Related papers: $\rho$-regularization subproblems: Strong duality …
We introduce a general framework for analyzing learning algorithms based on the notion of self-regularization, which captures implicit complexity control without requiring explicit regularization. This is motivated by previous observations…
We propose a flexible scenario-based regularized Sample Average Approximation (SBR-SAA) framework for stochastic optimization. This work is motivated by challenges in standard Wasserstein Distributionally Robust Optimization (WDRO), where…
A solution algorithm for a special class of optimal control problems subject to an ordinary differential equation is proposed. The controls possess a continuous-or-off structure and are priced by a convex function. Additionally, a total…
We consider Riemannian inequality-constrained optimization problems. Such problems inherit the benefits of Riemannian approach developed in the unconstrained setting and naturally arise from applications in control, machine learning, and…
This study investigates a robust screening problem under distributional ambiguity, where a seller is uncertain about a buyer's true valuation distribution, knowing only that it lies near a reference distribution measured by the Wasserstein…
The Trust Region Subproblem is a fundamental optimization problem that takes a pivotal role in Trust Region Methods. However, the problem, and variants of it, also arise in quite a few other applications. In this article, we present a…
In recent years, Wasserstein Distributionally Robust Optimization (DRO) has garnered substantial interest for its efficacy in data-driven decision-making under distributional uncertainty. However, limited research has explored the…
Entropic regularization of policies in Reinforcement Learning (RL) is a commonly used heuristic to ensure that the learned policy explores the state-space sufficiently before overfitting to a local optimal policy. The primary motivation for…
In this paper, we study second-order algorithms for solving nonconvex-strongly concave minimax problems, which have attracted much attention in recent years in many fields, especially in machine learning.We propose a gradient norm…
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…
Entropy regularization is a standard technique in reinforcement learning (RL) to enhance exploration, yet it yields negligible effects or even degrades performance in Large Language Models (LLMs). We attribute this failure to the cumulative…
Inverse reinforcement learning (IRL) is typically formulated as maximizing entropy subject to matching the distribution of expert trajectories. Classical (dual-ascent) IRL guarantees monotonic performance improvement but requires fully…
Inverse Reinforcement Learning (IRL) learns a reward function to explain expert demonstrations. Modern IRL methods often use the adversarial (minimax) formulation that alternates between reward and policy optimization, which often lead to…
Trust Region Policy Optimization (TRPO) is a popular and empirically successful policy search algorithm in reinforcement learning (RL). It iteratively solved the surrogate problem which restricts consecutive policies to be close to each…
Model-free reinforcement learning algorithms have seen remarkable progress, but key challenges remain. Trust Region Policy Optimization (TRPO) is known for ensuring monotonic policy improvement through conservative updates within a trust…
Trust region methods, such as TRPO, are often used to stabilize policy optimization algorithms in reinforcement learning (RL). While current trust region strategies are effective for continuous control, they typically require a…
This work introduces a novel algorithm to solve large-scale eigenvalue problems and seek a small set of eigenpairs. The method, called randomized Krylov-Schur (rKS), has a simple implementation and benefits from fast and efficient…
The field of risk-constrained reinforcement learning (RCRL) has been developed to effectively reduce the likelihood of worst-case scenarios by explicitly handling risk-measure-based constraints. However, the nonlinearity of risk measures…
This paper presents global optimal solutions to a nonconvex quadratic minimization problem over a sphere constraint. The problem is well-known as a trust region subproblem and has been studied extensively for decades. The main challenge is…
We study the problem of Distributionally Robust Constrained RL (DRC-RL), where the goal is to maximize the expected reward subject to environmental distribution shifts and constraints. This setting captures situations where training and…