Stochastic Gradient Descent (SGD) is a widely used algorithm for training machine learning models. Its iterative, noise-driven updates lead to sample trajectories that fluctuate as they descend the loss landscape. These trajectories may converge to the optimal solution at varying rates, depending on initialization, noise, and hyperparameters. Non-asymptotic Central Limit Theorems provides a probabilistic description of these fluctuations, quantifying the likelihood of deviations from the optimum within finite time.

In reinforcement learning, algorithms like Temporal Difference (TD) learning estimate value functions from noisy, sequential data. When combined with function approximation, these updates form a stochastic optimization process whose convergence behavior is often hard to analyze. The non-asymptotic Central Limit Theorem offers a way to understand the distribution of TD iterates around the true value function, enabling finite-sample guarantees and uncertainty-aware learning in complex environments.

Diffusion models are a class of generative models that learn to sample from complex data distributions. They iteratively refine random noise into structured outputs, such as images or text. Understanding the sampling error is crucial for ensuring high-quality outputs and controlling model behavior.

This research was motivated by my experience working with medical images, where the inherent difficulty of labeling radiology data often leads to noisy annotations from experts. In such applications, the proposed difficulty-clustering method can be used to generate a more reliable ground truth from multiple conflicting labels. This ultimately improves the quality of the data used for training and evaluating diagnostic AI models, enhancing their performance and robustness.