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Robust optimization (RO) is a powerful paradigm for decision making under uncertainty. Existing algorithms for solving RO, including the reformulation approach and the cutting-plane method, do not scale well, hindering the application of RO…

Aligning Large Language Models (LLMs) with human preferences is crucial, but standard methods like Reinforcement Learning from Human Feedback (RLHF) are often complex and unstable. In this work, we propose a new, simpler approach that…

Preference Optimization (PO), is gaining popularity as an alternative choice of Proximal Policy Optimization (PPO) for aligning Large Language Models (LLMs). Recent research on aligning LLMs iteratively with synthetic or partially synthetic…

Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…

Prompt optimization (PO) provides a practical way to improve response quality when users lack the time or expertise to manually craft effective prompts. Existing methods typically rely on LLMs' self-generation ability to optimize prompts.…

As the era of large language models (LLMs) unfolds, Preference Optimization (PO) methods have become a central approach to aligning LLMs with human preferences and improving performance. We propose Maximum a Posteriori Preference…

Preferential Bayesian optimization allows optimization of objectives that are either expensive or difficult to measure directly, by relying on a minimal number of comparative evaluations done by a human expert. Generating candidate…

In our previous work, a reduced order model (ROM) for a stochastic system was made, where noisy data was projected onto principal component analysis (PCA)-derived basis vectors to obtain an accurate reconstruction of the noise-free data.…

Robust Markov Decision Processes (MDPs) are a powerful framework for modeling sequential decision-making problems with model uncertainty. This paper proposes the first first-order framework for solving robust MDPs. Our algorithm interleaves…

Pairwise Ranking Prompting (PRP) elicits pairwise preference judgments from an LLM, which are then aggregated into a ranking, usually via classical sorting algorithms. However, judgments are noisy, order-sensitive, and sometimes…

Recent developments in Direct Preference Optimization (DPO) allow large language models (LLMs) to function as implicit ranking models by maximizing the margin between preferred and non-preferred responses. In practice, user feedback on such…

In this paper, we present a methodology based on a multiobjective optimization suggesting which facility to implement, in which location, and at which time. In this context, we define a new elicitation procedure to handle Decision Makers…

Multi-objective optimization (MOO) has been widely studied in literature because of its versatility in human-centered decision making in real-life applications. Recently, demand for dynamic MOO is fast-emerging due to tough market dynamics…

We offer a theoretical characterization of off-policy evaluation (OPE) in reinforcement learning using function approximation for marginal importance weights and $q$-functions when these are estimated using recent minimax methods. Under…

The allocation of limited resources to a large number of potential candidates presents a pervasive challenge. In the context of ranking and selecting top candidates from heteroscedastic units, conventional methods often result in…

Robust optimization (RO) has emerged as one of the leading paradigms to efficiently model parameter uncertainty. The recent connections between RO and problems in statistics and machine learning domains demand for solving RO problems in…

Direct Preference Optimization (DPO) has emerged as a de-facto approach for aligning language models with human preferences. Recent work has shown DPO's effectiveness relies on training data quality. In particular, clear quality differences…

We consider a general class of two-stage distributionally robust optimization (DRO) problems where the ambiguity set is constrained by fixed marginal probability laws that are not necessarily discrete. We derive primal and dual formulations…

Assortment optimization is a fundamental challenge in modern retail and recommendation systems, where the goal is to select a subset of products that maximizes expected revenue under complex customer choice behaviors. While recent advances…

Establishing a reliable and iteratively refined robotic system is essential for deploying real-world applications. While Vision-Language-Action (VLA) models are widely recognized as the foundation model for such robotic deployment, their…