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Applications · Computer Vision

Rongjin Guo, Guan Huankang, Rynson Lau

Salient Object Ranking (SOR) aims to study how humans visually explore complex scenes by predicting an ordered sequence of objects that attracts our attention. Existing SOR approaches typically model this ranking deterministically, assuming a single, fixed ranking sequence of attention. However, such deterministic SOR fails to capture the true nature of human attention. We observe that human attention shifts exhibit variability and stochasticity, showing that the next object of fixation is not a definitive choice but rather a probability distribution. Yet, existing SOR methods and evaluation metrics do not account for this inherent randomness. To address this fundamental problem, we propose ProbSOR, a novel Probabilistic Salient Object Ranking model that explicitly learns the uncertainty of attention shifts by incorporating Group Relative Policy Optimization (GRPO). We leverage a Vision-Language Model (VLM) as the foundation for ProbSOR to identify salient objects and infer their ranked order, utilizing a segmentation decoder for precise object extraction. We also propose a new metric tailored to ProbSOR, as existing SOR metrics only support deterministic rankings. Further, we construct a ProbSOR dataset comprising 15,000 probabilistic SOR samples, to support both model training and evaluation. Extensive experiments demonstrate that ProbSOR achieves strong performances in salient object ranking under both our proposed and traditional benchmarks.

Theory · Online Learning and Bandits

Anna Lunghi, Gianmarco Genalti, Alberto Marchesi, Matteo Castiglioni

We study the Awakening Crowd of Experts (ACE) problem, an online learning problem where the set of experts available to the learner grows at each round. ACE is a special case of the well-known sleeping experts problem (Kleinberg et al., 2010), where the number of experts is huge $(K=T)$. Existing results on sleeping experts preclude any learner from achieving a sublinear regret when the number of available experts is linear in $T$. Inspired by real-world applications, such as Q\&A platforms and social proof marketing, we thus focus on the awakening version of the sleeping experts problem, where a new expert arrives at every round and never leaves. We show that in the stochastic version of ACE, it is possible to obtain regret $\tilde{\mathcal{O}}(T^{2/3})$ using an unusual pessimism in the face of the uncertainty principle. Moreover, we characterize the dependence of the regret on the stability of an optimal strategy. For both results, we present matching lower bounds. Surprisingly, the adversarial version of ACE is sensibly harder. In particular, we provide a lower bound precluding sublinear $\alpha$-regret when the competitive ratio is constant. We provide an algorithm to face this crucial trade-off between competitive ratio and regret, and bound its $\alpha$-regret, almost matching the aforementioned lower bound. As a corollary, we get a $\tilde{\mathcal{O}}(\log(\log(T))$ competitive ratio when an optimal strategy enjoys a reward linear in $T$.

General Machine Learning · Causality

Jiacan Gao, Xinyan Su, Mingyuan Ma, Yiyan HUANG, Xiao Xu, Xinrui Wan, Tianqi Gu, Enyun Yu, Jiecheng Guo, Zhiheng Zhang

Estimating heterogeneous treatment effects is central to data-driven decision-making, yet industrial applications often face a fundamental tension between limited randomized controlled trial (RCT) budgets and abundant but biased observational data collected under historical targeting policies. Although observational logs offer the advantage of scale, they inherently suffer from severe policy-induced imbalance and overlap violations, rendering standalone estimation unreliable. We propose a budgeted active experimentation framework that iteratively enhances model training for causal effect estimation via active sampling. By leveraging observational priors, we develop an acquisition function targeting uplift estimation uncertainty, overlap deficits, and domain discrepancy to select the most informative units for randomized experiments. We establish finite-sample deviation bounds, asymptotic normality via martingale Central Limit Theorems (CLTs), and minimax lower bounds to prove information-theoretic optimality. Extensive experiments on industrial datasets demonstrate that our approach significantly outperforms standard randomized baselines in cost-constrained settings.

Deep Learning · Large Language Models

Zhi Hong, Qian Zhang, Jiahang Sun, Zhiwei Shang, Mingze Kong, Xiangyi Wang, Yao Shu, Zhongxiang Dai

Large Language Models (LLMs) have achieved significant success across a wide range of tasks, serving as the cognitive backbone for Multi-Agent Systems (MAS) designed to orchestrate complex practical workflows. Given that MAS performance is highly sensitive to input prompts and many deployment scenarios preclude MAS architecture modifications, prompt optimization emerges as a critical strategy for performance enhancement. However, real-world deployment is impeded by three key challenges: (1) the need for high sample efficiency due to prohibitive evaluation costs, (2) topology-induced coupling among prompts, and (3) the combinatorial explosion of the search space. To address these challenges, we introduce **MASPOB** (**M**ulti-**A**gent **S**ystem **P**rompt **O**ptimization via **B**andits), a novel sample-efficient framework based on bandits. By leveraging Upper Confidence Bound (UCB) to quantify uncertainty, the bandit framework balances exploration and exploitation, maximizing gains within a strictly limited budget. To handle topology-induced coupling, MASPOB integrates Graph Neural Networks (GNNs) to capture structural priors, learning topology-aware representations of prompt semantics. Furthermore, it employs coordinate ascent to decompose the optimization into univariate sub-problems, reducing search complexity from exponential to linear. Extensive experiments across diverse benchmarks demonstrate that MASPOB achieves state-of-the-art performance, consistently outperforming existing baselines.

General Machine Learning · Causality

Connor T Jerzak, Priyanshi Chandra, Rishi Hazra

We study offline learning of factored stochastic policies over extremely large, combinatorial action spaces and show how standard conjoint data can be used to estimate such policies with asymptotically valid uncertainty under conditions. Conjoint analyses typically report AMCEs by averaging over opponent attributes and thus ignore strategic interdependence. We instead learn \emph{stochastic interventions}---product-of-Categorical policies over factor levels—that (i) optimize expected outcomes in an average-case setting and (ii) extend to a two-player \emph{minimax} (adversarial) setting that realistically captures simultaneous strategic candidate selection. Methodologically, we derive a closed-form solution for the average-case optimizer under two-way interactions with $L_2$ variance regularization, and provide a general gradient-based procedure for richer model classes. Uncertainty from the outcome model propagates asymptotically to both the optimal policy and its value via a Delta method approximation. We further model institutional details (e.g., primaries) inside the minimax objective and introduce a data-driven measure of strategic divergence between parties. On synthetic data, we empirically characterize finite-sample error and coverage as dimensionality and $n$ vary. On a U.S. presidential conjoint, adversarially learned policies produce restricted-equilibrium vote shares that align with historical election ranges in our data, in stark contrast to non-adversarial (averaging) optimizers.

Jinghan Li, Junfeng Fang, Jinda Lu, Yuan Wang, Xiaoyan Guo, Tianyu Zhang, Xiang Wang, Xiangnan He

Reinforcement Learning with Verifiable Rewards (RLVR) and Group Relative Policy Optimization (GRPO) have significantly advanced the reasoning capabilities of large language models. Extending these methods to multimodal settings, however, faces a critical challenge: the instability of std-based normalization, which is easily distorted by extreme samples with nearly positive or negative rewards. Unlike pure-text LLMs, multimodal models are particularly sensitive to such distortions, as both perceptual and reasoning errors influence their responses. To address this, we characterize each sample by its difficulty, defined through perceptual complexity (measured via visual entropy) and reasoning uncertainty (captured by model confidence). Building on this characterization, we propose difficulty-aware group normalization (Durian), which re-groups samples by difficulty levels and shares the std within each group. Our approach preserves GRPO's intra-group distinctions while eliminating sensitivity to extreme cases, yielding significant performance gains across multiple multimodal reasoning benchmarks.

Deep Learning · Large Language Models

Haixin Wang, Hejie Cui, Chenwei Zhang, Jiahui Gao, Shuowei Jin, Shijie Geng, Xinyang Zhang, Nasser Zalmout, Zhenyu Shi, Yizhou Sun

Recent progress in multi-turn reinforcement learning (RL) has significantly improved reasoning LLMs' performances on complex interactive tasks. Despite advances in stabilization techniques such as fine-grained credit assignment and trajectory filtering, instability remains pervasive and often leads to training collapse. We argue that this instability stems from inefficient exploration in multi-turn settings, where policies continue to generate low-information actions that neither reduce uncertainty nor advance task progress. To address this issue, we propose Token- and Turn-level Policy Optimization (T$^2$PO), an uncertainty-aware framework that explicitly controls exploration at fine-grained levels. At the token level, T$^2$PO monitors uncertainty dynamics and triggers a thinking intervention once the marginal uncertainty change falls below a threshold. At the turn level, T$^2$PO identifies interactions with negligible exploration progress and dynamically resamples such turns to avoid wasted rollouts. We evaluate T$^2$PO in diverse environments, including WebShop, ALFWorld, and Search QA, demonstrating substantial gains in training stability and performance improvements with better exploration efficiency. Code is available at https://anonymous.4open.science/r/T2PO-ICML-3C21.

Optimization · Optimization and Learning under Uncertainty

Jiaqi Wen, Jianyi Yang

This paper studies Distributionally Robust Optimization (DRO), a fundamental framework for enhancing the robustness and generalization of statistical learning and optimization. An effective ambiguity set for DRO must involve distributions that remain consistent to the nominal distribution while being diverse enough to account for a variety of potential scenarios. Moreover, it should lead to tractable DRO solutions. To this end, we propose generative model-based ambiguity sets that capture various adversarial distributions beyond the nominal support space while maintaining consistency with the nominal distribution. Building on this generative ambiguity modeling, we propose DRO with Generative Ambiguity Set (GAS-DRO), a tractable DRO algorithm that solves the inner maximization over the parameterized generative model space. We formally establish the stationary convergence performance of GAS-DRO. We implement GAS-DRO with a diffusion model and empirically demonstrate its superior Out-of-Distribution (OOD) generalization performance in ML tasks.

Reinforcement Learning · Deep RL

Ruike Cao, Shaojie Bai, Fugen Yao, Liang Dong, Jian Xu, Li Xiao

Effective information seeking in multi-turn medical dialogues is critical for accurate diagnosis, especially when dealing with incomplete information. Aligning Large Language Models (LLMs) for these interactive scenarios is challenging due to the uncertainty inherent in user-agent interactions, which we formulate as a Hierarchical Markov Decision Process (H-MDP). While conventional Reinforcement Learning (RL) methods like Group Relative Policy Optimization (GRPO) struggle with long-horizon credit assignment and Proximal Policy Optimization (PPO) suffers from unstable value estimation in this context, we propose a novel uncertainty-aware Adaptive Tree Policy Optimization (ATPO) algorithm. Our method adaptively allocates the rollout budget to states with high uncertainty, quantified by a composite metric of Bellman error and action-value variance. This strategy enables more accurate value estimation, while fostering more efficient and diverse exploration. To mitigate the high computational cost of tree-based RL, we introduce two key optimizations: an uncertainty-guided pruning mechanism to minimize the number of rollouts, and an asynchronous search architecture that leverages KV cache reuse to maximize inference throughput. Extensive experiments on three public medical dialogue benchmarks demonstrate that our algorithm significantly outperforms several strong baselines, culminating in Qwen3-8B model surpassing the much larger GPT-4o (+0.92% accuracy).

Computer Vision · Classification and Understanding

Sen Tao, Kaiduo Feng, Jiawei Liu, Peng Zeng, Yongchao Xu, Yufei Zheng, Zheng-Jun Zha

Active Prompt Learning (APL) using vision-language models (\textit{e.g.}, CLIP) has attracted considerable attention for mitigating the dependence on fully labeled dataset in downstream task adaptation. However, existing methods fail to explicitly leverage prompt to guide sample selection, resulting in the selected samples being ineffective in facilitating the prompt template's downstream task adaptation, while also overlooking valuable complementary information in the unselected samples. To fill this gap, we propose a novel Prompt-Guided Self-Training Sampling Policy (PSP) for APL, which integrates Soft Actor-Critic with a customized real-pseudo hybrid reward and vectorized critics to incorporate prompts in guiding sample selection toward those that facilitate the optimization of prompt template, by jointly considering both selected and unselected samples. Specifically, PSP comprises two prominent components: Vectorized Soft Actor-Critic Sampling Policy (VSSP) and Uncertainty Augmented Self-Training (UST) mechanism. VSSP customizes a real-pseudo hybrid reward based on learned prompts and image features, which is fed into vectorized critics to estimate Q-value for each sample and compute gradients that optimize the actor, allowing it to refine its sampling policy in an End-to-End manner to identify the most informative samples for prompt learning. Moreover, UST leverages the CLIP from the previous round to generate reliable pseudo-labeled data based on uncertainty and confidence of average predictions, thereby deepening the understanding of the overall data. Extensive experiments conducted on diverse real-world datasets validate the effectiveness of our PSP.

Deep Learning · Generative Models and Autoencoders

Mehul Damani, Isha Puri, Stewart Slocum, Idan Shenfeld, Leshem Choshen, Yoon Kim, Jacob Andreas

When language models (LMs) are trained via reinforcement learning (RL) to generate natural language “reasoning chains”, their performance improves on a variety of difficult question answering tasks. Today, almost all successful applications of RL for reasoning use binary reward functions that evaluate the correctness of LM outputs. Because such reward functions do not penalize guessing or low-confidence outputs, they often have the unintended side-effect of degrading calibration and increasing the rate at which LMs generate incorrect responses (or “hallucinate”) in other problem domains. This paper describes RLCR (Reinforcement Learning with Calibration Rewards), an approach to training reasoning models that jointly improves accuracy and calibrated confidence estimation. During RLCR, LMs generate both predictions and numerical confidence estimates after reasoning. They are trained to optimize a reward function that augments a binary correctness score with a Brier score—a scoring rule for confidence estimates that incentivizes calibrated prediction. We first prove that this reward function (or any analogous reward function that uses a bounded, proper scoring rule) yields models whose predictions are both accurate and well-calibrated. We next show that across diverse datasets, RLCR substantially improves calibration with no loss in accuracy, on both in-domain and out-of-domain evaluations—outperforming both ordinary RL training and classifiers trained to assign post-hoc confidence scores. While ordinary RL hurts calibration, RLCR improves it. Finally, we demonstrate that verbalized confidence can be leveraged at test time to improve accuracy and calibration via confidence-weighted scaling methods. Our results show that explicitly optimizing for calibration can produce more generally reliable reasoning models.

Optimization · Optimization and Learning under Uncertainty

Rafael Oliveira, Dan Steinberg, Edwin Bonilla

We present a general strategy for turning generative models into candidate solution samplers for batch Bayesian optimization (BO). The use of generative models for BO enables large batch scaling as generative sampling, optimization of non-continuous design spaces, and high-dimensional and combinatorial design. Inspired by the success of direct preference optimization (DPO), we show that one can train a generative model with noisy, simple utility values directly computed from observations to then form proposal distributions whose densities are proportional to the expected utility, i.e., BO's acquisition function values. Furthermore, this approach is generalizable beyond preference-based feedback to general types of reward signals and loss functions. This perspective avoids the construction of surrogate (regression or classification) models, common in previous methods that have used generative models for black-box optimization. Theoretically, we show that the generative models within the BO process follow a sequence of distributions which asymptotically approximate an optimal target under certain conditions. We also evaluate the performance through experiments on challenging optimization problems involving large batches in high dimensions.

Applications · Health

Yulong Li, Xiwei Liu, Barrett Tang, Zhixiang Lu, Ming Hu, Yichen Li, Haochen Xue, Peixin Guo, Jionglong Su, Yutong Xie 等

Cross-modal representation learning is fundamental for extracting structured information from multimodal data to enable semantic understanding and reasoning. However, current methods optimize statistical objectives without explicit causal constraints, where nonlinear mappings can introduce spurious dependencies or eliminate critical mediators, leading to representation-induced structural drift that undermines the reliability of causal inference. Therefore, establishing theoretical guarantees for causal invariance in cross-modal representation learning remains a foundational challenge. To this end, we propose Causal Alignment and Representation Learning (CARL), which explicitly embeds causal structure preservation constraints into cross-modal alignment objectives. Specifically, CARL introduces a multi-consistency loss architecture that jointly optimizes conditional independence preservation and information bottleneck regularization to balance cross-modal compression with critical variable retention, ensuring low-density modalities are not masked by high-density reconstruction demands. We further incorporate monotonic alignment consistency loss to establish correspondence between semantic similarity and representation distance through Spearman correlation, and Markov boundary preservation loss to maintain identifiability conditions including backdoor, frontdoor, and instrumental variable criteria in the shared representation space. In synthetic experiments with known causal ground truth, CARL achieves state-of-the-art performance in preserving conditional independence patterns and maintaining causal query identifiability under structural uncertainty. Real-world validation on Human Phenotype Project data reveals that CARL successfully preserves causal structures between fundus vascular representations and cardiovascular events, demonstrating its capacity for reliable cross-modal causal inference in complex biomedical applications.

Reinforcement Learning · Batch/Offline

Haoxin Lin, Siyuan Xiao, Yi-Chen Li, Zhilong Zhang, Yihao Sun, Chengxing Jia, Yang Yu

Model-based methods for offline Reinforcement Learning transfer extensive policy exploration and evaluation to data-driven dynamics models, effectively saving real-world samples in the offline setting. We expect the dynamics model to allow the policy to roll out full-horizon episodes, which is crucial for ensuring sufficient exploration and reliable evaluation. However, many previous dynamics models exhibit limited capability in long-horizon prediction. This work follows the paradigm of the Any-step Dynamics Model (ADM) that improves future predictions by reducing bootstrapping prediction to direct prediction. We structurally decouple each recurrent forward of the RNN cell from the backtracked state and propose the second version of ADM (ADM-v2), making the direct prediction more flexible. ADM-v2 not only enhances the accuracy of direct predictions for making full-horizon roll-outs but also supports parallel estimation of the any-step prediction uncertainty to improve efficiency. The results on DOPE validate the reliability of ADM-v2 for policy evaluation. Moreover, via full-horizon roll-out, ADM-v2 for policy optimization enables substantial advancements, whereas other dynamics models degrade due to long-horizon error accumulation. We are the first to achieve SOTA under the full-horizon roll-out setting on both D4RL and NeoRL. The code is available at https://github.com/LAMDA-RL/adm2.

General Machine Learning · Everything Else

Maolin WANG, Zhiqi Li, Binhao Wang, Xuhui Chen, Tianshuo Wei, Wanyu Wang, Shikai Fang, Ruocheng Guo, Zenglin Xu, Xiangyu Zhao

Analyzing dynamic tensor streams is fundamentally challenged by complex, evolving temporal dynamics and the need to identify informative data from high-velocity streams. Existing methods often lack the expressiveness to model multi-scale temporal dependencies, limiting their ability to capture evolving patterns. We propose SONATA, a novel framework that unifies expressive dynamic embedding modeling with adaptive coreset selection. SONATA leverages principled machine learning techniques for efficient evaluation of each observation for uncertainty, novelty, influence, and information gain, and dynamically prioritizes learning from the most valuable data using Bellman-inspired optimization. Entity dynamics are modeled with Linear Dynamical Systems and expressive temporal kernels for fine-grained temporal representation. Experiments on synthetic and real-world datasets show that SONATA consistently outperforms state-of-the-art methods in modeling complex temporal patterns and improving predictive accuracy for dynamic tensor streams.

Reinforcement Learning · Deep RL

Guanting Dong, Hangyu Mao, Kai Ma, Licheng Bao, Yifei Chen, Zhongyuan Wang, Zhongxia Chen, Jiazhen Du, Huiyang Wang, Fuzheng Zhang 等

Large-scale reinforcement learning with verifiable rewards (RLVR) has proven effective in harnessing the potential of large language models (LLMs) for single-turn reasoning tasks. In realistic reasoning scenarios, LLMs often rely on external tools to assist in task-solving processes. However, current RL algorithms typically employ trajectory-level rollout sampling, consistently neglecting the fine-grained exploration of multi-turn tool-call steps. To bridge this gap, we propose Agentic Reinforced Policy Optimization (ARPO), a novel agentic RL algorithm tailored for training multi-turn LLM-based agents. Our preliminary experiments reveal that LLMs frequently exhibit increased uncertainty after tool-call steps, as evidenced by higher entropy in the distribution of generated tokens. Motivated by this, ARPO incorporates an entropy-based adaptive rollout mechanism, encouraging the policy model to adaptively branch sampling during high-entropy tool-call rounds, thereby promoting step-level exploration of latent tool-use behaviors. By integrating an advantage attribution estimation, ARPO enables LLMs to internalize advantage differences in stepwise tool-use interactions. Experiments across 13 challenging benchmarks demonstrate ARPO's superiority over trajectory-level RL algorithms. Remarkably, ARPO achieves improved performance using only half of the tool-use budget required by existing methods, offering a scalable solution for aligning LLM-based agents with real-time dynamic environments. Our codes are released at https://github.com/RUC-NLPIR/ARPO.

Deep Learning · Robustness

Xin Yang, Letian Li, Abudukelimu Wuerkaixi, Xuxin Cheng, Cao Liu, Ke Zeng, Xunliang Cai, Wenyuan Jiang

Large language models (LLMs) have demonstrated remarkable and steadily improving performance across a wide range of tasks. However, LLM performance may be highly sensitive to prompt variations especially in scenarios with limited openness or strict output formatting requirements, indicating insufficient robustness. In real-world applications, user prompts provided to LLMs often contain imperfections, which may undermine the quality of the model's responses. To address this issue, previous work has primarily focused on preprocessing prompts, employing external tools or even LLMs to refine prompt formulations in advance. However, these approaches overlook the intrinsic robustness of LLMs, and their reliance on external components introduces additional computational overhead and uncertainty. In this work, we propose a Contrastive Learning-based Inverse Direct Preference Optimization (CoIPO) method that minimizes the discrepancy between the label-aligned logits produced by the model under a clean prompt and its noisy counterpart, and conduct a detailed analysis using mutual information theory. We augment the FLAN dataset by constructing paired prompts, each consisting of a clean prompt and its corresponding noisy version for training. Additionally, to evaluate the effectiveness, we develop NoisyPromptBench, a benchmark enhanced and derived from the existing PromptBench. Experimental results conducted on NoisyPromptBench demonstrate that our proposed method achieves a significant improvement in average accuracy over the current state-of-the-art approaches. The source code of CoIPO, pair-wise FLAN datasets, and NoisyPromptBench have already been released on https://github.com/vegetable-yx/CoIPO.

General Machine Learning · Causality

Vy Vo, Haoxuan Li, Mingming Gong

Causal discovery is a critical yet persistently challenging task across scientific domains. Despite years of significant algorithmic advances, existing methods still struggle with inconsistent outcomes due to reliance on untestable assumptions, sensitivity to data perturbations, and optimization constraints. To this end, ensemble-based causal discovery has been actively pursued, aiming to aggregate multiple structural predictions for increased stability and uncertainty estimation. However, current aggregation methods are largely heuristic, lacking theoretical guarantees and guidance on how ensemble design choices affect performance. This work is proposed to address there fundamental limitations. We introduce a principled voting-based framework for structural ensembling, establishing conditions under which the aggregated structure recovers the true causal graph. Our analysis yields a theoretically justified weighted voting mechanism that informs optimal choices regarding the number, competency, and diversity of causal discovery experts in the ensemble. Extensive experiments on synthetic and real-world datasets verify the robustness and effectiveness of our approach, offering a rigorous alternative to existing heuristic ensemble methods.

Optimization · Optimization and Learning under Uncertainty

Yunzhen Yao, Lie He, Michael Gastpar

Conformal prediction provides prediction sets with coverage guarantees. The informativeness of conformal prediction depends on its efficiency, typically quantified by the expected size of the prediction set. Prior work on the efficiency of conformalized regression commonly treats the miscoverage level $\alpha$ as a fixed constant. In this work, we establish non-asymptotic bounds on the deviation of the prediction set length from the oracle interval length for conformalized quantile and median regression trained via SGD, under mild assumptions on the data distribution. Our bounds of order $\mathcal{O}(1/\sqrt{n} + 1/(\alpha^2 n) + 1/\sqrt{m} + \exp(-\alpha^2 m))$ capture the joint dependence of efficiency on the proper training set size $n$, the calibration set size $m$, and the miscoverage level $\alpha$. The results identify phase transitions in convergence rates across different regimes of $\alpha$, offering guidance for allocating data to control excess prediction set length. Empirical results are consistent with our theoretical findings.

Optimization · Optimization and Learning under Uncertainty

Tianming Zhao, Albert Zomaya

Algorithms with predictions leverage predictions for unknown inputs in online decision-making. These algorithms are analyzed by consistency, i.e., competitive ratio under perfect predictions, and robustness, i.e., competitive ratio under worst-case predictions. Smooth degrading performance with an increased prediction error is also desirable. This paper refines the notion of smoothness, a function of prediction error, defined as the competitive ratio over the problem instances where predictions are guaranteed to provide additional information. With our refined smoothness metric, we establish smoothness bounds for a few scheduling problems, including online total completion time minimization and makespan minimization. For a single machine to minimize the total completion time, we show a lower bound of $\eta$ and a $\eta^2$-smooth algorithm, where $\eta$ is the prediction error ($\eta \geq 1$); the bound holds for small errors. For parallel identical machines to minimize the makespan, we show a lower bound of $2 - O(\eta^{-2})$ and present an $O(\eta^2)$-smooth algorithm for small errors. Both bounds are tighter than the existing ones. For uniformly-related machines to minimize the makespan, we show a tight lower bound of $\lceil \log \eta \rceil$, matched by an $O(\log \eta)$-smooth algorithm.