A new weighted MLMC method improves efficiency in Monte Carlo simulations.
problem Improving efficiency in Monte Carlo simulations with correlated coarse level approximations.
method Generalization of MLMC to any number of levels with control variates and weights.
result Significant efficiency improvements possible, especially when coarse level approximations are poorly correlated.
Improved MLMC method boosts risk estimation efficiency.
problem Estimating risk measures like Value-at-Risk in financial risk management.
method Novel MLMC parametrization and antithetic sampling.
result Significantly improved performance in practical settings.
New framework reduces cost of financial option pricing simulations on FPGAs.
problem Efficiently simulate financial option pricing with reduced computational cost.
method Nested MLMC framework with low precision calculations on FPGAs.
result Higher computational savings compared to existing mixed-precision MLMC frameworks.
Proposes a method to reduce parallel complexity of MLMC in SGD.
problem Poor scalability of MLMC in SGD on parallel platforms.
method Proposes a delayed MLMC gradient estimator to reduce parallel complexity.
result Proves reduction in average parallel complexity per iteration at the cost of slightly worse convergence rate.
MLMC boosts Bayesian optimization's look-ahead efficiency.
problem Efficiently computing nested expectations in Bayesian optimization.
method Multilevel Monte Carlo (MLMC) for nested operations.
result MLMC achieves MC convergence rate for nested operations, improving BO performance.
New MLMC method reduces evidence estimation cost.
problem Efficiently estimating model evidence in Bayesian inference.
method Multilevel Monte Carlo (MLMC) sampling for unbiased estimation.
result Significant computational savings in estimating model evidence.
Improved MLMC method for robust and efficient probability and density estimation.
problem Stability and poor complexity of MLMC for low-regularity functionals.
method Numerical smoothing combined with MLMC for deterministic quadrature methods.
result Significant improvement in strong convergence and robustness of MLMC method.
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.
problem Estimating digital options with stochastic differential equations.
method Repeated path splitting, Multilevel Monte Carlo (MLMC).
result Estimator complexity similar to MLMC for Lipschitz payoffs.
Paper proposes nested MLMC for SNPE with intractable likelihoods.
problem Estimating posterior distributions from intractable likelihoods.
method Nested MLMC for loss function and gradients, with convergence results.
result Effective methods for approximating complex multimodal posteriors.
Improved MLMC method for barrier options with non-Lipschitz coefficients.
problem Efficiency improvement for barrier option pricing with non-Lipschitz diffusion.
method Interpolated Drift Implicit Euler MLMC method, Lamperti transformation, Brownian bridge technique.
result Improved efficiency of MLMC for barrier options with non-Lipschitz coefficients.
The paper improves Monte Carlo methods for optimization problems.
problem Efficiently solving optimization problems with biased Monte Carlo estimators.
method Introduces Multilevel Monte Carlo (MLMC) within Sample Average Approximation (SAA).
result Establishes uniform convergence and sample complexity for MLMC in SAA.
New method estimates nested expectations with biased and antithetic sampling.
problem Estimating nested expectations with biased and antithetic sampling.
method Nested multilevel Monte Carlo with biased and antithetic sampling.
result Estimator achieves order ε^(-2) asymptotic cost.
Review of MLMC in financial engineering, focusing on option pricing and risk management.
problem Efficient estimation of financial risks and option prices using Monte Carlo methods.
method Incorporation of importance sampling and adaptive sampling algorithms in MLMC framework.
result Hybrid algorithms reduce overall variance in estimating financial risks and option prices.
Paper proposes an unbiased optimization method for Bayesian experimental design.
problem Maximizing expected information gain in Bayesian experimental design.
method Randomized multilevel Monte Carlo (MLMC) method combined with stochastic gradient descent.
result An unbiased estimator for the gradient of expected information gain.
Bayesian inference for deep neural networks using trace-class priors and MLMC.
problem Efficient Bayesian inference for deep neural networks.
method Trace-class neural network priors and Multilevel Monte Carlo method.
result Optimal computational complexity for Bayesian inference of TNN models.
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.
problem Approximating solutions to Lévy-driven SDEs for financial derivatives pricing.
method Weak multilevel Monte-Carlo scheme with state space discretization of Lévy processes.
result Efficient approximation of financial derivatives pricing models.
We investigate the problem of computing a nested expectation of the form P [ E [ X ∣ Y ] ≥ 0 ] = E [ H ( E [ X ∣ Y ] ) ] \mathbb{P}[\mathbb{E}[X|Y] \!\geq\!0]\!=\!\mathbb{E}[\textrm{H}(\mathbb{E}[X|Y])] P [ E [ X ∣ Y ] ≥ 0 ] = E [ H ( E [ X ∣ Y ])] where H \textrm{H} 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.
problem Efficient learning for MDPs with large or continuous state and action spaces.
method Multilevel Monte Carlo (MLMC) algorithms integrating fixed-point iteration and stochastic approximation of the Bellman operator.
result MLMC with unbiased approximation of the Bellman operator achieves polynomial sample complexity.
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.
problem Computing SCR and stress tests for insurance companies.
method Multilevel Monte-Carlo (MLMC) estimator for maximum of conditional expectations.
result MLMC estimator is computationally more efficient and avoids regression issues.
Develops a multilevel Monte Carlo framework with dropout for efficient uncertainty quantification.
problem Efficiently quantify uncertainty in complex models using dropout.
method Integrates multilevel Monte Carlo with Monte Carlo dropout, creating coupled estimators to reduce variance.
result Demonstrates significant variance reduction and efficiency gains over single-level Monte Carlo dropout.
A new sampler tackles critical phenomena by leveraging scale invariance.
problem Scale invariance at criticality causes sampling difficulties in Monte Carlo simulations.
method RiGCS combines MLMC-HB with generative models to improve sampling efficiency.
result RiGCS achieves significantly higher effective sample size than existing methods.
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 ( Δ t ) O(Δt) O ( Δ t ) 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.
problem Finite sample analysis in robust reinforcement learning.
method Stochastic approximation framework with controlled bias, using MLMC techniques and geometric truncation.
result Order-optimal sample complexity of i l d e O ( ε − 2 ) ilde{\mathcal{O}}(ε^{-2}) i l d e O ( ε − 2 ) for robust policy evaluation. 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.
problem Gradient bias in policy gradient methods for concave scalarized multi-objective reinforcement learning.
method Developed a Natural Policy Gradient (NPG) algorithm with a multi-level Monte Carlo (MLMC) estimator.
result Achieved optimal O ~ ( ε − 2 ) \widetilde{\mathcal{O}}(ε^{-2}) O ( ε − 2 ) sample complexity for computing an ε ε ε -optimal policy. MUSE provides unbiased stopping estimates for optimal problems.
problem Estimating the utility of optimal stopping problems.
method Backward recursive construction of the Multilevel Unbiased Stopping Estimator (MUSE).
result MUSE achieves ε-accuracy with O(1/ε^2) computational cost.
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.
problem Optimizing with Markovian data where mixing time is unknown.
method Combines MLMC gradient estimation with adaptive learning.
result Achieves optimal convergence rate for convex problems.
New method improves training-free guidance for diffusion models, achieving state-of-the-art results.
problem Accurate, training-free guidance for conditional generation in diffusion models.
method Sequential Monte Carlo (SMC) framework with Multi-Level Monte Carlo (MLMC) variance reduction.
result Achieves state-of-the-art results on CIFAR-10 and ImageNet datasets with significant cost reduction.
DynBRO learns robustly from dynamic Byzantine workers.
problem Fault-tolerant distributed learning with dynamic Byzantine workers.
method Multi-level Monte Carlo (MLMC) gradient estimation and adaptive learning rate.
result DynaBRO nearly matches static setting's convergence rate with O ( T ) \mathcal{O}(\sqrt{T}) O ( T ) Byzantine worker changes. Adaptive Multilevel Monte Carlo improves probability estimation for complex random variables.
problem Estimating probabilities of complex random variables with multiple approximations.
method Adaptive Multilevel Monte Carlo framework for discontinuous functionals.
result Achieves optimal computational complexities for both smooth and discontinuous functionals.
New model-free DR-RL algorithm with finite sample complexity.
problem Limited model-free DR-RL methods with convergence guarantees or sample complexities.
method Integrates Multi-level Monte Carlo (MLMC) technique with threshold mechanism.
result First model-free DR-RL approach with finite sample complexity for total variation and Chi-square divergence.
Generative model for Lévy area improves SDE simulation accuracy.
problem Simulating Lévy areas for high-order SDEs is challenging due to non-Gaussian nature and lack of fast sampling algorithms.
method LévyGAN, a deep-learning model with a GNN-inspired architecture, generates approximate samples of Lévy area.
result LévyGAN matches all joint and conditional odd moments exactly and achieves state-of-the-art performance in 4D Brownian motion.
A new weighted MCC measure improves classifier performance evaluation.
problem Lack of measures sensitive to observation weights in multiclass classification.
method Proposes weighted versions of Pearson-Matthews Correlation Coefficient (MCC) for binary and multiclass classification.
result Weighted MCC values are higher for classifiers that perform better on highly weighted observations.
Stability of weighted extremal manifolds proven through blowups.
problem Stability of weighted extremal manifolds.
method Blowup technique to analyze weighted extremal Kähler manifolds.
result Proves weighted extremal manifolds are relatively weighted K-polystable.
Develops theory of weightings for Lie groupoids and algebroids.
problem Understanding differential geometry of weightings for Lie groupoids and algebroids.
method Extending work on weighted manifolds, defining weighted submanifolds, and developing theories of linear weightings and multiplicative weightings.
result Characterizes infinitesimally multiplicative weightings for Lie algebroids and classifies multiplicative weightings of Lie groupoids.
The paper extends spin geometry to weighted manifolds and defines a new mass for Ricci flow.
problem Generalizing spin geometry to weighted manifolds and defining a new mass.
method Investigates spectral properties of the weighted Dirac operator and defines a new mass.
result Defines a new mass for weighted asymptotically Euclidean manifolds and shows its monotonicity under Ricci flow.
Paper generalizes CR Obata theorem to weighted Sasakian manifolds.
problem Deriving eigenvalue estimates for weighted Kohn Laplacian.
method Derived weighted CR Reilly's formula and applied to Sasakian manifolds.
result CR Obata theorem proven for weighted Sasakian manifolds.
The study explores weightings on submanifolds and their geometric properties.
problem Understanding weightings on submanifolds and their geometric implications.
method Detailed exploration of weighted normal bundles, weighted deformation spaces, and weighted blow-ups.
result A description of weightings in terms of subbundles of higher tangent bundles, leading to new concepts for Lie algebroids and groupoids.
New mass and staticity concepts derived from weighted curvature maps.
problem Deriving mass and staticity concepts for weighted manifolds.
method Developed a weighted curvature map and its adjoint, leading to weighted mass and static metrics.
result Equivalence and uniqueness theorems for weighted static manifolds and Penrose inequality.
Proves existence and uniqueness of weighted metrics for smooth spaces.
problem Existence and uniqueness of weighted metrics for smooth metric measure spaces.
method Proves existence and uniqueness using weighted ambient metrics and Poincaré metrics.
result Existence and uniqueness of weighted metrics for smooth metric measure spaces.
Defines and proves properties of weighted renormalized volume coefficients.
problem None explicitly stated; focuses on mathematical definitions and proofs.
method Defines weighted renormalized volume coefficients and proves their variational nature and polynomial representation.
result Weighted renormalized volume coefficients are variational and can be expressed as polynomials of specific tensors.