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Offline reinforcement learning (RL) allows learning sequential behavior from fixed datasets. Since offline datasets do not cover all possible situations, many methods collect additional data during online fine-tuning to improve performance.…

Bi-causal optimal transport (OT) is a natural framework for comparing and coupling stochastic processes under nonanticipative information constraints, with important applications in robust finance, sequential uncertainty quantification, and…

Inference-time scaling methods rely on Process Reward Models (PRMs), which are often poorly calibrated and overestimate success probabilities. We propose, to our knowledge, the first use of conditional optimal transport for calibrating…

This thesis examines self-attention training through the lens of Optimal Transport (OT) and develops an OT-based alternative for tabular classification. The study tracks intermediate projections of the self-attention layer during training…

As deep neural networks are increasingly deployed in dynamic, real-world environments, relying on a single static model is often insufficient. Changes in input data distributions caused by sensor drift or lighting variations necessitate…

Optimal Transport (OT) has fueled machine learning (ML) across many domains. When paired data measurements $(\boldsymbol{\mu}, \boldsymbol{\nu})$ are coupled to covariates, a challenging conditional distribution learning setting arises.…

Offline reinforcement learning (RL) offers an appealing approach to real-world tasks by learning policies from pre-collected datasets without interacting with the environment. However, the performance of existing offline RL algorithms…

Behavior constrained policy optimization has been demonstrated to be a successful paradigm for tackling Offline Reinforcement Learning. By exploiting historical transitions, a policy is trained to maximize a learned value function while…

Different methods are used for a mobile robot to go to a specific target location. These methods work in different ways for online and offline scenarios. In the offline scenario, an environment map is created once, and fixed path planning…

The numerical solution of kinetic equations is challenging due to the high dimensionality of the underlying phase space. In this paper, we develop a dynamical low-rank method based on the projector-splitting integrator in tensor-train (TT)…

In sequential decision-making problems, Return-Conditioned Supervised Learning (RCSL) has gained increasing recognition for its simplicity and stability in modern decision-making tasks. Unlike traditional offline reinforcement learning (RL)…

Low-rank tensor models are widely used in statistics. However, most existing methods rely heavily on the assumption that data follows a sub-Gaussian distribution. To address the challenges associated with heavy-tailed distributions…

We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and…

This paper focuses on inverse reinforcement learning for autonomous navigation using distance and semantic category observations. The objective is to infer a cost function that explains demonstrated behavior while relying only on the…

Optimal transport (OT) is attracting increasing attention in machine learning. It aims to transport a source distribution to a target one at minimal cost. In its vanilla form, the source and target distributions are predetermined, which…

In dynamic decision-making scenarios across business and healthcare, leveraging sample trajectories from diverse populations can significantly enhance reinforcement learning (RL) performance for specific target populations, especially when…

Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…

Despite the predominant use of first-order methods for training deep learning models, second-order methods, and in particular, natural gradient methods, remain of interest because of their potential for accelerating training through the use…

Machine learning-based forecasting models are commonly used in Intelligent Transportation Systems (ITS) to predict traffic patterns and provide city-wide services. However, most of the existing models are susceptible to adversarial attacks,…

Extracting information about dynamical systems from models learned off simulation data has become an increasingly important research topic in the natural and engineering sciences. Modeling the Koopman operator semigroup has played a central…