Space mapping speeds up shape optimization for PDEs.
problem Efficiently solving shape optimization problems constrained by PDEs.
method Combines fine and coarse model optimizations using Riemannian metrics.
result Space mapping methods are highly efficient for complex shape optimization problems.
Optimal insurance policy for exponential utility maximization with convex premium calculation.
problem Maximizing terminal wealth utility with exponential utility function and convex premium formula.
method Necessary condition for optimal indemnity, numerical algorithm to compute it, convergence proof.
result Numerical algorithm converges to unique optimal indemnity.
LogEI improves Bayesian optimization by simplifying numerical computation of EI and related functions.
problem Numerical pathologies in optimizing EI and related acquisition functions.
method Proposes LogEI, a family of acquisition functions that simplify numerical optimization.
result LogEI members improve optimization performance and match or exceed state-of-the-art methods.
In this paper, we investigate a numerical algorithm for the pricing of swing options, relying on the so-called optimal quantization method. The numerical procedure is described in details and numerous simulations are provided to assert its efficiency. In particular, we carry out a comparison with the Longstaff-Schwartz…
New findings on optimal transport gradient for generative models, addressing numerical instabilities.
problem Numerical instabilities in training Wasserstein Generative Adversarial Networks (WGAN).
method Valid differentiation theorem for entropic regularized transport, semi-discrete gradient formulation, and optimization algorithm.
result Existence of optimal transport gradient for generative models under specified conditions.
This paper deals with numerical solutions to an impulse control problem arising from optimal portfolio liquidation with bid-ask spread and market price impact penalizing speedy execution trades. The corresponding dynamic programming (DP) equation is a quasi-variational inequality (QVI) with solvency constraint satisfie…
NCG methods improve shape optimization efficiency.
problem Shape optimization problems
method Nonlinear conjugate gradient methods
result NCG methods are efficient for shape optimization
Solves portfolio optimization with costs using numerical methods.
problem Dynamic portfolio optimization with transaction costs and constraints.
method Numerical dynamic programming techniques.
result Problems can now be solved tractably.
Optimizes over flag manifolds for numerical PDE and statistics.
problem Optimizing over flag manifolds for numerical PDE and statistics.
method Develops tools for Riemannian optimization on flag manifolds, deriving analytic expressions and parameterizations.
result Closed-form analytic expressions and parameterizations for various geometric objects on flag manifolds.
Optimal binning method for numeric targets using mathematical programming.
problem Optimizing the discretization of numeric variables for classification.
method Mathematical programming formulation for binary, continuous, and multi-class targets with constraints.
result Convex mixed-integer programming formulations for all target types.
Investigates numerical issues in GP interpolation parameter estimation.
problem Numerical issues in maximum likelihood parameter estimation for Gaussian process interpolation.
method Investigates and proposes strategies to improve open-source software implementations.
result Improves reliability and reproducibility of studies relying on GP implementations.
This paper develops numerical methods for finding optimal dividend pay-out and reinsurance policies. A generalized singular control formulation of surplus and discounted payoff function are introduced, where the surplus is modeled by a regime-switching process subject to both regular and singular controls. To approxima…
New method calculates cut locus on Riemannian manifolds using optimal transport.
problem Computing the cut locus on compact Riemannian manifolds.
method Characterization via optimal transport density solution of Monge-Kantorovich equations, numerical approximation.
result Proposed novel framework for numerical approximation of cut locus.
The study examines portfolio optimization with quadratic transaction costs, complicating the optimization process.
problem Portfolio optimization with quadratic transaction costs is more challenging than with linear costs.
method Introduced numerical algorithms to solve the optimization problem with quadratic transaction costs.
result Quadratic transaction costs significantly impact the expected returns of optimized portfolios.
Study investigates how errors in reinsurance parameters degrade optimal solutions.
problem Effectiveness of optimal reinsurance solutions degraded by errors in parameters and models.
method Asymptotic and numerical studies, including Value at Risk criteria and Bayesian integration.
result Rate of degradation often O ( 1 / n ) O(1/n) O ( 1/ n ) , but can be O ( 1 / n ) O(1/\sqrt{n}) O ( 1/ n ) for Value at Risk. A new method solves entropic optimal transport faster.
problem Efficiently solving entropic optimal transport problems.
method Logarithmic Newton iteration for optimality conditions.
result Quadratic convergence rate compared to Sinkhorn-Knopp.
PHS optimizes hyperparameters in parallel for expensive computations.
problem Optimizing hyperparameters in computationally expensive tasks.
method Bayesian optimization for parallel hyperparameter search.
result Efficient hyperparameter optimization on multiple instances.
Study optimal control with expectation constraint, proving smooth boundary and deriving numerical methods.
problem Optimal control with expectation constraint in a smooth boundary case.
method Uniform ellipticity proof, truncation argument, approximating sequence of PDEs, convergence analysis, numerical schemes.
result Proved smooth boundary and derived numerical methods for optimal control problem.
Study shows how numerical discretization affects reconstructions and parameter distributions in nano metrology.
problem Impact of numerical discretization on parameter reconstructions and model parameter distributions.
method Bayesian target vector optimization, finite element model, Gaussian process, stochastic machine learning surrogate models, Markov chain Monte Carlo sampler.
result Numerical discretization parameters impact the accuracy and distribution of reconstructed model parameters.
New method uses reinforced regression for solving optimal stopping problems.
problem Solving optimal stopping problems in mathematical finance.
method Reinforced regression based on previously estimated continuation values.
result Illustrated by a numerical example from mathematical finance.
This paper deals with numerical solutions of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is to derive the optimal insurance strategy which allows "lowering" the level of t…
The paper compares numerical schemes for nonholonomic systems using retraction maps.
problem Optimal control of nonholonomic systems with numerical approximations.
method Retraction maps used as seed for geometric integrators of Hamilton equations.
result Performance comparison of symplectic and non-symplectic integrators.
Paper solves investment problem with transaction costs using spectral method.
problem Optimal investment problem with transaction costs under potential utility.
method Spectral numerical method applied to a reformulated parabolic double obstacle problem.
result Spectral method proves more efficient for high precision solutions.
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal encoding/decoding strategies, which are of significant relevance to Computational Neuroscien…
Paper solves complex investment-consumption problem with numerical methods.
problem Optimal investment and consumption strategies with proportional transaction costs.
method Monte Carlo simulation and finite difference method for approximating gradients.
result Numerical results validate optimal trading strategies and properties.
Bayesian optimization uses triangulation candidates for better performance.
problem Non-convex and multi-modal optimization challenges in Bayesian optimization.
method Proposes using Delaunay triangulation candidates for discrete search over continuous optimization.
result Triangulation candidates outperform numerically optimized and random alternatives.
The paper analyzes optimal retirement timing considering age-dependent mortality risk.
problem Optimal retirement timing under age-dependent mortality risk.
method Formulated as a stochastic control and optimal stopping problem, transformed into a finite time horizon, three-dimensional degenerate optimal stopping problem.
result Existence of an optimal retirement boundary, characterized as a unique solution to a nonlinear integral equation.
Study optimizes nuclear power plant decommissioning risk management.
problem Optimizing risk management for decommissioning nuclear power plants.
method Numerical stochastic optimization approach linking risk aversion to an optimization problem.
result Optimal strategy involves de-risking similar to a concave strategy.
This paper examines critical points in deep linear autoencoders.
problem Locating critical points in non-convex surfaces for optimization.
method Investigated two sub-problems: sampling and numerical tolerance.
result Numerical methods often fail to sample all critical points and require strict numerical tolerance.
Optimizes parameter reconstruction for optical scatterometry using Gaussian process regression.
problem Efficiently reconstructing geometry parameters of micro/nanostructures from scatterometry measurements.
method Bayesian optimization with Gaussian-process regression to find optimal parameter values.
result Gaussian process regression accelerates the optimization process for numerical simulations.
Multi-stage financial decision optimization under uncertainty depends on a careful numerical approximation of the underlying stochastic process, which describes the future returns of the selected assets or asset categories. Various approaches towards an optimal generation of discrete-time, discrete-state approximations…
We consider rate swaps which pay a fixed rate against a floating rate in presence of bid-ask spread costs. Even for simple models of bid-ask spread costs, there is no explicit strategy optimizing an expected function of the hedging error. We here propose an efficient algorithm based on the stochastic gradient method to…
Optimal reinsurance strategies for multi-line insurance companies.
problem Choosing the best dynamic reinsurance policies for multi-line insurance companies.
method Characterized the optimal survival function as the unique nondecreasing viscosity solution of the HJB equation, solved numerically using the finite difference method.
result Provided proof of convergence of numerical solution to the survival probability function.
The paper solves numerical integration on graphs by optimizing vertex sampling and weights.
problem Finding efficient sampling and weights for graph functions.
method Rewriting integration as a geometric packing problem and constructing approximate solutions.
result Efficient numerical integration on graphs can be achieved through optimal packing of heat balls.
We consider a singular control problem with regime switching that arises in problems of optimal investment decisions of cash-constrained firms. The value function is proved to be the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation. Moreover, we give regularity properties of the value functi…
Develops a numerical algorithm for stochastic impulse control using regression surrogates.
problem Optimal impulse control in stochastic processes.
method Generates statistical surrogates for continuation and intervention functions, recursively trained over simulated state trajectories.
result Demonstrates flexibility and extensibility of the numerical scheme through case studies.
Proves existence and uniqueness of optimal trading strategy for multivariate returns.
problem Finding optimal trading strategy for multiple asset returns.
method Proves existence and uniqueness of optimal solution using fractional trading ansatz.
result Optimal trading strategy can be numerically found using steepest ascent methods.
Study optimal liquidation in markets with endogenous pressure to sell.
problem Optimal liquidation in markets with endogenous pressure to sell.
method Endogenously modeling price pressure, solving singular ODEs numerically.
result Optimal liquidation strategy consistent with square-root law.
A deep learning model speeds up computation of numerous implied volatilities.
problem Frequent computation of numerous implied volatilities using iteration methods like Newton-Raphson reaches processing speed limits.
method Emulated Newton-Raphson method using PyTorch and optimized with TensorRT.
result Up to 1,000 times faster than a benchmark implementation of Newton-Raphson.
Enhances optimization and sampling methods using ensemble-based gradient inference.
problem Improving ensemble-based methods for optimization and sampling.
method Ensemble-based gradient inference (EGI) to extract higher-order derivatives from particle ensembles.
result Augmented algorithms outperform gradient-free variants, especially in multimodal and non-Gaussian settings.
In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the rate of convergence of the method in terms of the time step used to discretize …
Study optimal dividend policies for firms with random profitability.
problem Firms face a trade-off between bankruptcy and profit extraction.
method General cash flow drifts (Ornstein-Uhlenbeck, CIR) considered; rigorous proofs, numerical scheme provided.
result Optimal strategy includes barrier and band strategies, voluntary liquidation.
Efficiently speeds up privacy-preserving logistic regression.
problem Privacy-preserving machine learning in collaborative studies.
method Customized numerical optimization for secure computing.
result Significant acceleration of logistic regression up to 8.1x.
SOO uses bandit theory to optimize functions with limited evaluations.
problem Optimizing functions with a limited number of evaluations.
method SOO is a machine learning approach that uses domain partitioning and a tradeoff between exploration and exploitation.
result SOO provides guarantees on the returned solution and is numerically efficient.
This work frames active inference through control as inference, offering robust control algorithms.
problem Active inference framework lacks practical sensorimotor control algorithms.
method Frame active inference through control as inference, presenting trajectory optimization as inference.
result AI may be framed as partially-observed CaI when the cost function is defined in observation states.
Optimizes plasmonic mirror filters using multi-fidelity Gaussian processes.
problem Optimizing transmission properties of plasmonic mirror color filters.
method Combining numerical methods with FDTD simulations and multi-fidelity Gaussian processes.
result Demonstrates improved optimization performance with multi-fidelity Gaussian processes.
Optimizes control of infectious disease spread using stochastic methods.
problem Optimizing control of highly infectious diseases like COVID-19.
method Reformulated Hamilton-Jacobi-Bellman equation as stochastic minimum principle, leading to forward-backward stochastic differential equations.
result Numerous numerical solutions presented under various scenarios.
We interpret policy optimization as Wasserstein gradient flows and develop efficient algorithms.
problem Unclear mathematical principle of policy optimization in reinforcement learning.
method Interpreting policy optimization as Wasserstein gradient flows, developing efficient algorithms to solve the corresponding discrete gradient flows.
result Policy optimization becomes a convex problem in terms of distribution optimization under specified circumstances.