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General Machine Learning · Everything Else

Sebastian Bruch, Aditya Krishnan, Franco Maria Nardini

Clustering-based nearest neighbor search algorithms partition points into shards to form an index, and search only a subset of shards to process a query. Even though search efficacy is heavily influenced by the algorithm that identifies the shards to probe, it has received little attention in the literature. We study routing in clustering-based maximum inner product search, which includes cosine similarity search. We unpack existing routers and notice the surprising role of optimism. We then take a page from the sequential decision making literature and formalize that insight following the principle of ``optimism in the face of uncertainty.'' In particular, we present a framework that incorporates the moments of the distribution of inner products within each shard to estimate the maximum inner product. We then develop a practical instance of our algorithm that uses only the first two moments to reach the same accuracy as state-of-the-art routers by probing up to $50\%$ fewer points on benchmark datasets without compromising efficiency. Our algorithm is also space-efficient: we design a sketch of the second moment whose size is independent of the number of points and requires $\mathcal{O}(1)$ vectors per shard.

Optimization · Optimization and Learning under Uncertainty

Lingxiao Huang, Zhize Li, Nisheeth K. Vishnoi, Runkai Yang, Haoyu Zhao

We study the problem of constructing coresets for $(k, z)$-clustering when the input dataset is corrupted by stochastic noise drawn from a known distribution. In this setting, evaluating the quality of a coreset is inherently challenging, as the true underlying dataset is unobserved. To address this, we investigate coreset construction using surrogate error metrics that are tractable and provably related to the true clustering cost. We analyze a traditional metric from prior work and introduce a new error metric that more closely aligns with the true cost. Although our metric is defined independent of the noise distribution, it enables approximation guarantees that scale with the noise level. We design a coreset construction algorithm based on this metric and show that, under mild assumptions on the data and noise, enforcing an $\varepsilon$-bound under our metric yields smaller coresets and tighter guarantees on the true clustering cost than those obtained via classical metrics. In particular, we prove that the coreset size can improve by a factor of up to $\mathrm{poly}(k)$, where $n$ is the dataset size. Experiments on real-world datasets support our theoretical findings and demonstrate the practical advantages of our approach.

Computer Vision · Classification and Understanding

Hongyang He, Xinyuan Song, Yangfan He, Zeyu Zhang, Yanshu Li, Haochen You, Lifan Sun, Wenqiao Zhang

We introduce TRiCo, a novel triadic game-theoretic co-training framework that rethinks the structure of semi-supervised learning by incorporating a teacher, two students, and an adversarial generator into a unified training paradigm. Unlike existing co-training or teacher-student approaches, TRiCo formulates SSL as a structured interaction among three roles: (i) two student classifiers trained on frozen, complementary representations, (ii) a meta-learned teacher that adaptively regulates pseudo-label selection and loss balancing via validation-based feedback, and (iii) a non-parametric generator that perturbs embeddings to uncover decision boundary weaknesses. Pseudo-labels are selected based on mutual information rather than confidence, providing a more robust measure of epistemic uncertainty. This triadic interaction is formalized as a Stackelberg game, where the teacher leads strategy optimization and students follow under adversarial perturbations. By addressing key limitations in existing SSL frameworks—such as static view interactions, unreliable pseudo-labels, and lack of hard sample modeling—TRiCo provides a principled and generalizable solution. Extensive experiments on CIFAR-10, SVHN, STL-10, and ImageNet demonstrate that TRiCo consistently achieves state-of-the-art performance in low-label regimes, while remaining architecture-agnostic and compatible with frozen vision backbones.

Optimization · Optimization and Learning under Uncertainty

Abhishek Sinha, Rahul Vaze

We study Online Convex Optimization with adversarial constraints (COCO). At each round a learner selects an action from a convex decision set and then an adversary reveals a convex cost and a convex constraint function. The goal of the learner is to select a sequence of actions to minimize both regret and the cumulative constraint violation (CCV) over a horizon of length $T$. The best-known policy for this problem achieves $O(\sqrt{T})$ regret and $\tilde{O}(\sqrt{T})$ CCV. In this paper, we improve this by trading off regret to achieve substantially smaller CCV. This trade-off is especially important in safety-critical applications, where satisfying the safety constraints is non-negotiable. Specifically, for any bounded convex cost and constraint functions, we propose an online policy that achieves $\tilde{O}(\sqrt{dT}+ T^\beta)$ regret and $\tilde{O}(dT^{1-\beta})$ CCV, where $d$ is the dimension of the decision set and $\beta \in [0,1]$ is a tunable parameter. We begin with a special case, called the $\textsf{Constrained Expert}$ problem, where the decision set is a probability simplex and the cost and constraint functions are linear. Leveraging a new adaptive small-loss regret bound, we propose a computationally efficient policy for the $\textsf{Constrained Expert}$ problem, that attains $O(\sqrt{T\ln N}+T^{\beta})$ regret and $\tilde{O}(T^{1-\beta} \ln N)$ CCV for $N$ number of experts. The original problem is then reduced to the $\textsf{Constrained Expert}$ problem via a covering argument. Finally, with an additional $M$-smoothness assumption, we propose a computationally efficient first-order policy attaining $O(\sqrt{MT}+T^{\beta})$ regret and $\tilde{O}(MT^{1-\beta})$ CCV.

Optimization · Optimization and Learning under Uncertainty

Senne Berden, Ali Mahmutoğulları, Dimos Tsouros, Tias Guns

Mathematical optimization is a fundamental tool for decision-making in a wide range of applications. However, in many real-world scenarios, the parameters of the optimization problem are not known a priori and must be predicted from contextual features. This gives rise to predict-then-optimize problems, where a machine learning model predicts problem parameters that are then used to make decisions via optimization. A growing body of work on decision-focused learning (DFL) addresses this setting by training models specifically to produce predictions that maximize downstream decision quality, rather than accuracy. While effective, DFL is computationally expensive, because it requires solving the optimization problem with the predicted parameters at each loss evaluation. In this work, we address this computational bottleneck for linear optimization problems, a common class of problems in both DFL literature and real-world applications. We propose a solver-free training method that exploits the geometric structure of linear optimization to enable efficient training with minimal degradation in solution quality. Our method is based on the insight that a solution is optimal if and only if it achieves an objective value that is at least as good as that of its adjacent vertices on the feasible polytope. Building on this, our method compares the estimated quality of the ground-truth optimal solution with that of its precomputed adjacent vertices, and uses this as loss function. Experiments demonstrate that our method significantly reduces computational cost while maintaining high decision quality.

Optimization · Optimization and Learning under Uncertainty

Guangyi He, Tobias Sutter, Lukas Gonon

In this paper, we study the robustness of classical deep hedging strategies under distributional shifts by leveraging the concept of adversarial attacks. We first demonstrate that standard deep hedging models are highly vulnerable to small perturbations in the input distribution, resulting in significant performance degradation. Motivated by this, we propose an adversarial training framework tailored to increase the robustness of deep hedging strategies. Our approach extends pointwise adversarial attacks to the distributional setting and introduces a computationally tractable reformulation of the adversarial optimization problem over a Wasserstein ball. This enables the efficient training of hedging strategies that are resilient to distributional perturbations. Through extensive numerical experiments, we show that adversarially trained deep hedging strategies consistently outperform their classical counterparts in terms of out-of-sample performance and resilience to model misspecification. Additional results indicate that the robust strategies maintain reliable performance on real market data and remain effective during periods of market change. Our findings establish a practical and effective framework for robust deep hedging under realistic market uncertainties.

Optimization · Optimization and Learning under Uncertainty

Christopher Yeh, Nicolas Christianson, Adam Wierman, Yisong Yue

While deep learning models often achieve high predictive accuracy, their predictions typically do not come with any provable guarantees on risk or reliability, which are critical for deployment in high-stakes applications. The framework of conformal risk control (CRC) provides a distribution-free, finite-sample method for controlling the expected value of any bounded monotone loss function and can be conveniently applied post-hoc to any pre-trained deep learning model. However, many real-world applications are sensitive to tail risks, as opposed to just expected loss. In this work, we develop a method for controlling the general class of Optimized Certainty-Equivalent (OCE) risks, a broad class of risk measures which includes as special cases the expected loss (generalizing the original CRC method) and common tail risks like the conditional value-at-risk (CVaR). Furthermore, standard post-hoc CRC can degrade average-case performance due to its lack of feedback to the model. To address this, we introduce "conformal risk training," an end-to-end approach that differentiates through conformal OCE risk control _during model training or fine-tuning_. Our method achieves provable risk guarantees while demonstrating significantly improved average-case performance over post-hoc approaches on applications to controlling classifiers' false negative rate and controlling financial risk in battery storage operation.

Optimization · Optimization and Learning under Uncertainty

Zefan Cai, Wen Xiao, Hanshi Sun, cheng Luo, Yikai Zhang, Ke Wan, Yucheng Li, Yeyang Zhou, Li-Wen Chang, Jiuxiang Gu 等

Reasoning models have demonstrated impressive performance in self-reflection and chain-of-thought reasoning. However, they often produce excessively long outputs, leading to prohibitively large key-value (KV) caches during inference. While chain-of-thought inference significantly improves performance on complex reasoning tasks, it can also lead to reasoning failures when deployed with existing KV cache compression approaches. To address this, we propose Redundancy-aware KV Cache Compression for Reasoning models (R-KV), a novel method specifically targeting redundant tokens in reasoning models. Our method preserves nearly 100% of the full KV cache performance using only 10% of the KV cache, substantially outperforming existing KV cache baselines, which reach only 60% of the performance. Remarkably, R-KV even achieves 105% of full KV cache performance with 38% of the KV cache. This KV-cache reduction also leads to a 50% memory saving and a 2x speedup over standard chain-of-thought reasoning inference. Experimental results show that R-KV consistently outperforms existing KV cache compression baselines across two mathematical reasoning datasets.

Optimization · Optimization and Learning under Uncertainty

Yunuo Zhang, Baiting Luo, Ayan Mukhopadhyay, Gabor Karsai, Abhishek Dubey

In Partially Observable Markov Decision Processes (POMDPs), maintaining and updating belief distributions over possible underlying states provides a principled way to summarize action-observation history for effective decision-making under uncertainty. As environments grow more realistic, belief distributions develop complexity that standard mathematical models cannot accurately capture, creating a fundamental challenge in maintaining representational accuracy. Despite advances in deep learning and probabilistic modeling, existing POMDP belief approximation methods fail to accurately represent complex uncertainty structures such as high-dimensional, multi-modal belief distributions, resulting in estimation errors that lead to suboptimal agent behaviors. To address this challenge, we present ESCORT (Efficient Stein-variational and sliced Consistency-Optimized Representation for Temporal beliefs), a particle-based framework for capturing complex, multi-modal distributions in high-dimensional belief spaces. ESCORT extends SVGD with two key innovations: correlation-aware projections that model dependencies between state dimensions, and temporal consistency constraints that stabilize updates while preserving correlation structures. This approach retains SVGD's attractive-repulsive particle dynamics while enabling accurate modeling of intricate correlation patterns. Unlike particle filters prone to degeneracy or parametric methods with fixed representational capacity, ESCORT dynamically adapts to belief landscape complexity without resampling or restrictive distributional assumptions. We demonstrate ESCORT's effectiveness through extensive evaluations on both POMDP domains and synthetic multi-modal distributions of varying dimensionality, where it consistently outperforms state-of-the-art methods in terms of belief approximation accuracy and downstream decision quality.

Deep Learning · Generative Models and Autoencoders

Shigui Li, Wei Chen, Delu Zeng

Diffusion models (DMs) excel in image generation, but suffer from slow inference and the training-inference discrepancies. Although gradient-based solvers like DPM-Solver accelerate the denoising inference, they lack theoretical foundations in information transmission efficiency. In this work, we introduce an information-theoretic perspective on the inference processes of DMs, revealing that successful denoising fundamentally reduces conditional entropy in reverse transitions. This principle leads to our key insights into the inference processes: (1) data prediction parameterization outperforms its noise counterpart, and (2) optimizing conditional variance offers *a reference-free way* to minimize both transition and reconstruction errors. Based on these insights, we propose an entropy-aware variance optimized method for the generative process of DMs, called *EVODiff*, which systematically reduces uncertainty by optimizing conditional entropy during denoising. Extensive experiments on DMs validate our insights and demonstrate that our method significantly and consistently outperforms state-of-the-art (SOTA) gradient-based solvers. For example, compared to the DPM-Solver++, EVODiff reduces the reconstruction error by up to *45.5\%* (FID improves from 5.10 to 2.78) at 10 function evaluations (NFE) on CIFAR-10, cuts the NFE cost by *25\%* (from 20 to 15 NFE) for high-quality samples on ImageNet-256, and improves text-to-image generation while reducing artifacts. Code is available at https://github.com/ShiguiLi/EVODiff.

Computer Vision · Vision Models & Multimodal

zhentao he, Can Zhang, Ziheng Wu, Zhenghao Chen, Yufei Zhan, Yifan Li, Zhao Zhang, Xian Wang, Minghui Qiu

Recent advancements in multimodal large language models (MLLMs) have enhanced document understanding by integrating textual and visual information. However, existing models exhibit incompleteness within their paradigm in real-world scenarios, particularly under visual degradation (e.g., blur, occlusion, low contrast). In such conditions, the current response paradigm often fails to adequately perceive visual degradation and ambiguity, leading to overreliance on linguistic priors or misaligned visual-textual reasoning. This difficulty in recognizing uncertainty frequently results in the generation of hallucinatory content, especially when a precise answer is not feasible. To better demonstrate and analyze this phenomenon and problem, we propose KIE-HVQA, the first benchmark dedicated to evaluating OCR hallucination in degraded document understanding. This dataset includes test samples spanning identity cards, invoices, and prescriptions, with simulated real-world degradations and pixel-level annotations for OCR reliability. This setup allows for evaluating models' capacity, under degraded input, to distinguish reliable visual information and answer accordingly, thereby highlighting the challenge of avoiding hallucination on uncertain data. To achieve vision-faithful reasoning and thereby avoid the aforementioned issues, we further introduce a Group Relative Policy Optimization (GRPO)-based framework featuring a novel reward mechanism. By incorporating a self-awareness of visual uncertainty and an analysis method that initiates refusal to answer to increase task difficulty within our supervised fine-tuning and reinforcement learning framework, we successfully mitigated hallucinations in ambiguous regions. Experiments on Qwen2.5-VL demonstrate that our 7B-parameter model achieves a ~28% absolute improvement in hallucination-free accuracy over GPT-4o on KIE-HVQA and there is no significant performance drop in standard tasks, highlighting both effectiveness and robustness. This work advances the development of reliable MLLMs for real-world document analysis by addressing critical challenges in visual-linguistic alignment under degradation.

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

Yichen Yan, Ming Zhong, Qi Zhu, Xiaoling Gu, Jinpeng Chen, Huan Li

Multimodal large language models (MLLMs) rely heavily on instruction tuning to align vision and language capabilities, yet the computational cost of training on large-scale datasets remains a major bottleneck. Existing data selection methods aim to mitigate this by selecting important and diverse subsets, but they often suffer from two critical drawbacks: high computational overhead from processing the entire dataset and suboptimal data selection due to separate treatment of importance and diversity. We introduce CoIDO, a novel dual-objective framework that jointly optimizes data importance and diversity to overcome these challenges. Unlike existing approaches that require costly evaluations across the whole dataset, CoIDO employs a lightweight plug-in scorer. This scorer is trained on just a small random sample of data to learn the distribution of the candidate set, drastically reducing computational demands. By leveraging a homoscedastic uncertainty-based formulation, CoIDO effectively balances importance and diversity during training, enabling the scorer to assign CoIDO scores to all data points. This unified scoring approach allows for direct ranking and selection of the most valuable subsets, completely bypassing the need for specialized algorithms. In our experiments, we trained the CoIDO Scorer using only 20% of randomly sampled data. Once trained, CoIDO was applied to the entire dataset to select a 20% subset for instruction tuning. On the widely used LLaVA-1.5-7B model across ten downstream tasks, this selected subset achieved an impressive 98.2% of the performance of full-data fine-tuning, on average. Moreover, CoIDO outperforms all competitors in terms of both efficiency (lowest training FLOPs) and aggregated accuracy. Our code is available at: https://github.com/SuDIS-ZJU/CoIDO

Reinforcement Learning · Everything Else

Runqing Miao, Sheng Xu, Runyi Zhao, Wai Kin (Victor) Chan, Guiliang Liu

Recent advancements in diffusion policies have demonstrated promising performance in decision-making tasks. To align these policies with human preferences, a common approach is incorporating Preference-based Reinforcement Learning (PbRL) into policy tuning. However, since preference data is practically collected from populations with different backgrounds, a key challenge lies in handling the inherent uncertainties in people's preferences during policy updates. To address this challenge, we propose the Diff-UAPA algorithm, designed for uncertainty-aware preference alignment in diffusion policies. Specifically, Diff-UAPA introduces a novel iterative preference alignment framework in which the diffusion policy adapts incrementally to preferences from different user groups. To accommodate this online learning paradigm, Diff-UAPA employs a maximum posterior objective, which aligns the diffusion policy with regret-based preferences under the guidance of an informative Beta prior. This approach enables direct optimization of the diffusion policy without specifying any reward functions, while effectively mitigating the influence of inconsistent preferences across different user groups. We conduct extensive experiments across both simulated and real-world robotics tasks, and diverse human preference configurations, demonstrating the robustness and reliability of Diff-UAPA in achieving effective preference alignment. The project page is available at https://anonymous.4open.science/w/Diff-UAPA-5827.

Optimization · Optimization and Learning under Uncertainty

Yashas Annadani, Syrine Belakaria, Stefano Ermon, Stefan Bauer, Barbara Engelhardt

Offline multi-objective optimization aims to identify Pareto-optimal solutions given a dataset of designs and their objective values. In this work, we propose a preference-guided diffusion model that generates Pareto-optimal designs by leveraging a classifier-based guidance mechanism. Our guidance classifier is a preference model trained to predict the probability that one design dominates another, directing the diffusion model toward optimal regions of the design space. Crucially, this preference model generalizes beyond the training distribution, enabling the discovery of Pareto-optimal solutions outside the observed dataset. We introduce a novel diversity-aware preference guidance, augmenting Pareto dominance preference with diversity criteria. This ensures that generated solutions are optimal and well-distributed across the objective space, a capability absent in prior generative methods for offline multi-objective optimization. We evaluate our approach on various continuous offline multi-objective optimization tasks and find that it consistently outperforms other inverse/generative approaches while remaining competitive with forward/ surrogate-based optimization methods. Our results highlight the effectiveness of classifier-guided diffusion models in generating diverse and high-quality solutions that approximate the Pareto front well.

Optimization · Optimization and Learning under Uncertainty

XianJun, Davin Choo, Yuqi Pan, Tonghan Wang, Milind Tambe, Alastair van Heerden, Cheryl Johnson

We study a sequential decision-making problem on a $n$-node graph $\mathcal{G}$ where each node has an unknown label from a finite set $\mathbf{\Omega}$, drawn from a joint distribution $\mathcal{P}$ that is Markov with respect to $\mathcal{G}$. At each step, selecting a node reveals its label and yields a label-dependent reward. The goal is to adaptively choose nodes to maximize expected accumulated discounted rewards. We impose a frontier exploration constraint, where actions are limited to neighbors of previously selected nodes, reflecting practical constraints in settings such as contact tracing and robotic exploration. We design a Gittins index-based policy that applies to general graphs and is provably optimal when $\mathcal{G}$ is a forest. Our implementation runs in $\mathcal{O}(n^2 \cdot |\mathbf{\Omega}|^2)$ time while using $\mathcal{O}(n \cdot |\mathbf{\Omega}|^2)$ oracle calls to $\mathcal{P}$ and $\mathcal{O}(n^2 \cdot |\mathbf{\Omega}|)$ space. Experiments on synthetic and real-world graphs show that our method consistently outperforms natural baselines, including in non-tree, budget-limited, and undiscounted settings. For example, in HIV testing simulations on real-world sexual interaction networks, our policy detects nearly all positive cases with only half the population tested, substantially outperforming other baselines.

Optimization · Optimization and Learning under Uncertainty

Han Wang, Chao Ning

Conformal Prediction (CP) is a powerful statistical machine learning tool to construct uncertainty sets with coverage guarantees, which has fueled its extensive adoption in generating prediction regions for decision-making tasks, e.g., Trajectory Optimization (TO) in uncertain environments. However, existing methods predominantly employ a sequential scheme, where decisions rely unidirectionally on the prediction regions, and consequently the information from decision-making fails to be fed back to instruct CP. In this paper, we propose a novel Feedback-Based CP (Fb-CP) framework for shrinking-horizon TO with a joint risk constraint over the entire mission time. Specifically, a CP-based posterior risk calculation method is developed by fully leveraging the realized trajectories to adjust the posterior allowable risk, which is then allocated to future times to update prediction regions. In this way, the information in the realized trajectories is continuously fed back to the CP, enabling attractive feedback-based adjustments of the prediction regions and a provable online improvement in trajectory performance. Furthermore, we theoretically prove that such adjustments consistently maintain the coverage guarantees of the prediction regions, thereby ensuring provable safety. Additionally, we develop a decision-focused iterative risk allocation algorithm with theoretical convergence analysis for allocating the posterior allowable risk which closely aligns with Fb-CP. Furthermore, we extend the proposed method to handle distribution shift. The effectiveness and superiority of the proposed method are demonstrated through benchmark experiments.

Applications · Time Series

Yisong Fu, Zezhi Shao, Chengqing Yu, Yujie Li, Zhulin An, Qi Wang, Yongjun Xu, Fei Wang

Benefiting from high capacity for capturing complex temporal patterns, deep learning (DL) has significantly advanced time series forecasting (TSF). However, deep models tend to suffer from severe overfitting due to the inherent vulnerability of time series to noise and anomalies. The prevailing DL paradigm uniformly optimizes all timesteps through the MSE loss and learns those uncertain and anomalous timesteps without difference, ultimately resulting in overfitting. To address this, we propose a novel selective learning strategy for deep TSF. Specifically, selective learning screens a subset of the whole timesteps to calculate the MSE loss in optimization, guiding the model to focus on generalizable timesteps while disregarding non-generalizable ones. Our framework introduces a dual-mask mechanism to target timesteps: (1) an uncertainty mask leveraging residual entropy to filter uncertain timesteps, and (2) an anomaly mask employing residual lower bound estimation to exclude anomalous timesteps. Extensive experiments across eight real-world datasets demonstrate that selective learning can significantly improve the predictive performance for typical state-of-the-art deep models, including 37.4% MSE reduction for Informer, 8.4% for TimesNet, and 6.5% for iTransformer.

Theory · Reinforcement Learning and Planning

Eline M. Bovy, Caleb Probine, Marnix Suilen, Ufuk Topcu, Nils Jansen

Multi-environment POMDPs (ME-POMDPs) extend standard POMDPs with discrete model uncertainty. ME-POMDPs represent a finite set of POMDPs that share the same state, action, and observation spaces, but may arbitrarily vary in their transition, observation, and reward models. Such models arise, for instance, when multiple domain experts disagree on how to model a problem. The goal is to find a single policy that is robust against any choice of POMDP within the set, *i.e.*, a policy that maximizes the worst-case reward across all POMDPs. We generalize and expand on existing work in the following way. First, we show that ME-POMDPs can be generalized to POMDPs *with sets of initial beliefs*, which we call *adversarial-belief POMDPs* (AB-POMDPs). Second, we show that any arbitrary ME-POMDP can be reduced to a ME-POMDP that only varies in its transition and reward functions or only in its observation and reward functions, while preserving (optimal) policies. We then devise exact and approximate (point-based) algorithms to compute robust policies for AB-POMDPs, and thus ME-POMDPs. We demonstrate that we can compute policies for standard POMDP benchmarks extended to the multi-environment setting.

Theory · Domain Adaptation and Transfer Learning

Yixuan Zhang, Ruihao Zhu, Qiaomin Xie

We study contextual online pricing with biased offline data. For the scalar price elasticity case, we identify the instance-dependent quantity $\delta^2$ that measures how far the offline data lies from the (unknown) online optimum. We show that the time length $T$, bias bound $V$, size $N$ and dispersion $\lambda_{\min}(\hat{\Sigma})$ of the offline data, and $\delta^2$ jointly determine the statistical complexity. An Optimism‑in‑the‑Face‑of‑Uncertainty (OFU) policy achieves a minimax-optimal, instance-dependent regret bound $\tilde{\mathcal{O}}\big(d\sqrt{T} \wedge (V^2T + \frac{dT }{\lambda_{\min}(\hat{\Sigma}) + (N \wedge T) \delta^2})\big)$. For general price elasticity, we establish a worst‑case, minimax-optimal rate $\tilde{\mathcal{O}}\big(d\sqrt{T} \wedge (V^2T + \frac{dT }{\lambda_{\min}(\hat{\Sigma})})\big)$ and provide a generalized OFU algorithm that attains it. When the bias bound $V$ is unknown, we design a robust variant that always guarantees sub‑linear regret and strictly improves on purely online methods whenever the exact bias is small. These results deliver the first tight regret guarantees for contextual pricing in the presence of biased offline data. Our techniques also transfer verbatim to stochastic linear bandits with biased offline data, yielding analogous bounds.

Optimization · Optimization and Learning under Uncertainty

Ziyad Benomar, Romain Cosson, Alexander Lindermayr, Jens Schlöter

In non-clairvoyant scheduling, the goal is to minimize the total job completion time without prior knowledge of individual job processing times. This classical online optimization problem has recently gained attention through the framework of learning-augmented algorithms. We introduce a natural setting in which the scheduler receives continuous feedback in the form of progress bars—estimates of the fraction of each job completed over time. We design new algorithms for both adversarial and stochastic progress bars and prove strong competitive bounds. Our results in the adversarial case surprisingly induce improved guarantees for learning-augmented scheduling with job size predictions. We also introduce a general method for combining scheduling algorithms, yielding further insights in scheduling with predictions. Finally, we propose a stochastic model of progress bars as a more optimistic alternative to conventional worst-case models, and present an asymptotically optimal scheduling algorithm in this setting.