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Reinforcement learning (RL) algorithms can be divided into two classes: model-free algorithms, which are sample-inefficient, and model-based algorithms, which suffer from model bias. Dyna-style algorithms combine these two approaches by…

Model-free approaches for reinforcement learning (RL) and continuous control find policies based only on past states and rewards, without fitting a model of the system dynamics. They are appealing as they are general purpose and easy to…

Proximal policy optimization (PPO) is one of the most successful deep reinforcement-learning methods, achieving state-of-the-art performance across a wide range of challenging tasks. However, its optimization behavior is still far from…

We consider the minimization of non-convex functions that typically arise in machine learning. Specifically, we focus our attention on a variant of trust region methods known as cubic regularization. This approach is particularly attractive…

We develop a trust-region method for efficiently minimizing the sum of a smooth function, a nonsmooth convex function, and the composition of a finite-valued support function with a smooth function. Optimization problems with this structure…

Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore…

High dimensional integration is essential to many areas of science, ranging from particle physics to Bayesian inference. Approximating these integrals is hard, due in part to the difficulty of locating and sampling from regions of the…

To reduce complexity and achieve scalable performance in high-dimensional black-box settings, we propose a distributed method for nonconvex derivative-free optimization of continuous variables with an additively separable objective, subject…

We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…

Real-world black-box optimization often involves time-consuming or costly experiments and simulations. Multi-fidelity optimization (MFO) stands out as a cost-effective strategy that balances high-fidelity accuracy with computational…

We propose a new inferential framework for constructing confidence regions and testing hypotheses in statistical models specified by a system of high dimensional estimating equations. We construct an influence function by projecting the…

This thesis presents recent advances in model order reduction methods with the primary aim to construct online-efficient reduced surrogate models for parameterized multiscale phenomena and accelerate large-scale PDE-constrained parameter…

In this paper, we investigate a special class of quadratic-constrained quadratic programming (QCQP) with semi-definite constraints. Traditionally, since such a problem is non-convex and N-hard, the neural network (NN) is regarded as a…

We present a computationally efficient framework, called $\texttt{FlowDRO}$, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets while aiming to find continuous worst-case…

Distributionally Favorable Optimization (DFO) is an important framework for decision-making under uncertainty, with applications across fields such as reinforcement learning, online learning, robust statistics, chance-constrained…

Bayesian optimization is widely employed for optimizing complex black-box functions but struggles with the curse of dimensionality. Random embedding, as a dimension reduction strategy, simplifies tasks that possess the effective dimension…

This article introduces an algorithm for implicit High Dimensional Model Representation (HDMR) of the Bellman equation. This approximation technique reduces memory demands of the algorithm considerably. Moreover, we show that HDMR enables…

Uncertainty quantification (UQ) is a crucial but challenging task in many high-dimensional regression or learning problems to increase the confidence of a given predictor. We develop a new data-driven approach for UQ in regression that…

We consider trust-region methods for solving optimization problems where the objective is the sum of a smooth, nonconvex function and a nonsmooth, convex regularizer. We extend the global convergence theory of such methods to include…

Sampling-based controllers, such as Model Predictive Path Integral (MPPI) methods, offer substantial flexibility but often suffer from high variance and low sample efficiency. To address these challenges, we introduce a hybrid…