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Applications · Robotics

Heeju Ko, Sung June Kim, Gyeongrok Oh, Jeongyoon YOON, Honglak Lee, Sujin Jang, Seungryong Kim, Sangpil Kim

Vision-Language Navigation (VLN) policies trained on offline datasets often exhibit degraded task performance when deployed in unfamiliar navigation environments at test time, where agents are typically evaluated without access to external interaction or feedback. Entropy minimization has emerged as a practical solution for reducing prediction uncertainty at test time; however, it can suffer from accumulated errors, as agents may become overconfident in incorrect actions without sufficient contextual grounding. To tackle these challenges, we introduce ATENA (Active TEst-time Navigation Agent), a test-time active learning framework that enables a practical human-robot interaction via episodic feedback on uncertain navigation outcomes. In particular, ATENA learns to increase certainty in successful episodes and decrease it in failed ones, improving uncertainty calibration. Here, we propose mixture entropy optimization, where entropy is obtained from a combination of the action and pseudo-expert distributions—a hypothetical action distribution assuming the agent's selected action to be optimal—controlling both prediction confidence and action preference. In addition, we propose a self-active learning strategy that enables an agent to evaluate its navigation outcomes based on confident predictions. As a result, the agent stays actively engaged throughout all iterations, leading to well-grounded and adaptive decision-making. Extensive evaluations on challenging VLN benchmarks—REVERIE, R2R, and R2R-CE—demonstrate that ATENA successfully overcomes distributional shifts at test time, outperforming the compared baseline methods across various settings.

John Vastola, Samuel J Gershman, Kanaka Rajan

Learning rules—prescriptions for updating model parameters to improve performance—are typically assumed rather than derived. Why do some learning rules work better than others, and under what assumptions can a given rule be considered optimal? We propose a theoretical framework that casts learning rules as policies for navigating (partially observable) loss landscapes, and identifies optimal rules as solutions to an associated optimal control problem. A range of well-known rules emerge naturally within this framework under different assumptions: gradient descent from short-horizon optimization, momentum from longer-horizon planning, natural gradients from accounting for parameter space geometry, non-gradient rules from partial controllability, and adaptive optimizers like Adam from online Bayesian inference of loss landscape shape. We further show that continual learning strategies like weight resetting can be understood as optimal responses to task uncertainty. By unifying these phenomena under a single objective, our framework clarifies the computational structure of learning and offers a principled foundation for designing adaptive algorithms.

Reinforcement Learning · Batch Offline

Tianpai Luo, Xinyuan Fan, Weichi Wu

This work presents the first theoretically justified simultaneous inference framework for off-policy evaluation (OPE). In contrast to existing methods that focus on point estimates or pointwise confidence intervals (CIs), the new framework quantifies global uncertainty across an infinite or continuous initial state space, offering valid inference over the entire state space. Our method leverages sieve-based Q-function estimation and (high-dimensional) Gaussian approximation techniques over convex regions, which further motivates a new multiplier bootstrap algorithm for constructing asymptotically correct simultaneous confidence regions (SCRs). The widths of the SCRs exceed those of the pointwise CIs by only a logarithmic factor, indicating that our procedure is nearly optimal in terms of efficiency. The effectiveness of the proposed approach is demonstrated through simulations and analysis of the OhioT1DM dataset.

Optimization · Optimization and Learning under Uncertainty

Weidong Liu, Jiyuan Tu, Xi Chen, Yichen Zhang

Reinforcement learning has emerged as one of the prominent topics attracting attention in modern statistical learning, with policy evaluation being a key component. Unlike the traditional machine learning literature on this topic, our work emphasizes statistical inference for the model parameters and value functions of reinforcement learning algorithms. While most existing analyses assume random rewards to follow standard distributions, we embrace the concept of robust statistics in reinforcement learning by simultaneously addressing issues of outlier contamination and heavy-tailed rewards within a unified framework. In this paper, we develop a fully online robust policy evaluation procedure, and establish the Bahadur-type representation of our estimator. Furthermore, we develop an online procedure to efficiently conduct statistical inference based on the asymptotic distribution. This paper connects robust statistics and statistical inference in reinforcement learning, offering a more versatile and reliable approach to online policy evaluation. Finally, we validate the efficacy of our algorithm through numerical experiments conducted in simulations and real-world reinforcement learning experiments.

Reinforcement Learning · Deep RL

Ke Sun, Yingnan Zhao, Enze Shi, Yafei Wang, Xiaodong Yan, Bei Jiang, Linglong Kong

The remarkable empirical performance of distributional reinforcement learning~(RL) has garnered increasing attention to understanding its theoretical advantages over classical RL. By decomposing the categorical distributional loss commonly employed in distributional RL, we find that the potential superiority of distributional RL can be attributed to a derived distribution-matching entropy regularization. This less-studied entropy regularization aims to capture additional knowledge of return distribution beyond only its expectation, contributing to an augmented reward signal in policy optimization. In contrast to the vanilla entropy regularization in MaxEnt RL, which explicitly encourages exploration by promoting diverse actions, the novel entropy regularization derived from categorical distributional loss implicitly updates policies to align the learned policy with (estimated) environmental uncertainty. Finally, extensive experiments verify the significance of this uncertainty-aware regularization from distributional RL on the empirical benefits over classical RL. Our study offers an innovative exploration perspective to explain the intrinsic benefits of distributional learning in RL.

Optimization · Optimization and Learning under Uncertainty

Avrajit Ghosh, Bai Cong, Rio Yokota, Saiprasad Ravishankar, Rongrong Wang, Molei Tao, Mohammad Emtiyaz Khan, Thomas Möllenhoff

Variational Learning (VL) has recently gained popularity for training deep neural networks. Part of its empirical success can be explained by theories such as PAC-Bayes bounds, minimum description length and marginal likelihood, but little has been done to unravel the implicit regularization in play. Here, we analyze the implicit regularization of VL through the Edge of Stability (EoS) framework. EoS has previously been used to show that gradient descent can find flat solutions and we extend this result to show that VL can find even flatter solutions. This result is obtained by controlling the shape of the variational posterior as well as the number of posterior samples used during training. The derivation follows in a similar fashion as in the standard EoS literature for deep learning, by first deriving a result for a quadratic problem and then extending it to deep neural networks. We empirically validate these findings on a wide variety of large networks, such as ResNet and ViT, to find that the theoretical results closely match the empirical ones. Ours is the first work to analyze the EoS dynamics of~VL.

Theory · Reinforcement Learning and Planning

Bhavya, Lenart Treven, Carmelo Sferrazza, Florian Dorfler, Pieter Abbeel, Andreas Krause

We address the challenge of efficient exploration in model-based reinforcement learning (MBRL), where the system dynamics are unknown and the RL agent must learn directly from online interactions. We propose **S**calable and **O**ptimistic **MBRL** (SOMBRL), an approach based on the principle of optimism in the face of uncertainty. SOMBRL learns an uncertainty-aware dynamics model and *greedily* maximizes a weighted sum of the extrinsic reward and the agent's epistemic uncertainty. SOMBRL is compatible with any policy optimizers or planners, and under common regularity assumptions on the system, we show that SOMBRL has sublinear regret for nonlinear dynamics in the (*i*) finite-horizon, (*ii*) discounted infinite-horizon, and (*iii*) non-episodic setting. Additionally, SOMBRL offers a flexible and scalable solution for principled exploration. We evaluate SOMBRL on state-based and visual-control environments, where it displays strong performance across all tasks and baselines. We also evaluate SOMBRL on a dynamic RC car hardware and show SOMBRL outperforms the state-of-the-art, illustrating the benefits of principled exploration for MBRL.

General Machine Learning · Transfer, Multitask and Meta-learning

Xueqing Sun, Renzhen Wang, Quanziang Wang, Yichen WU, Xixi Jia, Deyu Meng

Pseudo-labeling is a commonly used paradigm in semi-supervised learning, yet its application to semi-supervised regression (SSR) remains relatively under-explored. Unlike classification, where pseudo-labels are discrete and confidence-based filtering is effective, SSR involves continuous outputs with heteroscedastic noise, making it challenging to assess pseudo-label reliability. As a result, naive pseudo-labeling can lead to error accumulation and overfitting to incorrect labels. To address this, we propose an uncertainty-aware pseudo-labeling framework that dynamically adjusts pseudo-label influence from a bi-level optimization perspective. By jointly minimizing empirical risk over all data and optimizing uncertainty estimates to enhance generalization on labeled data, our method effectively mitigates the impact of unreliable pseudo-labels. We provide theoretical insights and extensive experiments to validate our approach across various benchmark SSR datasets, and the results demonstrate superior robustness and performance compared to existing methods.

Computer Vision · Vision Models & Multimodal

Jun Wang, Fuyuan CAO, ZhixinXue, Xingwang Zhao, Jiye Liang

Existing early and late fusion frameworks in multimodal learning are confronted with the fundamental challenge of modality imbalance, wherein disparities in representational capacities induce inter-modal competition during training. Current research methodologies primarily rely on modality-level contribution assessments to measure gaps in representational capabilities and enhance poorly learned modalities, overlooking the dynamic variations of modality contributions across individual samples. To address this, we propose a Causal-aware Modality valuation approach for Balanced multimodal learning (CMoB). We define a benefit function based on Shannon's theory of informational uncertainty to evaluate the changes in the importance of samples across different stages of multimodal training. Inspired by human cognitive science, we propose a causal-aware modality contribution quantification method from a causal perspective to capture fine-grained changes in modality contribution degrees within samples. In the iterative training of multimodal learning, we develop targeted modal enhancement strategies that dynamically select and optimize modalities based on real-time evaluation of their contribution variations across training samples. Our method enhances the discriminative ability of key modalities and the learning capacity of weak modalities while achieving fine-grained balance in multimodal learning. Extensive experiments on benchmark multimodal datasets and multimodal frameworks demonstrate the superiority of our CMoB approach for balanced multimodal learning.

Optimization · Optimization and Learning under Uncertainty

Ziliang Zhang, Tianming Zhao, Albert Zomaya

Online portfolio selection seeks to determine a sequence of allocations to maximize capital growth. Classical universal strategies asymptotically match the best constant-rebalanced portfolio but ignore potential forecasts, whereas heuristic methods often collapse when belief fails. We formalize this tension in a learning-augmented setting in which an investor observes (possibly erroneous) predictions prior to each decision moment, and we introduce the Rebalanced Arithmetic Mean portfolio with predictions (RAM). Under arbitrary return sequences, we prove that RAM captures at least a constant fraction of the hindsight-optimal wealth when forecasts are perfect while still exceeding the geometric mean of the sequence even when the predictions are adversarial. Comprehensive experiments on large-scale equity data strengthen our theory, spanning both synthetic prediction streams and production-grade machine-learning models. RAM advantages over universal-portfolio variants equipped with side information across various regimes. These results demonstrate that modest predictive power can be reliably converted into tangible gains without sacrificing worst-case guarantees.

Optimization · Optimization and Learning under Uncertainty

Omar Bennouna, Amine Bennouna, Saurabh Amin, Asuman Ozdaglar

We study the fundamental question of how informative a dataset is for solving a given decision-making task. In our setting, the dataset provides partial information about unknown parameters that influence task outcomes. Focusing on linear programs, we characterize when a dataset is sufficient to recover an optimal decision, given an uncertainty set on the cost vector. Our main contribution is a sharp geometric characterization that identifies the directions of the cost vector that matter for optimality, relative to the task constraints and uncertainty set. We further develop a practical algorithm that, for a given task, constructs a minimal or least-costly sufficient dataset. Our results reveal that small, well-chosen datasets can often fully determine optimal decisions---offering a principled foundation for task-aware data selection.

Reinforcement Learning · Deep RL

Heiko Hoppe, Léo Baty, Louis Bouvier, Axel Parmentier, Maximilian Schiffer

Reinforcement learning (RL) is increasingly applied to real-world problems involving complex and structured decisions, such as routing, scheduling, and assortment planning. These settings challenge standard RL algorithms, which struggle to scale, generalize, and exploit structure in the presence of combinatorial action spaces. We propose Structured Reinforcement Learning (SRL), a novel actor-critic paradigm that embeds combinatorial optimization-layers into the actor neural network. We enable end-to-end learning of the actor via Fenchel-Young losses and provide a geometric interpretation of SRL as a primal-dual algorithm in the dual of the moment polytope. Across six environments with exogenous and endogenous uncertainty, SRL matches or surpasses the performance of unstructured RL and imitation learning on static tasks and improves over these baselines by up to 92\% on dynamic problems, with improved stability and convergence speed.

Optimization · Optimization and Learning under Uncertainty

Ji Won Park, Kyunghyun Cho

Accurately estimating *semantic* aleatoric and epistemic uncertainties in large language models (LLMs) is particularly challenging in free-form question answering (QA), where obtaining stable estimates often requires many expensive generations. We introduce a **diversity-steered sampler** that discourages semantically redundant outputs during decoding, covers both autoregressive and masked diffusion paradigms, and yields substantial sample-efficiency gains. The key idea is to inject a continuous semantic-similarity penalty into the model’s proposal distribution using a natural language inference (NLI) model lightly finetuned on partial prefixes or intermediate diffusion states. We debias downstream uncertainty estimates with importance reweighting and shrink their variance with control variates. Across four QA benchmarks, our method matches or surpasses baselines while covering more semantic clusters with the same number of samples. Being modular and requiring no gradient access to the base LLM, the framework promises to serve as a drop-in enhancement for uncertainty estimation in risk-sensitive model deployments.

Optimization · Optimization and Learning under Uncertainty

Spyros Angelopoulos, Bertrand Simon

Online bidding is a classic optimization problem, with several applications in online decision-making, the design of interruptible systems, and the analysis of approximation algorithms. In this work, we study online bidding under learning-augmented settings that incorporate stochasticity, in either the prediction oracle or the algorithm itself. In the first part, we study bidding under distributional predictions, and find Pareto-optimal algorithms that offer the best-possible tradeoff between the consistency and the robustness of the algorithm. In the second part, we study the power and limitations of randomized bidding algorithms, by presenting upper and lower bounds on the consistency/robustness tradeoffs. Previous works focused predominantly on oracles that do not leverage stochastic information on the quality of the prediction, and deterministic algorithms.

Optimization · Optimization and Learning under Uncertainty

Rahul Vaze, Abhishek Sinha

The constrained version of the standard online convex optimization (OCO) framework, called COCO is considered, where on every round, a convex cost function and a convex constraint function are revealed to the learner after it chooses the action for that round. The objective is to simultaneously minimize the static regret and cumulative constraint violation (CCV). An algorithm is proposed that guarantees a static regret of $O(\sqrt{T})$ and a CCV of $\min\{{\cal V}, O(\sqrt{T}\log T) \}$, where ${\cal V}$ depends on the distance between the consecutively revealed constraint sets, the shape of constraint sets, dimension of action space and the diameter of the action space. When constraint sets have additional structure, ${\cal V}=O(1)$. Compared to the state of the art results, static regret of $O(\sqrt{T})$ and CCV of $O(\sqrt{T}\log T)$, that were universal, the new result on CCV is instance dependent, which is derived by exploiting the geometric properties of the constraint sets.

Optimization · Optimization and Learning under Uncertainty

Xiang Li, Yunai Li, Huiying Zhong, Lihua Lei, Zhun Deng

Performativity of predictions refers to the phenomenon where prediction-informed decisions influence the very targets they aim to predict—a dynamic commonly observed in policy-making, social sciences, and economics. In this paper, we initiate an end-to-end framework of statistical inference under performativity. Our contributions are twofold. First, we establish a central limit theorem for estimation and inference in the performative setting, enabling standard inferential tasks such as constructing confidence intervals and conducting hypothesis tests in policy-making contexts. Second, we leverage this central limit theorem to study prediction-powered inference (PPI) under performativity. This approach yields more precise estimates and tighter confidence regions for the model parameters (i.e., policies) of interest in performative prediction. We validate the effectiveness of our framework through numerical experiments. To the best of our knowledge, this is the first work to establish a complete statistical inference under performativity, introducing new challenges and inference settings that we believe will provide substantial value to policy-making, statistics, and machine learning.

Optimization · Optimization and Learning under Uncertainty

Nan Bao, Yifan Zhao, Lin Zhu, Jia Li

Semantic segmentation has achieved great success in ideal conditions. However, when facing extreme conditions (e.g., insufficient light, fierce camera motion), most existing methods suffer from significant information loss of RGB, severely damaging segmentation results. Several researches exploit the high-speed and high-dynamic event modality as a complement, but event and RGB are naturally heterogeneous, which leads to feature-level mismatch and inferior optimization of existing multi-modality methods. Different from these researches, we delve into the edge secret of both modalities for resilient fusion and propose a novel Edge-awareness Semantic Concordance framework to unify the multi-modality heterogeneous features with latent edge cues. In this framework, we first propose Edge-awareness Latent Re-coding, which obtains uncertainty indicators while realigning event-RGB features into unified semantic space guided by re-coded distribution, and transfers event-RGB distributions into re-coded features by utilizing a pre-established edge dictionary as clues. We then propose Re-coded Consolidation and Uncertainty Optimization, which utilize re-coded edge features and uncertainty indicators to solve the heterogeneous event-RGB fusion issues under extreme conditions. We establish two synthetic and one real-world event-RGB semantic segmentation datasets for extreme scenario comparisons. Experimental results show that our method outperforms the state-of-the-art by a 2.55% mIoU on our proposed DERS-XS, and possesses superior resilience under spatial occlusion. Our code and datasets are publicly available at https://github.com/iCVTEAM/ESC.

Applications · Health

Silas Ruhrberg Estévez, Nicolás Astorga, Mihaela van der Schaar

There is growing interest in using machine learning (ML) to support clinical diagnosis, but most approaches rely on static, fully observed datasets and fail to reflect the sequential, resource-aware reasoning clinicians use in practice. Diagnosis remains complex and error prone, especially in high-pressure or resource-limited settings, underscoring the need for frameworks that help clinicians make timely and cost-effective decisions. We propose ACTMED (Adaptive Clinical Test selection via Model-based Experimental Design), a diagnostic framework that integrates Bayesian Experimental Design (BED) with large language models (LLMs) to better emulate real-world diagnostic reasoning. At each step, ACTMED selects the test expected to yield the greatest reduction in diagnostic uncertainty for a given patient. LLMs act as flexible simulators, generating plausible patient state distributions and supporting belief updates without requiring structured, task-specific training data. Clinicians can remain in the loop; reviewing test suggestions, interpreting intermediate outputs, and applying clinical judgment throughout. We evaluate ACTMED on real-world datasets and show it can optimize test selection to improve diagnostic accuracy, interpretability, and resource use. This represents a step toward transparent, adaptive, and clinician-aligned diagnostic systems that generalize across settings with reduced reliance on domain-specific data.

Probabilistic Methods

Gerardo Duran-Martin, Leandro Sánchez-Betancourt, Alvaro Cartea, Kevin Murphy

We introduce scalable algorithms for online learning of neural network parameters and Bayesian sequential decision making. Unlike classical Bayesian neural networks, which induce predictive uncertainty through a posterior over model parameters, our methods adopt a predictive-first perspective based on martingale posteriors. In particular, we work directly with the one-step-ahead posterior predictive, which we parameterize with a neural network and update sequentially with incoming observations. This decouples Bayesian decision-making from parameter-space inference: we sample from the posterior predictive for decision making, and update the parameters of the posterior predictive via fast, frequentist Kalman-filter-like recursions. Our algorithms operate in a fully online, replay-free setting, providing principled uncertainty quantification without costly posterior sampling. Empirically, they achieve competitive performance–speed trade-offs in non-stationary contextual bandits and Bayesian optimization, offering 10–100 times faster inference than classical Thompson sampling while maintaining comparable or superior decision performance.

Applications · Language, Speech and Dialog

Dong Li, Xujiang Zhao, Linlin Yu, Yanchi Liu, Wei Cheng, Zhengzhang Chen, Zhong Chen, Feng Chen, Chen Zhao, Haifeng Chen

Large Language Models (LLMs) offer promising capabilities for tackling complex reasoning tasks, including optimization problems. However, existing methods either rely on prompt engineering, which leads to poor generalization across problem types, or require costly supervised training. We introduce SolverLLM, a training-free framework that leverages test-time scaling to solve diverse optimization problems. Rather than solving directly, SolverLLM generates mathematical formulations and translates them into solver-ready code, guided by a novel Monte Carlo Tree Search (MCTS) strategy. To enhance the search process, we modify classical MCTS with (1) dynamic expansion for adaptive formulation generation, (2) prompt backpropagation to guide exploration via outcome-driven feedback, and (3) uncertainty backpropagation to incorporate reward reliability into decision-making. Experiments on six standard benchmark datasets demonstrate that SolverLLM outperforms both prompt-based and learning-based baselines, achieving strong generalization without additional training.