arXiv subjects

Cheol Woo Kim

Publications and source records attributed to Cheol Woo Kim.

13 recordsLinked to original sources

arXiv2026

Generating Robust Portfolios of Optimization Models using Large Language Models

Mathematical optimization is a powerful tool for structured decision-making across domains such as resource allocation and planning. Formulating optimization models faithful to reality, though, remains a significant bottleneck as it typically demands both domain expertise and optimization knowledge that are often scarce. Recent advances in large language models (LLMs) promise to bridge this gap, enabling the generation of candidate optimization models from natural language descriptions. However, there is no guarantee that any single LLM-generated model is reliable, and existing approaches that output only one model are therefore risky. In this work, we propose a novel algorithm that generates a portfolio of optimization models, designed to be robust to the limitations of LLMs. Our method exploits the observation that a single LLM can play two distinct roles $\unicode{x2014}$ as a stochastic generator and as a reasoning evaluator $\unicode{x2014}$ and proposes a unified framework that leverages both capabilities in a complementary manner. We provide theoretical guarantees showing that, as long as either the generator or the evaluator is well-aligned with human preferences, the portfolio is guaranteed to contain high-quality candidates, enabling a principled human-in-the-loop process in which a decision-maker can review multiple candidates before committing to one. We further validate our approach empirically, demonstrating strong performance across a range of optimization modeling tasks.

cs.AI↗

arXiv2026

Bilevel Optimization of Synthetic Trajectories for Multi-Turn LLM Fine-Tuning

While LLMs excel at single-turn generation, they struggle with long-horizon, multi-turn interactions. Offline reinforcement learning (RL) offers a scalable approach, yet its performance hinges on the availability and quality of multi-turn trajectory data. A common remedy is to augment training with synthetic trajectories generated by LLMs or simulators, but synthetic data is highly heterogeneous in quality, and naively treating all trajectories as equally informative can degrade performance. We propose BOOST, a bilevel optimization framework where the inner level trains the LLM on reweighted data and the outer level trains a lightweight reweighting head on held-out real validation tasks, assigning continuous trajectory-level weights without requiring an external judge. To ground this approach, we derive a PAC-Bayesian bound revealing a three-way trade-off: synthetic data increases diversity but risks task-shift, while concentrating weight on high-quality trajectories improves empirical performance at the cost of effective sample size. Empirically, our method consistently outperforms multiple baselines. Analysis reveals it upweights synthetic trajectories that align with the real data distribution and exhibit higher qualitative merit.

cs.LG↗

arXiv2026

Optimal Control of Multiclass Fluid Queueing Networks: A Machine Learning Approach

We propose a machine learning approach to the optimal control of multiclass fluid queueing networks (MFQNETs) that provides explicit and insightful control policies. We prove that a piecewise constant optimal policy exists for MFQNET control problems, with segments separated by hyperplanes passing through the origin. We use Optimal Classification Trees with hyperplane splits (OCT-H) to learn an optimal control policy for MFQNETs. We use numerical solutions of MFQNET control problems as a training set and apply OCT-H to learn explicit control policies. Furthermore, we show that both the theoretical results and the proposed algorithm extend to robust MFQNETs with uncertain service and arrival rates. We report experimental results with up to 33 servers and 99 classes that demonstrate that the learned policies achieve 100% accuracy on the test set. While the offline training of OCT-H can take days in large networks, the online application takes milliseconds.

cs.LG↗

arXiv2026

Optimal Control of Fluid Restless Multi-armed Bandits: A Machine Learning Approach

We present a novel machine learning framework for the optimal control of fluid restless multi-armed bandit problems (FRMABPs) with state equations that are either affine or quadratic in the state variables. By establishing fundamental properties of FRMABPs, we develop an efficient numerical algorithm that generates a comprehensive training set by solving multiple instances with diverse initial states. We further enhance this training set by applying a nonlinear transformation to the feature vectors, leveraging structural properties of FRMABPs. A time-dependent state feedback policy is then learned using Optimal Classification Trees with hyperplane splits (OCT-H). We test our approach on machine maintenance, epidemic control, and fisheries control problems, demonstrating that our method yields high-quality state feedback policies. Furthermore, once a policy is learned, it achieves a speed-up of up to 26 million times compared to the direct numerical algorithm.

cs.LG↗

arXiv2026

A Machine Learning Approach to Two-Stage Adaptive Robust Optimization

We propose an approach based on machine learning to solve two-stage linear adaptive robust optimization (ARO) problems with binary here-and-now variables and polyhedral uncertainty sets. We encode the optimal here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the optimal wait-and-see decisions into what we denote as the strategy. We solve multiple similar ARO instances in advance using the column and constraint generation algorithm and extract the optimal strategies to generate a training set. We train machine learning models that predict high-quality strategies for the here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the wait-and-see decisions. The models can be applied to problems with varying dimensions. We also introduce novel methods to expedite training data generation and reduce the number of different target classes the machine learning algorithm needs to be trained on. We apply the proposed approach to the facility location, the multi-item inventory control and the unit commitment problems. Our approach solves ARO problems drastically faster than the state-of-the-art algorithms with high accuracy.

cs.LG↗

arXiv2026

Many Preferences, Few Policies: Towards Scalable Language Model Personalization

The holy grail of LLM personalization is a single LLM for each user, perfectly aligned with that user's preferences. However, maintaining a separate LLM per user is impractical due to constraints on compute, memory, and system complexity. We address this challenge by developing a principled method for selecting a small portfolio of LLMs that captures representative behaviors across heterogeneous users. We model user preferences across multiple traits (e.g., safety, humor, brevity) through a multi-dimensional weight vector. Given reward functions across these dimensions, our algorithm PALM (Portfolio of Aligned LLMs) generates a small portfolio of LLMs such that, for any weight vector, the portfolio contains a near-optimal LLM for the corresponding scalarized objective. To the best of our knowledge, this is the first result that provides theoretical guarantees on both the size and approximation quality of LLM portfolios for personalization. It characterizes the trade-off between system cost and personalization, as well as the diversity of LLMs required to cover the landscape of user preferences. We provide empirical results that validate these guarantees and demonstrate greater output diversity over common baselines.

cs.CL↗

arXiv2026

Incentive-Aware AI Safety via Strategic Resource Allocation: A Stackelberg Security Games Perspective

As AI systems grow more capable and autonomous, ensuring their safety and reliability requires not only model-level alignment but also strategic oversight of the humans and institutions involved in their development and deployment. Existing safety frameworks largely treat alignment as a static optimization problem (e.g., tuning models to desired behavior) while overlooking the dynamic, adversarial incentives that shape how data are collected, how models are evaluated, and how they are ultimately deployed. We propose a new perspective on AI safety grounded in Stackelberg Security Games (SSGs): a class of game-theoretic models designed for adversarial resource allocation under uncertainty. By viewing AI oversight as a strategic interaction between defenders (auditors, evaluators, and deployers) and attackers (malicious actors, misaligned contributors, or worst-case failure modes), SSGs provide a unifying framework for reasoning about incentive design, limited oversight capacity, and adversarial uncertainty across the AI lifecycle. We illustrate how this framework can inform (1) training-time auditing against data/feedback poisoning, (2) pre-deployment evaluation under constrained reviewer resources, and (3) robust multi-model deployment in adversarial environments. This synthesis bridges algorithmic alignment and institutional oversight design, highlighting how game-theoretic deterrence can make AI oversight proactive, risk-aware, and resilient to manipulation.

cs.AI↗

arXiv2026

Generative AI for Social Impact

AI for Social Impact (AI4SI) has achieved compelling results in public health, conservation, and security, yet scaling these successes remains difficult due to a persistent deployment bottleneck. We characterize this bottleneck through three coupled gaps: observational scarcity resulting from limited or unreliable data; policy synthesis challenges involving combinatorial decisions and nonstationarity; and the friction of human-AI alignment when incorporating tacit expert knowledge and dynamic constraints. We argue that Generative AI offers a unified pathway to bridge these gaps. LLM agents assist in human-AI alignment by translating natural-language guidance into executable objectives and constraints for downstream planners, while diffusion models generate realistic synthetic data and support uncertainty-aware modeling to improve policy robustness and transfer across deployments. Together, these tools enable scalable, adaptable, and human-aligned AI systems for resource optimization in high-stakes settings.

cs.CY↗

arXiv2025

Preference Robustness for DPO with Applications to Public Health

We study an LLM fine-tuning task for designing reward functions for sequential resource allocation problems in public health, guided by human preferences expressed in natural language. This setting presents a challenging testbed for alignment due to complex and ambiguous objectives and limited data availability. We propose DPO-PRO, a robust fine-tuning algorithm based on Direct Preference Optimization (DPO), which accounts for uncertainty in the preference distribution using a lightweight Distributionally Robust Optimization (DRO) formulation. Unlike prior DRO-based DPO methods, DPO-PRO is significantly less conservative. We evaluate DPO-PRO on a real-world maternal mobile health program operated by the non-profit organization ARMMAN, as well as on standard alignment benchmarks. Experimental results demonstrate that our method consistently improves robustness to noisy preference signals compared to existing DPO variants. Moreover, DPO-PRO achieves comparable performance to prior self-reflection-based baseline for reward function design, while requiring significantly lower inference-time cost.

cs.LG↗

arXiv2025

Lightweight Robust Direct Preference Optimization

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. Recent works have proposed using distributionally robust optimization (DRO) to address potential noise and distributional shift in the data. However, these methods often suffer from excessive conservatism and high computational cost. We propose DPO-PRO (DPO with Preference Robustness), a robust fine-tuning algorithm based on DPO which accounts for uncertainty in the preference distribution through a lightweight DRO formulation. Unlike prior DRO-based variants, DPO-PRO focuses solely on uncertainty in preferences, avoiding unnecessary conservatism and incurring negligible computational overhead. We further show that DPO-PRO is equivalent to a regularized DPO objective that penalizes model overconfidence under weak preference signals. We evaluate DPO-PRO on standard alignment benchmarks and a real-world public health task. Experimental results show that our method consistently improves robustness to noisy preference signals compared to existing DPO variants.

cs.LG↗

arXiv2025

Robust Optimization with Diffusion Models for Green Security

In green security, defenders must forecast adversarial behavior, such as poaching, illegal logging, and illegal fishing, to plan effective patrols. These behavior are often highly uncertain and complex. Prior work has leveraged game theory to design robust patrol strategies to handle uncertainty, but existing adversarial behavior models primarily rely on Gaussian processes or linear models, which lack the expressiveness needed to capture intricate behavioral patterns. To address this limitation, we propose a conditional diffusion model for adversary behavior modeling, leveraging its strong distribution-fitting capabilities. To the best of our knowledge, this is the first application of diffusion models in the green security domain. Integrating diffusion models into game-theoretic optimization, however, presents new challenges, including a constrained mixed strategy space and the need to sample from an unnormalized distribution to estimate utilities. To tackle these challenges, we introduce a mixed strategy of mixed strategies and employ a twisted Sequential Monte Carlo (SMC) sampler for accurate sampling. Theoretically, our algorithm is guaranteed to converge to an epsilon equilibrium with high probability using a finite number of iterations and samples. Empirically, we evaluate our approach on both synthetic and real-world poaching datasets, demonstrating its effectiveness.

cs.CY↗

arXiv2025

Navigating the Social Welfare Frontier: Portfolios for Multi-objective Reinforcement Learning

In many real-world applications of reinforcement learning (RL), deployed policies have varied impacts on different stakeholders, creating challenges in reaching consensus on how to effectively aggregate their preferences. Generalized $p$-means form a widely used class of social welfare functions for this purpose, with broad applications in fair resource allocation, AI alignment, and decision-making. This class includes well-known welfare functions such as Egalitarian, Nash, and Utilitarian welfare. However, selecting the appropriate social welfare function is challenging for decision-makers, as the structure and outcomes of optimal policies can be highly sensitive to the choice of $p$. To address this challenge, we study the concept of an $α$-approximate portfolio in RL, a set of policies that are approximately optimal across the family of generalized $p$-means for all $p \in [-\infty, 1]$. We propose algorithms to compute such portfolios and provide theoretical guarantees on the trade-offs among approximation factor, portfolio size, and computational efficiency. Experimental results on synthetic and real-world datasets demonstrate the effectiveness of our approach in summarizing the policy space induced by varying $p$ values, empowering decision-makers to navigate this landscape more effectively.

cs.LG↗

arXiv2025

LLM-based Agent Simulation for Maternal Health Interventions: Uncertainty Estimation and Decision-focused Evaluation

Agent-based simulation is crucial for modeling complex human behavior, yet traditional approaches require extensive domain knowledge and large datasets. In data-scarce healthcare settings where historic and counterfactual data are limited, large language models (LLMs) offer a promising alternative by leveraging broad world knowledge. This study examines an LLM-driven simulation of a maternal mobile health program, predicting beneficiaries' listening behavior when they receive health information via automated messages (control) or live representatives (intervention). Since uncertainty quantification is critical for decision-making in health interventions, we propose an LLM epistemic uncertainty estimation method based on binary entropy across multiple samples. We enhance model robustness through ensemble approaches, improving F1 score and model calibration compared to individual models. Beyond direct evaluation, we take a decision-focused approach, demonstrating how LLM predictions inform intervention feasibility and trial implementation in data-limited settings. The proposed method extends to public health, disaster response, and other domains requiring rapid intervention assessment under severe data constraints. All code and prompts used for this work can be found at https://github.com/sarahmart/LLM-ABS-ARMMAN-prediction.

cs.AI↗