arXiv research

Optimal L2 extension theorem for holomorphic vector bundles with singular metrics.

Optimal $L^2$ extension of sections from subvarieties in Kähler manifolds.

Study optimal holomorphic extensions on complex manifolds with transitivity property.

A new machine learning approach for generating high-quality chordal extensions.

Study optimal holomorphic extensions for jets along submanifolds as tensor powers increase.

The paper characterizes positivity of holomorphic vector bundles via $L^p$-estimates and extensions.

Submodular extensions of an energy function can be used to efficiently compute approximate marginals via variational inference. The accuracy of the marginals depends crucially on the quality of the submodular extension. To identify the best possible extension, we show an equivalence between the submodular extensions of…

We introduce a solution scheme for portfolio optimization problems with cardinality constraints. Typical portfolio optimization problems are extensions of the classical Markowitz mean-variance portfolio optimization model. We solve such type of problems using a method similar to column generation. In this scheme, the o…

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 $L^{2}$ 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…

This paper introduces Jensen, an easily extensible and scalable toolkit for production-level machine learning and convex optimization. Jensen implements a framework of convex (or loss) functions, convex optimization algorithms (including Gradient Descent, L-BFGS, Stochastic Gradient Descent, Conjugate Gradient, etc.), …

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…

In this note, we reveal that our solution of Demailly's strong openness conjecture implies a matrix version of the conjecture; our solutions of two conjectures of Demailly-Kollár and Jonsson-Mustată implies the truth of twisted versions of the strong openness conjecture; our optimal $L^{2}$ extension implies Berndtsson…

RPO uses past and future state-action info for better policy optimization.

We propose practical extensions to Bayesian optimization for solving dynamic problems. We model dynamic objective functions using spatiotemporal Gaussian process priors which capture all the instances of the functions over time. Our extensions to Bayesian optimization use the information learnt from this model to guide…

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.

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.

Solves Merton's investment-consumption problem with certainty equivalent approach.

PALS extends PAL for optimizing stochastic simulators efficiently.

We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot of attention in the Big Data context. Although it has been invented decades ago…

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…

Recent work has extended the theoretical analysis of boosting algorithms to multiclass problems and to online settings. However, the multiclass extension is in the batch setting and the online extensions only consider binary classification. We fill this gap in the literature by defining, and justifying, a weak learning…

Modified K-means ensures local optimality with same complexity.

Local conditions on boundaries of $C^\infty$ 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.

ODTLearn learns optimal decision trees for predictive and prescriptive 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 $W^T H$ to model the Poisson noise or the Gaussian noise.…

Model shows how discount rates affect intergenerational equity in climate mitigation.

The Skorokhod Embedding Problem (SEP) is one of the classical problems in the study of stochastic processes, with applications in many different fields (cf.~ the surveys \cite{Ob04,Ho11}). Many of these applications have natural multi-marginal extensions leading to the \emph{(optimal) multi-marginal Skorokhod problem} …

Sample inefficiency is a long-lasting problem in reinforcement learning (RL). The state-of-the-art estimates the optimal action values while it usually involves an extensive search over the state-action space and unstable optimization. Towards the sample-efficient RL, we propose ranking policy gradient (RPG), a policy …

We study the notion of algebraic tangent cones at singularities of reflexive sheaves. These correspond to extensions of reflexive sheaves across a negative divisor. We show the existence of optimal extensions in a constructive manner, and we prove the uniqueness in a suitable sense. The results here are an algebro-geom…

A new method for constrained Bayesian optimization using Max-Value Entropy Search.

Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This extension is of particular interest for reduced-order modeling in various applicative …

Given a quasisymmetric homeomorphism $\varphi$ of the circle, Bonsante and Schlenker proved the existence and uniqueness of the minimal Lagrangian extension $f_\varphi:\mathbb{H}^2\to\mathbb{H}^2$ to the hyperbolic plane. By previous work of the author, its maximal dilatation satisfies $\log K(f_\varphi)\leq C||\varphi…

We describe a novel extension of soft actor-critics for hierarchical Deep Q-Networks (HDQN) architectures using mutual information metric. The proposed extension provides a suitable framework for encouraging explorations in such hierarchical networks. A natural utilization of this framework is an adversarial setting, w…

New algorithm for online optimization over symmetric cones, unifying previous methods.

This paper describes Plumbing for Optimization with Asynchronous Parallelism (POAP) and the Python Surrogate Optimization Toolbox (pySOT). POAP is an event-driven framework for building and combining asynchronous optimization strategies, designed for global optimization of expensive functions where concurrent function …

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…

Paper extends cohomology classes and holomorphic sections on subvarieties.

MOBO-OSD optimizes multi-objective functions using orthogonal search directions.

A new convex loss function optimizes set predictions with balanced size and coverage.

In this paper, we provide new insights on the Unadjusted Langevin Algorithm. We show that this method can be formulated as a first order optimization algorithm of an objective functional defined on the Wasserstein space of order $2$. Using this interpretation and techniques borrowed from convex optimization, we give a …

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…

When hyperparameter optimization of a machine learning algorithm is repeated for multiple datasets it is possible to transfer knowledge to an optimization run on a new dataset. We develop a new hyperparameter-free ensemble model for Bayesian optimization that is a generalization of two existing transfer learning extens…