Related papers: Bias-Variance Techniques for Monte Carlo Optimizat…

The binomial tree method and the Monte Carlo (MC) method are popular methods for solving option pricing problems. However in both methods there is a trade-off between accuracy and speed of computation, both of which are important in…

Cross-validation plays a fundamental role in Machine Learning, enabling robust evaluation of model performance and preventing overestimation on training and validation data. However, one of its drawbacks is the potential to create data…

Modern quantum Monte Carlo (QMC) methods often capture electron correlation through both explicitly correlating Jastrow factors and small to mid-sized configuration interaction (CI) expansions. Here, we study the additional optimization…

This paper extends the Multilevel Monte Carlo variance reduction technique to nonlinear filtering. In particular, Multilevel Monte Carlo is applied to a certain variant of the particle filter, the Ensemble Transform Particle Filter. A key…

This thesis develops theoretical frameworks and algorithms that advance constrained reinforcement learning (RL) across control, preference learning, and alignment of large language models. The first contribution addresses constrained Markov…

Continual learning aims to learn multiple tasks sequentially. A key challenge in continual learning is balancing between two objectives: retaining knowledge from old tasks (stability) and adapting to new tasks (plasticity). Experience…

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…

In this paper, we evaluate the performance of the multilevel Monte Carlo method (MLMC) for deterministic and uncertain hyperbolic systems, where randomness is introduced either in the modeling parameters or in the approximation algorithms.…

Existing studies on preference optimization (PO) have centered on constructing pairwise preference data following simple heuristics, such as maximizing the margin between preferred and dispreferred completions based on human (or AI) ranked…

Training machine learning models inherently involves a resource-intensive and noisy iterative learning procedure that allows epoch-wise monitoring of the model performance. However, the insights gained from the iterative learning procedure…

Model calibration aims to align confidence with prediction correctness. The Cross-Entropy (CE) loss is widely used for calibrator training, which enforces the model to increase confidence on the ground truth class. However, we find the CE…

Large language models (LLMs) trained with reinforcement objectives often achieve superficially correct answers via shortcut strategies, pairing correct outputs with spurious or unfaithful reasoning and degrading under small causal…

The bias-variance trade-off is a well-known problem in machine learning that only gets more pronounced the less available data there is. In active learning, where labeled data is scarce or difficult to obtain, neglecting this trade-off can…

Multi-objective optimization (MOO) problems require balancing competing objectives, often under constraints. The Pareto optimal solution set defines all possible optimal trade-offs over such objectives. In this work, we present a novel…

This paper considers the problem of optimizing the average tracking error for an elliptic partial differential equation with an uncertain lognormal diffusion coefficient. In particular, the application of the multilevel quasi-Monte Carlo…

Many machine learning problems optimize an objective that must be measured with noise. The primary method is a first order stochastic gradient descent using one or more Monte Carlo (MC) samples at each step. There are settings where…

In recent years, explainability in machine learning has gained importance. In this context, counterfactual explanation (CE), which is an explanation method that uses examples, has attracted attention. However, it has been pointed out that…

The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…

K-fold cross validation (CV) is a popular method for estimating the true performance of machine learning models, allowing model selection and parameter tuning. However, the very process of CV requires random partitioning of the data and so…

Variational inference has recently emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) in large-scale Bayesian inference. The core idea is to trade statistical accuracy for computational efficiency. In this…