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Optimization · Optimization and Learning under Uncertainty

Belinda Li, Been Kim, Zi Wang

Large language models (LLMs) have shown impressive performance on reasoning benchmarks like math and logic. While many works have largely assumed well-defined tasks, real-world queries are often underspecified and only solvable by acquiring missing information. We formalize this information-gathering problem as a constraint satisfaction problem (CSP) with missing variable assignments. Using a special case where only one necessary variable assignment is missing, we can evaluate an LLM's ability to identify the minimal necessary question to ask. We present QuestBench, a set of underspecified reasoning tasks solvable by asking at most one question, which includes: (1) Logic-Q: logical reasoning tasks with one missing proposition, (2) Planning-Q: PDDL planning problems with partially-observed initial states, (3) GSM-Q: human-annotated grade school math problems with one unknown variable, and (4) GSME-Q: equation-based version of GSM-Q. The LLM must select the correct clarification question from multiple options. While current models excel at GSM-Q and GSME-Q, they achieve only 40-50% accuracy on Logic-Q and Planning-Q. Analysis shows that the ability to solve well-specified reasoning problems is not sufficient for success on our benchmark: models struggle to identify the right question even when they can solve the fully specified version. This highlights the need for specifically optimizing models' information acquisition capabilities.

Applications · Physics

Ana Rivera Him, Anvita Bhagavathula, Alvaro Carbonero, Priya Donti

Power flow (PF) calculations are the backbone of real-time grid operations, across workflows such as contingency analysis (where repeated PF evaluations assess grid security under outages) and topology optimization (which involves PF-based searches over combinatorially large action spaces). Running these calculations at operational timescales or across large evaluation spaces remains a major computational bottleneck. Additionally, growing uncertainty in power system operations from the integration of renewables and climate-induced extreme weather also calls for tools that can accurately and efficiently simulate a wide range of scenarios and operating conditions. Machine learning methods offer a potential speedup over traditional solvers, but their performance has not been systematically assessed on benchmarks that capture real-world variability. This paper introduces PF∆, a benchmark dataset for power flow that captures diverse variations in load, generation, and topology. PF∆ contains 859,800 solved power flow instances spanning six different bus system sizes, capturing three types of contingency scenarios (N , N –1, and N –2), and including close-to-infeasible cases near steady-state voltage stability limits. We evaluate traditional solvers and GNN-based methods, highlighting key areas where existing approaches struggle, and identifying open problems for future research. Our dataset is available at https://huggingface.co/datasets/pfdelta/pfdelta/tree/main and our code with data generation scripts and model implementations is at https: //github.com/MOSSLab-MIT/pfdelta

Optimization · Optimization and Learning under Uncertainty

Yeongjong Kim, Dabeen Lee

This paper considers stochastic-constrained stochastic optimization where the stochastic constraint is to satisfy that the expectation of a random function is below a certain threshold. In particular, we study the setting where data samples are drawn from a Markov chain and thus are not independent and identically distributed. We generalize the drift-plus-penalty framework, a primal-dual stochastic gradient method developed for the i.i.d. case, to the Markov chain sampling setting. We propose three variants of drift-plus-penalty; two are for the case when the mixing time of the underlying Markov chain is known while the other is for the case of unknown mixing time. In fact, our algorithms apply to a more general setting of constrained online convex optimization where the sequence of constraint functions follows a Markov chain. The algorithms are adaptive in that the first two work without knowledge of the time horizon while the third uses AdaGrad-style algorithm parameters, which is of independent interest. We demonstrate the effectiveness of our proposed methods through numerical experiments on classification with fairness constraints.

Theory · Learning Theory

Na Li, Zewu Zheng, Wei Ni, Hangguan Shan, Wenjie Zhang, Xinyu Li

Multi-agent reinforcement learning (MARL), as a thriving field, explores how multiple agents independently make decisions in a shared dynamic environment. Due to environmental uncertainties, policies in MARL must remain robust to tackle the sim-to-real gap. We focus on robust two-player zero-sum Markov games (TZMGs) in offline settings, specifically on tabular robust TZMGs (RTZMGs). We propose a model-based algorithm (*RTZ-VI-LCB*) for offline RTZMGs, which is optimistic robust value iteration combined with a data-driven Bernstein-style penalty term for robust value estimation. By accounting for distribution shifts in the historical dataset, the proposed algorithm establishes near-optimal sample complexity guarantees under partial coverage and environmental uncertainty. An information-theoretic lower bound is developed to confirm the tightness of our algorithm's sample complexity, which is optimal regarding both state and action spaces. To the best of our knowledge, RTZ-VI-LCB is the first to attain this optimality, sets a new benchmark for offline RTZMGs, and is validated experimentally.

Reinforcement Learning · Multi-agent

Simin Li, Zihao Mao, Hanxiao Li, Zonglei Jing, Zhuohang bian, Jun Guo, Li Wang, Zhuoran Han, Ruixiao Xu, Xin Yu 等

In cooperative Multi-Agent Reinforcement Learning (MARL), it is a common practice to tune hyperparameters in ideal simulated environments to maximize cooperative performance. However, policies tuned for cooperation often fail to maintain robustness and resilience under real-world uncertainties. Building trustworthy MARL systems requires a deep understanding of \emph{robustness}, which ensures stability under uncertainties, and \emph{resilience}, the ability to recover from disruptions—a concept extensively studied in control systems but largely overlooked in MARL. In this paper, we present a large-scale empirical study comprising over 82,620 experiments to evaluate cooperation, robustness, and resilience in MARL across 4 real-world environments, 13 uncertainty types, and 15 hyperparameters. Our key findings are: (1) Under mild uncertainty, optimizing cooperation improves robustness and resilience, but this link weakens as perturbations intensify. Robustness and resilience also varies by algorithm and uncertainty type. (2) Robustness and resilience do not generalize across uncertainty modalities or agent scopes: policies robust to action noise for all agents may fail under observation noise on a single agent. (3) Hyperparameter tuning is critical for trustworthy MARL: surprisingly, standard practices like parameter sharing, GAE, and PopArt can hurt robustness, while early stopping, high critic learning rates, and Leaky ReLU consistently help. By optimizing hyperparameters only, we observe substantial improvement in cooperation, robustness and resilience across all MARL backbones, with the phenomenon also generalizing to robust MARL methods across these backbones.

Data-centric AI · Data-centric AI methods and tools

Yang Zhao, Kai Xiong, Xiao Ding, Li Du, Yangou Ouyang, Zhouhao Sun, Jiannan Guan, Wenbin Zhang, Bin Liu, Dong Hu 等

A primary impediment to scaling reinforcement learning (RL) for large language model (LLM) training is the substantial computational cost, predominantly arising from the necessity of multi-sampling for policy optimization and evaluation. This underscores the critical yet challenging nature of efficient training data selection. Drawing inspiration from the Zone of Proximal Development (ZPD) theory, which posits that learners acquire knowledge more effectively from tasks of intermediate difficulty, we hypothesize that LLMs exhibit optimal learning from data they have not yet mastered but demonstrate the potential to comprehend. Conventional methodologies for assessing data difficulty or informativeness typically rely on computationally intensive multi-sampling or iterative procedures. To address this limitation, we introduce UFO-RL (**U**ncertainty-**F**ocused **O**ptimization for **R**einforcement **L**earning), a novel framework that employs a computationally efficient single-pass uncertainty estimation technique to identify informative training instances. This method, requiring only a single forward pass and obviating the need for iterative next-token computation, achieves a significant acceleration (up to 185$\times$) in data evaluation compared to multi-sampling approaches. UFO-RL leverages this efficient metric to select data within the model's estimated ZPD for training. Extensive experimentation across diverse LLMs and mathematical benchmarks demonstrates that training with a mere 10\% of the data, carefully selected by UFO-RL, yields performance comparable to or even surpassing that of full-data training. Furthermore, this targeted data selection results in up to a 16$\times$ reduction in overall training time, concurrently enhancing training stability and improving generalization capabilities. Thus, UFO-RL presents a practical and highly efficient strategy for scaling RL fine-tuning of LLMs by focusing learning efforts on the most informative and valuable data, thereby mitigating the computational bottlenecks associated with traditional RL training.

Applications · Chemistry and Drug Discovery

Lianghong Chen, Dongkyu Kim, Mike Domaratzki, Pingzhao Hu

Designing de novo 3D molecules with desirable properties remains a fundamental challenge in drug discovery and molecular engineering. While diffusion models have demonstrated remarkable capabilities in generating high-quality 3D molecular structures, they often struggle to effectively control complex multi-objective constraints critical for real-world applications. In this study, we propose an uncertainty-aware Reinforcement Learning (RL) framework to guide the optimization of 3D molecular diffusion models toward multiple property objectives while enhancing the overall quality of the generated molecules. Our method leverages surrogate models with predictive uncertainty estimation to dynamically shape reward functions, facilitating balance across multiple optimization objectives. We comprehensively evaluate our framework across three benchmark datasets and multiple diffusion model architectures, consistently outperforming baselines for molecular quality and property optimization. Additionally, Molecular Dynamics (MD) simulations and ADMET profiling of top generated candidates indicate promising drug-like behavior and binding stability, comparable to known Epidermal Growth Factor Receptor (EGFR) inhibitors. Our results demonstrate the strong potential of RL-guided generative diffusion models for advancing automated molecular design.

Social Aspects · Trustworthy Machine Learning

Jin Hu, Jiakai Wang, linna Jing, Haolin Li, Liu haodong, Haotong Qin, Aishan Liu, Ke Xu, Xianglong Liu

Recently, semantically constrained adversarial examples (SemanticAE), which are directly generated from natural language instructions, have become a promising avenue for future research due to their flexible attacking forms, but have not been thoroughly explored yet. To generate SemanticAEs, current methods fall short of satisfactory attacking ability as the key underlying factors of semantic uncertainty in human instructions, such as $\textit{referring diversity}$, $\textit{descriptive incompleteness}$, and $\textit{boundary ambiguity}$, have not been fully investigated. To tackle the issues, this paper develops a multi-dimensional $\textbf{ins}$truction $\textbf{u}$ncertainty $\textbf{r}$eduction ($\textbf{InSUR}$) framework to generate more satisfactory SemanticAE, $\textit{i.e.}$, transferable, adaptive, and effective. Specifically, in the dimension of the sampling method, we propose the residual-driven attacking direction stabilization to alleviate the unstable adversarial optimization caused by the diversity of language references. By coarsely predicting the language-guided sampling process, the optimization process will be stabilized by the designed ResAdv-DDIM sampler, therefore releasing the transferable and robust adversarial capability of multi-step diffusion models. In task modeling, we propose the context-encoded attacking scenario constraint to supplement the missing knowledge from incomplete human instructions. Guidance masking and renderer integration are proposed to regulate the constraints of 2D/3D SemanticAE, activating stronger scenario-adapted attacks. Moreover, in the dimension of generator evaluation, we propose the semantic-abstracted attacking evaluation enhancement by clarifying the evaluation boundary based on the label taxonomy, facilitating the development of more effective SemanticAE generators. Extensive experiments demonstrate the superiority of the transfer attack performance of InSUR. Besides, it is worth highlighting that we realize the reference-free generation of semantically constrained 3D adversarial examples by utilizing language-guided 3D generation models for the first time.

Optimization · Optimization and Learning under Uncertainty

Gongwei Chen, Lirong Jie, Lexiao Zou, Weili Guan, Miao Zhang, Liqiang Nie

Benefiting from the availability of extensive navigation trajectories, both manually and automatically annotated, current graphical user interface (GUI) agents have achieved remarkable advancements in performance. However, these annotated datasets often contain substantial noise, which impedes effective agent training and underscores the necessity for rigorous trajectory quality assessment. In contrast to existing prompting-based evaluators that rely on proprietary multimodal large language models (MLLMs), we propose an Uncertainty-aware Reinforced Self-Training (URST) framework to train lightweight MLLMs for efficient and reliable trajectory evaluation. URST iteratively fine-tunes MLLMs using their own generated thoughts and judgments to enable self-improvement, while its uncertainty-aware sampling strategy ensures the selection of the most informative training examples. To further enhance reasoning and judgment capabilities, we propose a simplified group policy optimization approach that effectively leverages diverse positive and negative samples for evaluator learning. Our evaluator demonstrates superior judgment performance across both in-domain and out-of-domain datasets. When used to filter navigation datasets, it consistently leads to performance improvements in training GUI agents.

Optimization · Optimization and Learning under Uncertainty

Ilan Cohen, Debmalya Panigrahi

In online allocation problems, an algorithm must choose from a set of options at each step, where each option incurs a set of costs/rewards associated with a set of $d$ agents. The goal is to minimize/maximize a function of the accumulated costs/rewards assigned to the agents over the course of the entire allocation process. Such problems are common in combinatorial optimization, including minimization problems such as machine scheduling and network routing, as well as maximization problems such as fair allocation for welfare maximization. In this paper, we develop a general learning-augmented algorithmic framework for online allocation problems that produces a nearly optimal solution using only a single $d$-dimensional vector of learned weights. Using this general framework, we derive learning-augmented online algorithms for a broad range of application problems in routing, scheduling, and fair allocation. Our main tool is convex programming duality, which may also have further implications for learning-augmented algorithms in the future.

Optimization · Optimization and Learning under Uncertainty

Faraz Zargari, Hossein Jazi, Lyndon Hallett, Bo Sun, Xiaoqi Tan

We study the online multi-class selection problem with group fairness guarantees, where limited resources must be allocated to sequentially arriving agents. Our work addresses two key limitations in the existing literature. First, we introduce a novel lossless rounding scheme that ensures the integral algorithm achieves the same expected performance as any fractional solution. Second, we explicitly address the challenges introduced by agents who belong to multiple classes. To this end, we develop a randomized algorithm based on a relax-and-round framework. The algorithm first computes a fractional solution using a resource reservation approach---referred to as the *set-aside* mechanism---to enforce fairness across classes. The subsequent rounding step preserves these fairness guarantees without degrading performance. Additionally, we propose a learning-augmented variant that incorporates untrusted machine-learned predictions to better balance fairness and efficiency in practical settings.

Lei Li, Hehuan Liu, Yaxin Zhou, ZhaoYang Gui, Xudong Weng, Yi Yuan, Zheng Wei, Zang Li

Direct Preference Optimization (DPO) has recently emerged as an efficient and effective method for aligning large language models with human preferences. However, constructing high-quality preference datasets remains challenging, often necessitating expensive manual or powerful LM annotations. Additionally, standard DPO exhibits suboptimal performance in complex reasoning tasks, such as mathematical and code reasoning. In this paper, we introduce an approach to collect preference pairs through iterative sampling and execution feedback, tailored to the current learning state (e.g. well-learned, mis-learned, and unlearned) of the policy model. To alleviate the failures of DPO and improve its applicability in reasoning tasks, we propose , an iterative uncertainty-aware preference optimization method that achieves fine-grained preference control by assessing model confidence. We validate our approach across three reasoning tasks, incorporating five established reasoning datasets and one self-curated dataset. Our experimental results demonstrate an overall improvement of 3.6% over the standard DPO method and show the model exhibits promising generalizability.

Aoqiang Zhu, Min Hu, Xiaohua Wang, Jiaoyun Yang, Yiming Tang, Ning An

Multimodal Sentiment Analysis (MSA) with incomplete data has gained significant attention recently. Existing studies focus on optimizing model structures to handle modality missingness, but models still face challenges in robustness when dealing with uncertain missingness. To this end, we propose a data-centric robust multimodal sentiment analysis method, Proxy-Driven Robust Multimodal Fusion (P-RMF). First, we map unimodal data to the latent space of Gaussian distributions to capture core features and structure, thereby learn stable modality representation. Then, we combine the quantified inherent modality uncertainty to learn stable multimodal joint representation (i.e., proxy modality), which is further enhanced through multi-layer dynamic cross-modal injection to increase its diversity. Extensive experimental results show that P-RMF outperforms existing models in noise resistance and achieves state-of-the-art performance on multiple benchmark datasets. Code will be available at https://github.com/***/P-RMF.

Applications · Computer Vision

Xuelin Shen, Jiayin Xu, Kangsheng Yin, Wenhan Yang

The improved semantic understanding of vision-language pretrained (VLP) models has made it increasingly difficult to protect publicly posted images from being exploited by search engines and other similar tools. In this context, this paper seeks to protect users' privacy by implementing defenses at the image compression stage to prevent exploitation. Specifically, we propose a flexible coding method, termed Privacy-Shielded Image Compression (PSIC), that can produce bitstreams with multiple decoding options. By default, the bitstream is decoded to preserve satisfactory perceptual quality while preventing interpretation by VLP models. Our method also retains the original image compression functionality. With a customizable input condition, the proposed scheme can reconstruct the image that preserves its full semantic information. A Conditional Latent Trigger Generation (CLTG) module is proposed to produce bias information based on customizable conditions to guide the decoding process into different reconstructed versions, and an Uncertainty-Aware Encryption-Oriented (UAEO) optimization function is designed to leverage the soft labels inferred from the target VLP model's uncertainty on the training data. This paper further incorporates an adaptive multi-objective optimization strategy to obtain improved encrypting performance and perceptual quality simultaneously within a unified training process. The proposed scheme is plug-and-play and can be seamlessly integrated into most existing Learned Image Compression (LIC) models. Extensive experiments across multiple downstream tasks have demonstrated the effectiveness of our design.

Deep Learning · Large Language Models

Zongqian Wu, Baoduo Xu, Ruochen Cui, Mengmeng Zhan, Xiaofeng Zhu, Lei Feng

Chain-of-thought (CoT) reasoning has emerged as an effective approach for activating latent capabilities in LLMs. Interestingly, we observe that both CoT reasoning and self-training share the core objective: iteratively leveraging model-generated information to progressively reduce prediction uncertainty. Building on this insight, we propose a novel CoT framework to improve reasoning performance. Our framework integrates two key components: (i) a task-specific prompt module that optimizes the initial reasoning process, and (ii) an adaptive reasoning iteration module that dynamically refines the reasoning process and addresses the limitations of previous CoT approaches, i.e., over-reasoning and high similarity between consecutive reasoning iterations. Extensive experiments show that the proposed method achieves significant advantages in both performance and computational efficiency. Our code is available at: https://github.com/zongqianwu/ST-COT.

Probabilistic Methods · Graphical Models

Wen-Bo Du, Hao-Yi Lei, Lue Tao, Tian-Zuo Wang, Zhi-Hua Zhou

In the field of machine learning (ML), an essential type of decision-related problem is known as AUF (Avoiding Undesired Future): if an ML model predicts an undesired outcome, how can decisions be made to prevent it? Recently, a novel framework called *rehearsal learning* has been proposed to address the AUF problem. Despite its utility in modeling uncertainty for decision-making, it remains unclear *under what conditions* and *how* optimal actions that maximize the *AUF probability* can be identified. In this paper, we propose *CARE* (CAnonical REctangle), a condition under which the maximum AUF probability can be achieved. Under the CARE condition, we present a projection-Newton algorithm to select actions and prove that the algorithm achieves superlinear convergence to the optimal one. Besides, we provide a generalization method for adopting the algorithm to AUF scenarios beyond the CARE condition. Finally, we demonstrate that a closed-form solution exists when the outcome is a singleton variable, substantially reducing the time complexity of decision-making. Experiments validate the effectiveness and efficiency of our method.

General Machine Learning · Representation Learning

Siyuan Duan, Yuan Sun, Dezhong Peng, Guiduo Duan, Xi Peng, Peng Hu

Multi-view learning methods primarily focus on enhancing decision accuracy but often neglect the uncertainty arising from the intrinsic drawbacks of data, such as noise, conflicts, etc. To address this issue, several trusted multi-view learning approaches based on the Evidential Theory have been proposed to capture uncertainty in multi-view data. However, their performance is highly sensitive to conflicting views, and their uncertainty estimates, which depend on the total evidence and the number of categories, often underestimate uncertainty for conflicting multi-view instances due to the neglect of inherent conflicts between belief masses. To accurately classify conflicting multi-view instances and precisely estimate their intrinsic uncertainty, we present a novel Deep \underline{Fu}zzy \underline{M}ulti-View \underline{L}earning (\textbf{FUML}) method. Specifically, FUML leverages Fuzzy Set Theory to model the outputs of a classification neural network as fuzzy memberships, incorporating both possibility and necessity measures to quantify category credibility. A tailored loss function is then proposed to optimize the category credibility. To further enhance uncertainty estimation, we propose an entropy-based uncertainty estimation method leveraging category credibility. Additionally, we develop a Dual Reliable Multi-view Fusion (DRF) strategy that accounts for both view-specific uncertainty and inter-view conflict to mitigate the influence of conflicting views in multi-view fusion. Extensive experiments demonstrate that our FUML achieves state-of-the-art performance in terms of both accuracy and reliability.

Reinforcement Learning · Batch/Offline

Shoukai Xu, ZihaoLian, Mingkui Tan, Liu Liu, Zhong Zhang, Peilin Zhao

Offline reinforcement learning is widely applied in multiple fields due to its advantages in efficiency and risk control. However, a major problem it faces is the distribution shift between offline datasets and online environments. This mismatch leads to out-of-distribution (OOD) state-action pairs that fall outside the scope of the training data. Therefore, existing conservative training policies may not provide reliable decisions when the test environment deviates greatly from the offline dataset. In this paper, we propose Test-time Adapted Reinforcement Learning (TARL) to address this problem. TARL constructs unsupervised test-time optimization objectives for discrete and continuous control tasks, using test data without depending on environmental rewards. In discrete control tasks, it minimizes the entropy of predicted action probabilities to decrease uncertainty and avoid OOD state-action pairs. For continuous control tasks, it represents and minimizes action uncertainty based on the normal distribution of policy network outputs. Moreover, to prevent model bias caused by overfitting and error accumulation during the test-time update process, TARL enforces a KL divergence constraint between the fine-tuned policy and the original policy. For efficiency, TARL only updates the layer normalization layer parameters during testing. Extensive experiments on popular Atari game benchmarks and the D4RL dataset demonstrate the superiority of our method. Our method achieved a significant improvement over CQL, with a 13.6% episode return relative increase on the hopper-expert-v2 task.

General Machine Learning · Causality

Ke Zhu, Shu Yang, Xiaofei Wang

External controls from historical trials or observational data can augment randomized controlled trials when large-scale randomization is impractical or unethical, such as in drug evaluation for rare diseases. However, non-randomized external controls can introduce biases, and existing Bayesian and frequentist methods may inflate the type I error rate, particularly in small-sample trials where external data borrowing is most critical. To address these challenges, we propose a randomization inference framework that ensures finite-sample exact and model-free type I error rate control, adhering to the “analyze as you randomize” principle to safeguard against hidden biases. Recognizing that biased external controls reduce the power of randomization tests, we leverage conformal inference to develop an individualized test-then-pool procedure that selectively borrows comparable external controls to improve power. Our approach incorporates selection uncertainty into randomization tests, providing valid post-selection inference. Additionally, we propose an adaptive procedure to optimize the selection threshold by minimizing the mean squared error across a class of estimators encompassing both no-borrowing and full-borrowing approaches. The proposed methods are supported by non-asymptotic theoretical analysis, validated through simulations, and applied to a randomized lung cancer trial that integrates external controls from the National Cancer Database.

General Machine Learning

Jie Bao, Chuangyin Dang, Rui Luo, Hanwei Zhang, Zhixin Zhou

As deep learning models are increasingly deployed in high-risk applications, robust defenses against adversarial attacks and reliable performance guarantees become paramount. Moreover, accuracy alone does not provide sufficient assurance or reliable uncertainty estimates for these models. This study advances adversarial training by leveraging principles from Conformal Prediction. Specifically, we develop an adversarial attack method, termed OPSA (OPtimal Size Attack), designed to reduce the efficiency of conformal prediction at any significance level by maximizing model uncertainty without requiring coverage guarantees. Correspondingly, we introduce OPSA-AT (Adversarial Training), a defense strategy that integrates OPSA within a novel conformal training paradigm. Experimental evaluations demonstrate that our OPSA attack method induces greater uncertainty compared to baseline approaches for various defenses. Conversely, our OPSA-AT defensive model significantly enhances robustness not only against OPSA but also other adversarial attacks, and maintains reliable prediction. Our findings highlight the effectiveness of this integrated approach for developing trustworthy and resilient deep learning models for safety-critical domains. Our code is available at https://github.com/bjbbbb/Enhancing-Adversarial-Robustness-with-Conformal-Prediction.