arXiv research

A new weighted MLMC method improves efficiency in Monte Carlo simulations.

Improved MLMC method boosts risk estimation efficiency.

New framework reduces cost of financial option pricing simulations on FPGAs.

Proposes a method to reduce parallel complexity of MLMC in SGD.

MLMC boosts Bayesian optimization's look-ahead efficiency.

Improved MLMC method for robust and efficient probability and density estimation.

In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators of the model evidence have been often used as stochastic objectives because the existing debiasing techniques are computationally costly to a…

In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong convergence. We exemplify thi…

New estimator for digital options using path splitting and MLMC.

Paper proposes nested MLMC for SNPE with intractable likelihoods.

Improved MLMC method for barrier options with non-Lipschitz coefficients.

The paper improves Monte Carlo methods for optimization problems.

New method estimates nested expectations with biased and antithetic sampling.

Review of MLMC in financial engineering, focusing on option pricing and risk management.

Paper proposes an unbiased optimization method for Bayesian experimental design.

Bayesian inference for deep neural networks using trace-class priors and MLMC.

We develop a framework that allows the use of the multi-level Monte Carlo (MLMC) methodology (Giles2015) to calculate expectations with respect to the invariant measure of an ergodic SDE. In that context, we study the (over-damped) Langevin equations with a strongly concave potential. We show that, when appropriate con…

Novel weak MLMC scheme for Lévy-driven SDEs, applied to financial derivatives pricing.

We investigate the problem of computing a nested expectation of the form $\mathbb{P}[\mathbb{E}[X|Y] \!\geq\!0]\!=\!\mathbb{E}[\textrm{H}(\mathbb{E}[X|Y])]$ where $\textrm{H}$ is the Heaviside function. This nested expectation appears, for example, when estimating the probability of a large loss from a financial portfo…

New algorithms reduce complexity for learning in MDPs with entropy regularization.

Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different risk scenarios and (b) evaluating the loss of the portfolio is expensive and the …

Paper uses MLMC for SCR calculation and stress tests, showing computational efficiency.

Develops a multilevel Monte Carlo framework with dropout for efficient uncertainty quantification.

A new sampler tackles critical phenomena by leveraging scale invariance.

In this paper we introduce a new multilevel Monte Carlo (MLMC) estimator for multi-dimensional SDEs driven by Brownian motions. Giles has previously shown that if we combine a numerical approximation with strong order of convergence $O(Δt)$ with MLMC we can reduce the computational complexity to estimate expected value…

In this work, we propose a smart idea to couple importance sampling and Multilevel Monte Carlo (MLMC). We advocate a per level approach with as many importance sampling parameters as the number of levels, which enables us to compute the different levels independently. The search for parameters is carried out using samp…

New method reduces sample complexity for robust reinforcement learning.

In this paper a novel modification of the multilevel Monte Carlo approach, allowing for further significant complexity reduction, is proposed. The idea of the modification is to use the method of control variates to reduce variance at level zero. We show that, under a proper choice of control variates, one can reduce t…

This work overcomes bias in concave multi-objective reinforcement learning.

MUSE provides unbiased stopping estimates for optimal problems.

We are interested in strong approximations of one-dimensional SDEs which have non-Lipschitz coefficients and which take values in a domain. Under a set of general assumptions we derive an implicit scheme that preserves the domain of the SDEs and is strongly convergent with rate one. Moreover, we show that this general …

Option valuation problems are often solved using standard Monte Carlo (MC) methods. These techniques can often be enhanced using several strategies especially when one discretizes the dynamics of the underlying asset, of which we assume follows a diffusion process. We consider the combination of two methodologies in th…

We propose a variance reduction framework for variational inference using the Multilevel Monte Carlo (MLMC) method. Our framework is built on reparameterized gradient estimators and "recycles" parameters obtained from past update history in optimization. In addition, our framework provides a new optimization algorithm …

New method adapts to unknown mixing time in stochastic optimization.

New method improves training-free guidance for diffusion models, achieving state-of-the-art results.

DynBRO learns robustly from dynamic Byzantine workers.

Adaptive Multilevel Monte Carlo improves probability estimation for complex random variables.

New model-free DR-RL algorithm with finite sample complexity.

Generative model for Lévy area improves SDE simulation accuracy.

A new weighted MCC measure improves classifier performance evaluation.

Stability of weighted extremal manifolds proven through blowups.

Develops theory of weightings for Lie groupoids and algebroids.

The paper extends spin geometry to weighted manifolds and defines a new mass for Ricci flow.

The study explores weightings on submanifolds and their geometric properties.

New mass and staticity concepts derived from weighted curvature maps.

Proves existence and uniqueness of weighted metrics for smooth spaces.

Defines and proves properties of weighted renormalized volume coefficients.

A new weighted FDA method improves face recognition accuracy.