant acceleration along geodesics.
Solves Merton's investment-consumption problem with certainty equivalent approach.
problem Maximizing CRRA utility of consumption over time and investment mix.
method Identifies a certainty equivalent problem for the Merton problem, reformulates it as an SOCP, and applies it to model predictive control.
result The certainty equivalent problem can be solved as an SOCP, facilitating model predictive control.
PALS extends PAL for optimizing stochastic simulators efficiently.
problem Optimizing stochastic simulators with high output variance and expensive evaluations.
method Bayesian optimization with probabilistic models, extending PAL for stochastic settings.
result PALS outperforms other methods in optimizing stochastic simulators.
The maximal dilatation of certain minimal Lagrangian extensions is bounded by a constant.
problem Bounding the maximal dilatation of minimal Lagrangian extensions.
method Analyzing two one-parameter families of minimal Lagrangian extensions.
result Constraints on the optimal constant C for the maximal dilatation.
Extends boosting to online multiclass problems with optimal algorithms.
problem Online multiclass classification challenges.
method Defines and justifies a weak learning condition for online multiclass boosting. Proposes an adaptive algorithm.
result Optimal boosting algorithm for online multiclass problems.
Study tangent cones of reflexive sheaves, proving existence and uniqueness.
problem Understanding singularities of reflexive sheaves and their extensions.
method Constructive proof of existence and suitable uniqueness proof.
result Existence and uniqueness of optimal extensions of reflexive sheaves.
Regularized empirical risk minimization with constrained labels (in contrast to fixed labels) is a remarkably general abstraction of learning. For common loss and regularization functions, this optimization problem assumes the form of a mixed integer program (MIP) whose objective function is non-convex. In this form, t…
New approach solves multi-marginal Skorokhod Embedding Problem.
problem Solving multi-marginal Skorokhod Embedding Problem.
method Extending theory from one-marginal to multi-marginal setup.
result All classical optimal embeddings have natural multi-marginal counterparts.
Modified K-means ensures local optimality with same complexity.
problem Lack of rigorous analysis on local optimality guarantees of K-means.
method Proposed modifications to K-means ensuring local optimality.
result Proposed methods provide improved locally optimal solutions.
Local conditions on boundaries of C∞ Levi-flat hypersurfaces, in case the boundary is a generic submanifold, are studied. For nontrivial real analytic boundaries we get an extension and uniqueness result, which forces the hypersurface to be real analytic. This allows us to classify all real analytic generic bou…
Bayes-optimal learning of deep random networks with Gaussian weights is studied.
problem Learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights.
method Closed-form expressions for Bayes-optimal test error, ridge regression, kernel and random features regression are computed.
result Optimally regularized ridge regression and kernel regression achieve Bayes-optimal performances, while logistic loss yields a near-optimal test error for classification.
ODTLearn learns optimal decision trees for predictive and prescriptive tasks.
problem Learning optimal decision trees for high-stakes predictive and prescriptive tasks.
method Mixed-integer optimization framework and object-oriented design.
result Implementation of optimal decision trees for various tasks.
Non-negative matrix factorization (NMF) approximates a non-negative matrix X by a product of two non-negative low-rank factor matrices W and H. NMF and its extensions minimize either the Kullback-Leibler divergence or the Euclidean distance between X and WTH to model the Poisson noise or the Gaussian noise.…
Model shows how discount rates affect intergenerational equity in climate mitigation.
problem Intergenerational equity in climate mitigation decisions.
method Extended DICE model with stochastic discount rates and financing extensions.
result Discount-rate uncertainty amplifies intergenerational inequality in climate mitigation.
A new method for constrained Bayesian optimization using Max-Value Entropy Search.
problem Optimizing expensive functions with unknown constraints.
method Constrained Max-value Entropy Search (cMES), a novel acquisition function.
result cMES outperforms prior work on constrained hyperparameter optimization problems.
Paper presents optimal low-rank DMD for better system analysis.
problem Improving DMD for low-rank approximations in non-linear systems.
method Developed a closed-form optimal solution using SVD.
result Demonstrated superior performance compared to existing methods.
New analysis of Langevin Monte Carlo via convex optimization.
problem Sampling from logconcave smooth and non-smooth target distributions.
method Formulation as a convex optimization problem, analysis using convex optimization techniques.
result Non-asymptotic analysis of Unadjusted Langevin Algorithm and new sampling methods.
POAP and pySOT improve surrogate optimization of expensive functions.
problem Optimizing expensive functions with concurrent evaluations.
method Event-driven asynchronous framework for optimization strategies.
result Asynchronous computation offers significant speed-up advantages.
New algorithm for online optimization over symmetric cones, unifying previous methods.
problem Online convex optimization over symmetric cones.
method Symmetric-Cone Multiplicative Weights Update (SCMWU) algorithm.
result SCMWU is a no-regret algorithm.
We provide some theoretical extensions and a calibration protocol for our former dynamic optimal execution model. The Hawkes parameters and the propagator are estimated independently on financial data from stocks of the CAC40. Interestingly, the propagator exhibits a smoothly decaying form with one or two dominant time…
This paper proposes an out-of-sample extension framework for a global manifold learning algorithm (Isomap) that uses temporal information in out-of-sample points in order to make the embedding more robust to noise and artifacts. Given a set of noise-free training data and its embedding, the proposed framework extends t…
RPG improves sample efficiency in RL by learning optimal action ranks.
problem Sample inefficiency in reinforcement learning.
method Ranking Policy Gradient (RPG) method that learns optimal rank of discrete actions.
result RPG reduces sample complexity and improves sample efficiency for large-scale problems.
Paper extends cohomology classes and holomorphic sections on subvarieties.
problem Tackles extension of cohomology classes and holomorphic sections on subvarieties.
method Uses quotient sheaves of multiplier ideal sheaves of quasi-plurisubharmonic functions.
result Provides positive answers to questions and generalizes existing L2 extension theorems. MOBO-OSD optimizes multi-objective functions using orthogonal search directions.
problem Challenging multi-objective optimization problem.
method Solves multiple constrained optimization problems along orthogonal search directions.
result Consistently outperforms state-of-the-art algorithms.
A new convex loss function optimizes set predictions with balanced size and coverage.
problem Optimizing set predictions with balanced size and coverage.
method Proposes a convex loss function using Choquet integrals for nondecreasing subset-valued functions.
result Optimal trade-offs between conditional probabilistic coverage and set size.
We prove the existence of optimal strategies for agents with cumulative prospect theory preferences who trade in a continuous-time illiquid market, transcending known results which pertained only to risk-averse utility maximizers. The arguments exploit an extension of Skorohod's representation theorem for tight sequenc…
The paper develops optimal strategies for high-dimensional statistical arbitrage using factor models and stochastic control.
problem Optimal strategies for high-dimensional statistical arbitrage in a factor model setting.
method Combines factor models with stochastic control to derive optimal strategies.
result Closed-form optimal strategies for market-neutral portfolios in a high-dimensional setting.
Paper develops privacy-preserving algorithms for online submodular optimization.
problem Online submodular optimization under differential privacy constraints.
method Develops algorithms for both full information and bandit feedback settings, using Lovasz extensions and unbiased estimates.
result Achieves low expected regret with differential privacy guarantees in both settings.