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Combinatorial optimization assumes that all parameters of the optimization problem, e.g. the weights in the objective function is fixed. Often, these weights are mere estimates and increasingly machine learning techniques are used to for…
This paper studies the robustness of reinforcement learning algorithms to errors in the learning process. Specifically, we revisit the benchmark problem of discrete-time linear quadratic regulation (LQR) and study the long-standing open…
Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…
Large language models (LLMs) are still struggling in aligning with human preference in complex tasks and scenarios. They are prone to overfit into the unexpected patterns or superficial styles in the training data. We conduct an empirical…
Human preference alignment is critical in building powerful and reliable large language models (LLMs). However, current methods either ignore the multi-dimensionality of human preferences (e.g. helpfulness and harmlessness) or struggle with…
Hyperparameter optimization (HPO) is a billion-dollar problem in machine learning, which significantly impacts the training efficiency and model performance. However, achieving efficient and robust HPO in deep reinforcement learning (RL) is…
Optimizing policies based on human preferences is key to aligning language models with human intent. This work focuses on reward modeling, a core component in reinforcement learning from human feedback (RLHF), and offline preference…
We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite…
Ensuring safety is important for the practical deployment of reinforcement learning (RL). Various challenges must be addressed, such as handling stochasticity in the environments, providing rigorous guarantees of persistent state-wise…
Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted formulation that exhibits desirable stability properties under mild assumptions that…
Policy optimization methods are powerful algorithms in Reinforcement Learning (RL) for their flexibility to deal with policy parameterization and ability to handle model misspecification. However, these methods usually suffer from slow…
In this paper, we study several important geometric optimization problems arising in machine learning. First, we revisit the Minimum Enclosing Ball (MEB) problem in Euclidean space $\mathbb{R}^d$. The problem has been extensively studied…
Near isometric orthogonal embeddings to lower dimensions are a fundamental tool in data science and machine learning. In this paper, we present the construction of such embeddings that minimizes the maximum distortion for a given set of…
Since DeepSeek-R1 popularized, Group Relative Policy Optimization (GRPO) has become the core part of training Reasoning LLMs. However, we find some deficiency that influences RL stability and inference efficiency, like zero-variance in…
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…
Lasso, or $\ell^1$ regularized least squares, has been explored extensively for its remarkable sparsity properties. It is shown in this paper that the solution to Lasso, in addition to its sparsity, has robustness properties: it is the…
Inverse reinforcement learning (IRL) aims to recover the reward function and the associated optimal policy that best fits observed sequences of states and actions implemented by an expert. Many algorithms for IRL have an inherently nested…
Direct Preference Optimization (DPO) has become a popular method for fine-tuning large language models (LLMs) due to its stability and simplicity. However, it is also known to be sensitive to noise in the data and prone to overfitting.…
The metric uncapacitated facility location problem (UFL) enjoys a special stature in approximation algorithms as a testbed for various techniques. Two generalizations of UFL are capacitated facility location (CFL) and lower-bounded facility…
Replicability is a fundamental challenge in reinforcement learning (RL), as RL algorithms are empirically observed to be unstable and sensitive to variations in training conditions. To formally address this issue, we study \emph{list…