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Insup Lee

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12 papers

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AAAI Conference 2026 Conference Paper

Conformal Constrained Policy Optimization for Cost-Effective LLM Agents

Wenwen Si
Sooyong Jang
Insup Lee
Osbert Bastani

While large language models (LLMs) have recently made tremendous progress towards solving challenging AI problems, they have done so at increasingly steep computational and API costs. We propose a novel strategy where we combine multiple LLM models with varying cost/accuracy tradeoffs in an agentic manner, where models and tools are run in sequence as determined by an orchestration model to minimize cost subject to a user-specified level of reliability; this constraint is formalized using conformal prediction to provide guarantees. To solve this problem, we propose Conformal Constrained Policy Optimization (CCPO), a training paradigm that integrates constrained policy optimization with off-policy reinforcement learning and recent advances in online conformal prediction. CCPO jointly optimizes a cost-aware policy (score function) and an adaptive threshold. Across two multi-hop question answering benchmarks, CCPO achieves up to a 30% cost reduction compared to other cost-aware baselines and LLM-guided methods without compromising reliability. Our approach provides a principled and practical framework for deploying LLM agents that are significantly more cost-effective while maintaining reliability.

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TMLR Journal 2026 Journal Article

On Calibration of Multilingual Question Answering LLMs

Yahan Yang
Soham Dan
Dan Roth
Insup Lee

Multilingual pre-trained Large Language Models (LLMs) are incredibly effective at Question Answering (QA), a core task in Natural Language Understanding, achieving high accuracies on several multilingual benchmarks. However, little is known about how well their confidences are calibrated. In this paper, we comprehensively benchmark the calibration of several multilingual LLMs (MLLMs) on a variety of QA tasks. We perform extensive experiments, spanning encoder-only, encoder-decoder, and decoder-only QA models (size varying from 110M to 7B parameters) and diverse languages, including both high- and low-resource ones. We study different dimensions of calibration in in-distribution, out-of-distribution, and cross-lingual transfer settings, and investigate strategies to improve it, including post-hoc methods and regularized fine-tuning. For decoder-only LLMs such as LlaMa2, we additionally find that in-context learning improves confidence calibration on multilingual data. We also conduct several ablation experiments to study the effect of language distances, language corpus size, and model size on calibration, and how multilingual models compare with their monolingual counterparts for diverse tasks and languages. Our experiments suggest that the multilingual QA models are poorly calibrated for languages other than English and incorporating a small set of cheaply translated multilingual samples during fine-tuning/calibration effectively enhances the calibration performance.

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AAAI Conference 2026 Conference Paper

Quantifying and Improving Adaptivity in Conformal Prediction Through Input Transformations

Sooyong Jang
Insup Lee

Conformal prediction constructs a set of labels instead of a single point prediction, while providing a probabilistic coverage guarantee. Beyond the coverage guarantee, adaptiveness to example difficulty is an important property. It means that the method should produce larger prediction sets for more difficult examples, and smaller ones for easier examples. Existing evaluation methods for adaptiveness typically analyze coverage rate violation or average set size across bins of examples grouped by difficulty. However, these approaches often suffer from imbalanced binning, which can lead to inaccurate estimates of coverage or set size. To address this issue, we propose a binning method that leverages input transformations to sort examples by difficulty, followed by uniform-mass binning. Building on this binning, we introduce two metrics to better evaluate adaptiveness. These metrics provide more reliable estimates of coverage rate violation and average set size due to balanced binning, leading to more accurate adaptivity assessment. Through experiments, we demonstrate that our proposed metric correlates more strongly with the desired adaptiveness property compared to existing ones. Furthermore, motivated by our findings, we propose a new adaptive prediction set algorithm that groups examples by estimated difficulty and applies group-conditional conformal prediction. This allows us to determine appropriate thresholds for each group. Experimental results on both (a) an Image Classification (ImageNet) (b) a medical task (visual acuity prediction) show that our method outperforms existing approaches according to the new metrics.

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AAAI Conference 2025 Conference Paper

Assessing Modality Bias in Video Question Answering Benchmarks with Multimodal Large Language Models

Jean Park
Kuk Jin Jang
Basam Alasaly
Sriharsha Mopidevi
Andrew Zolensky
Eric Eaton
Insup Lee
Kevin Johnson

Multimodal large language models (MLLMs) can simultaneously process visual, textual, and auditory data, capturing insights that complement human analysis. However, existing video question-answering (VidQA) benchmarks and datasets often exhibit a bias toward a single modality, despite the goal of requiring advanced reasoning skills that integrate diverse modalities to answer the queries. In this work, we introduce the modality importance score (MIS) to identify such bias. It is designed to assess which modality embeds the necessary information to answer the question. Additionally, we propose an innovative method using state-of-the-art MLLMs to estimate the modality importance, which can serve as a proxy for human judgments of modality perception. With this MIS, we demonstrate the presence of unimodal bias and the scarcity of genuinely multimodal questions in existing datasets. We further validate the modality importance score with multiple ablation studies to evaluate the performance of MLLMs on permuted feature sets. Our results indicate that current models do not effectively integrate information due to modality imbalance in existing datasets. Our proposed MLLM-derived MIS can guide the curation of modality-balanced datasets that advance multimodal learning and enhance MLLMs' capabilities to understand and utilize synergistic relations across modalities.

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NeurIPS Conference 2024 Conference Paper

AR-Pro: Counterfactual Explanations for Anomaly Repair with Formal Properties

Xiayan Ji
Anton Xue
Eric Wong
Oleg Sokolsky
Insup Lee

Anomaly detection is widely used for identifying critical errors and suspicious behaviors, but current methods lack interpretability. We leverage common properties of existing methods and recent advances in generative models to introduce counterfactual explanations for anomaly detection. Given an input, we generate its counterfactual as a diffusion-based repair that shows what a non-anomalous version $\textit{should have looked like}$. A key advantage of this approach is that it enables a domain-independent formal specification of explainability desiderata, offering a unified framework for generating and evaluating explanations. We demonstrate the effectiveness of our anomaly explainability framework, AR-Pro, on vision (MVTec, VisA) and time-series (SWaT, WADI, HAI) anomaly datasets. The code used for the experiments is accessible at: https: //github. com/xjiae/arpro.

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AAAI Conference 2024 Conference Paper

Conformal Prediction Regions for Time Series Using Linear Complementarity Programming

Matthew Cleaveland
Insup Lee
George J. Pappas
Lars Lindemann

Conformal prediction is a statistical tool for producing prediction regions of machine learning models that are valid with high probability. However, applying conformal prediction to time series data leads to conservative prediction regions. In fact, to obtain prediction regions over T time steps with confidence 1--delta, previous works require that each individual prediction region is valid with confidence 1--delta/T. We propose an optimization-based method for reducing this conservatism to enable long horizon planning and verification when using learning-enabled time series predictors. Instead of considering prediction errors individually at each time step, we consider a parameterized prediction error over multiple time steps. By optimizing the parameters over an additional dataset, we find prediction regions that are not conservative. We show that this problem can be cast as a mixed integer linear complementarity program (MILCP), which we then relax into a linear complementarity program (LCP). Additionally, we prove that the relaxed LP has the same optimal cost as the original MILCP. Finally, we demonstrate the efficacy of our method on case studies using pedestrian trajectory predictors and F16 fighter jet altitude predictors.

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TMLR Journal 2024 Journal Article

Credal Bayesian Deep Learning

Michele Caprio
Souradeep Dutta
Kuk Jin Jang
Vivian Lin
Radoslav Ivanov
Oleg Sokolsky
Insup Lee

Uncertainty quantification and robustness to distribution shifts are important goals in machine learning and artificial intelligence. Although Bayesian Neural Networks (BNNs) allow for uncertainty in the predictions to be assessed, different sources of uncertainty are indistinguishable. We present Credal Bayesian Deep Learning (CBDL). Heuristically, CBDL allows to train an (uncountably) infinite ensemble of BNNs, using only finitely many elements. This is possible thanks to prior and likelihood finitely generated credal sets (FGCSs), a concept from the imprecise probability literature. Intuitively, convex combinations of a finite collection of prior-likelihood pairs are able to represent infinitely many such pairs. After training, CBDL outputs a set of posteriors on the parameters of the neural network. At inference time, such posterior set is used to derive a set of predictive distributions that is in turn utilized to distinguish between aleatoric and epistemic uncertainties, and to quantify them. The predictive set also produces either (i) a collection of outputs enjoying desirable probabilistic guarantees, or (ii) the single output that is deemed the best, that is, the one having the highest predictive lower probability -- another imprecise-probabilistic concept. CBDL is more robust than single BNNs to prior and likelihood misspecification, and to distribution shift. We show that CBDL is better at quantifying and disentangling different types of uncertainties than single BNNs and ensemble of BNNs. In addition, we apply CBDL to two case studies to demonstrate its downstream tasks capabilities: one, for motion prediction in autonomous driving scenarios, and two, to model blood glucose and insulin dynamics for artificial pancreas control. We show that CBDL performs better when compared to an ensemble of BNNs baseline.

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AAAI Conference 2022 Conference Paper

iDECODe: In-Distribution Equivariance for Conformal Out-of-Distribution Detection

Ramneet Kaur
Susmit Jha
Anirban Roy
Sangdon Park
Edgar Dobriban
Oleg Sokolsky
Insup Lee

Machine learning methods such as deep neural networks (DNNs), despite their success across different domains, are known to often generate incorrect predictions with high confidence on inputs outside their training distribution. The deployment of DNNs in safety-critical domains requires detection of out-of-distribution (OOD) data so that DNNs can abstain from making predictions on those. A number of methods have been recently developed for OOD detection, but there is still room for improvement. We propose the new method iDECODe, leveraging in-distribution equivariance for conformal OOD detection. It relies on a novel base non-conformity measure and a new aggregation method, used in the inductive conformal anomaly detection framework, thereby guaranteeing a bounded false detection rate. We demonstrate the efficacy of iDECODe by experiments on image and audio datasets, obtaining state-of-the-art results. We also show that iDECODe can detect adversarial examples. Code, pre-trained models, and data are available at https: //github. com/ramneetk/iDECODe.

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NeurIPS Conference 2022 Conference Paper

PAC Prediction Sets for Meta-Learning

Sangdon Park
Edgar Dobriban
Insup Lee
Osbert Bastani

Uncertainty quantification is a key component of machine learning models targeted at safety-critical systems such as in healthcare or autonomous vehicles. We study this problem in the context of meta learning, where the goal is to quickly adapt a predictor to new tasks. In particular, we propose a novel algorithm to construct \emph{PAC prediction sets}, which capture uncertainty via sets of labels, that can be adapted to new tasks with only a few training examples. These prediction sets satisfy an extension of the typical PAC guarantee to the meta learning setting; in particular, the PAC guarantee holds with high probability over future tasks. We demonstrate the efficacy of our approach on four datasets across three application domains: mini-ImageNet and CIFAR10-C in the visual domain, FewRel in the language domain, and the CDC Heart Dataset in the medical domain. In particular, our prediction sets satisfy the PAC guarantee while having smaller size compared to other baselines that also satisfy this guarantee.

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TCS Journal 2012 Journal Article

PADS: An approach to modeling resource demand and supply for the formal analysis of hierarchical scheduling

Anna Philippou
Insup Lee
Oleg Sokolsky

As real-time embedded systems become more complex, resource partitioning is increasingly used to guarantee real-time performance. Recently, several compositional frameworks of resource partitioning have been proposed using real-time scheduling theory with various notions of real-time tasks running under restricted resource supply environments. However, these real-time scheduling-based approaches are limited in their expressiveness in that, although capable of describing resource-demand tasks, they are unable to model resource supply. This paper describes a process algebraic framework PADSfor reasoning about resource demand and resource supply inspired by the timed process algebra ACSR. In ACSR, real-time tasks are specified by enunciating their consumption needs for resources. To also accommodate resource-supply processes in PADS, given a resource c p u, we write c p u ¯ to denote the availability of c p u for a requesting task process. Using PADS, we define a supply-demand relation where a pair ( T, S ) belongs to the relation if the demand process T can be scheduled under supply S. We develop a theory of compositional schedulability analysis as well as a technique for synthesizing an optimal supply process for a set of tasks. Furthermore, we define ordering relations between supplies which describe when a supply offers more resource capacity than another. With this notion it is possible to formally represent hierarchical scheduling approaches that assign more “generous” resource allocations to tasks in exchange for a simple representation. We illustrate our techniques via a number of examples.

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I&C Journal 1997 Journal Article

A Complete Axiomatization of Finite-state ACSR Processes

Patrice Brémond-Grégoire
Jin-Young Choi
Insup Lee

A real-time process algebra, called ACSR, has been developed to facilitate the specification and analysis of real-time systems. ACSR supports synchronous timed actions and asynchronous instantaneous events. Timed actions are used to represent the usage of resources and to model the passage of time. Events are used to capture synchronization between processes. To be able to specify real-time systems accurately, ACSR supports a notion of priority that can be used to arbitrate among timed actions competing for the use of resources and among events that are ready for synchronization. In addition to operators common to process algebra, ACSR includes the scope operator, which can be used to model timeouts and interrupts. Equivalence between ACSR terms is based on the notion of strong bisimulation. This paper briefly describes the syntax and semantics of ACSR and then presents a set of algebraic laws that can be used to prove equivalence of ACSR processes. The contribution of this paper is the soundness and completeness proofs of this set of laws. The completeness proof is for finite-state ACSR processes, which are defined to be processes without free variables under parallel operator or scope operator.

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TCS Journal 1997 Journal Article

A process algebra of communicating shared resources with dense time and priorities

Patrice Brémond-Grégoire
Insup Lee

The correctness of real-time distributed systems depends not only on the function they compute but also on their timing characteristics. Furthermore, those characteristics are strongly influenced by the delays due to synchronization and resource availability. Process algebras have been used successfully to define and prove correctness of distributed systems. More recently, there has been a lot of activity to extend their application to real-time systems. The problem with most current approaches is that they ignore resource constraints and assume either maximum parallelism (i. e. , unlimited resources) or pure interleaving (i. e. , single resource). Algebra of communicating shared resources (ACSR) is a process algebra designed for the formal specification and manipulation of distributed systems with resources and real-time constraints. A dense time domain provides a more natural way of specifying systems compared to the usual discrete time. Priorities provide a measure of urgency for each action and can be used to ensure that deadlines are met. In ACSR, processes are specified using resource bound, timed actions and instantaneous synchronization events. Processes can be combined using traditional operators such as nondeterministic choice and parallel execution. Specialized operators allow the specification of real-time behavior and constraints. The semantics of ACSR is defined as a labeled transition system. Equivalence between processes is based on the notion of strong bisimulation. A sound and complete set of algebraic laws can be used to transform almost any ACSR process into a normal form.

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