论文检索

Reinforcement Learning · Batch/Offline

Yujia Zhang, Lin Li, Wei Wei, Jianguo Wu, Yi Ma, Jiye Liang

Offline reinforcement learning (RL) seeks to learn an optimal policy from a fixed dataset, but distributional shift between the dataset and the learned policy often leads to suboptimal real-world performance. Existing methods typically use behavior policy regularization to constrain the learned policy, but these conservative approaches can limit performance and generalization, especially when the behavior policy is suboptimal. We propose a Peer-Influenced Constraint (PIC) framework with a ``peer review" mechanism. Specifically, we construct a set of similar states and use the corresponding actions as candidates, from which we select the optimal action to constrain the policy. This method helps the policy escape local optima while approximately ensuring the staying within the in-distribution space, boosting both performance and generalization. We also introduce an improved version, Ensemble Peer-Influenced Constraint (EPIC), which combines ensemble methods to achieve strong performance while maintaining high efficiency. Additionally, we uncover the Coupling Effect between PIC and uncertainty estimation, providing valuable insights for offline RL. We evaluate our methods on classic continuous control tasks from the D4RL benchmark, with both PIC and EPIC achieving competitive performance compared to state-of-the-art approaches.

Reinforcement Learning · Deep RL

Tim Schneider, Cristiana de Farias, Roberto Calandra, Liming Chen, Jan Peters

Active perception is a fundamental skill that enables us humans to deal with uncertainty in our inherently partially observable environment. For senses such as touch, where the information is sparse and local, active perception becomes crucial. In recent years, active perception has emerged as an important research domain in robotics. However, current methods are often bound to specific tasks or make strong assumptions, which limit their generality. To address this gap, this work introduces APPLE (Active Perception Policy Learning) – a novel framework that leverages reinforcement learning (RL) to address a range of different active perception problems. APPLE jointly trains a transformer-based perception module and decision-making policy with a unified optimization objective, learning how to actively gather information. By design, APPLE is not limited to a specific task and can, in principle, be applied to a wide range of active perception problems. We evaluate two variants of APPLE across different tasks, including tactile exploration problems from the Tactile MNIST benchmark. Experiments demonstrate the efficacy of APPLE, achieving high accuracies on both regression and classification tasks. These findings underscore the potential of APPLE as a versatile and general framework for advancing active perception in robotics. Project page: https://timschneider42.github.io/apple

Deep Learning · Everything Else

Paulius Rauba, Mihaela van der Schaar

Large neural networks are typically trained for a fixed computational budget, creating a rigid trade-off between performance and efficiency that is ill-suited for deployment in resource-constrained or dynamic environments. Existing approaches to this problem present a difficult choice: training a discrete collection of specialist models is computationally prohibitive, while dynamic methods like slimmable networks often lack the flexibility to be applied to large, pre-trained foundation models. In this work, we propose *Nested Subspace Networks (NSNs)*, a novel architectural paradigm that enables a single model to be dynamically and granularly adjusted across a continuous spectrum of compute budgets at inference time. The core of our approach is to re-parameterize linear layers to satisfy a nested subspace property, such that the function computed at a given rank is a strict subspace of the function at any higher rank. We show that this entire hierarchy of models can be optimized jointly via an uncertainty-aware objective that learns to balance the contributions of different ranks based on their intrinsic difficulty. We demonstrate empirically that NSNs can be surgically applied to pre-trained LLMs and unlock a smooth and predictable compute-performance frontier. For example, a single NSN-adapted model can achieve a 50\% reduction in inference FLOPs with only a 5 percentage point loss in accuracy. Our findings establish NSNs as a powerful framework for creating the next generation of adaptive foundation models.

Optimization · Optimization and Learning under Uncertainty

Aymeric Capitaine, Maxime Haddouche, Eric Moulines, Michael Jordan, Etienne Boursier, Alain Oliviero Durmus

Decision-focused learning (DFL) is an increasingly popular paradigm for training predictive models whose outputs are used in decision-making tasks. Instead of merely optimizing for predictive accuracy, DFL trains models to directly minimize the loss associated with downstream decisions. However, existing studies focus solely on scenarios where a fixed batch of data is available and the objective function does not change over time. We instead investigate DFL in dynamic environments where the objective function and data distribution evolve over time. This setting is challenging for online learning because the objective function has zero or undefined gradients, which prevents the use of standard first-order optimization methods, and is generally non-convex. To address these difficulties, we (i) regularize the objective to make it differentiable and (ii) use perturbation techniques along with a near-optimal oracle to overcome non-convexity. Combining those techniques yields two original online algorithms tailored for DFL, for which we establish respectively static and dynamic regret bounds. These are the first provable guarantees for the online decision-focused problem. Finally, we showcase the effectiveness of our algorithms on a knapsack experiment, where they outperform two standard benchmarks.

General Machine Learning · Probabilistic Methods

Wenbin Zhou, Agni Orfanoudaki, Shixiang Zhu

High-stakes decisions in healthcare, energy, and public policy have long depended on human expertise and heuristics, but are now increasingly supported by predictive and optimization-based tools. A prevailing paradigm in operations research is predict-then-optimize, where predictive models estimate uncertain inputs and optimization models recommend decisions. However, such approaches often sideline human judgment, creating a disconnect between algorithmic outputs and expert intuition that undermines trust and adoption in practice. To bridge this gap, we propose CREDO, a framework that, for any candidate decision proposed by human experts, provides a distribution-free upper bound on the probability of suboptimality---informed by both the optimization structure and the data distribution. By combining inverse optimization geometry with conformal generative prediction, CREDO delivers statistically rigorous yet practically interpretable risk certificates. This framework allows human decision-makers to audit and validate their decisions under uncertainty, strengthening the alignment between algorithmic tools and human intuition.

Reinforcement Learning · Everything Else

Xuan Zhang, Ruixiao Li, Zhijian Zhou, Long Li, Yulei Qin, Ke Li, Xing Sun, Xiaoyu Tan, Chao Qu, Yuan Qi

Reinforcement Learning (RL) has become a compelling way to strengthen the multi step reasoning ability of Large Language Models (LLMs). However, prevalent RL paradigms still lean on sparse outcome-based rewards and limited exploration, which often drives LLMs toward repetitive and suboptimal reasoning patterns. In this paper, we study the central question of how to design exploration for LLM reasoning and introduce MERCI (Motivating Exploration in LLM Reasoning with Count-based Intrinsic Rewards), a novel RL algorithm that augments policy optimization with a principled intrinsic reward. Building on the idea of count-based exploration, MERCI leverages a lightweight Coin Flipping Network (CFN) to estimate the pseudo count and further epistemic uncertainty over reasoning trajectories, and converts them into an intrinsic reward that values novelty while preserving the learning signal from task rewards. We integrate MERCI into some advanced RL frameworks like Group Relative Policy Optimization (GRPO). Experiments on complex reasoning benchmarks demonstrate that MERCI encourages richer and more varied chains of thought, significantly improves performance over strong baselines, and helps the policy escape local routines to discover better solutions. It indicates that our targeted intrinsic motivation can make exploration reliable for language model reasoning.

Reinforcement Learning · Deep RL

Yuanfu Wang, Zhixuan Liu, Xiangtian Li, Chaochao Lu, yang chao

The dominant paradigm for training large reasoning models—combining Supervised Fine-Tuning (SFT) with Reinforcement Learning with Verifiable Rewards (RLVR)—is fundamentally constrained by its reliance on high-quality, human-annotated reasoning data and external verifiers. This dependency incurs significant data-collection costs, risks embedding human cognitive biases, and confines the reinforcement learning stage to objectively assessable domains like mathematics and coding, leaving a vast landscape of unverifiable tasks unaddressed. To overcome these limitations, we introduce Native Reasoning Training (NRT), a novel framework that cultivates complex reasoning by having the model generate its own reasoning traces using only standard question-answer pairs, thereby obviating the need for expert-written demonstrations. NRT reframes the training problem by treating the reasoning process as a latent variable. It employs a unified training objective that models reasoning as an optimization problem, intrinsically rewarding paths that increase the model's likelihood of producing the ground-truth answer. This unified perspective allows us to analyze intrinsic failure modes of prior methods, such as policy collapse, and systematically design more robust reward aggregation functions, creating a self-correcting feedback loop where the model learns to \textit{think} in ways that resolve its own uncertainty. Empirical evaluation on Llama and Mistral model families demonstrates that NRT achieves state-of-the-art performance among verifier-free methods, significantly outperforming standard SFT baselines and prior verifier-free RL methods. Our approach yields particularly strong performance gains in complex reasoning domains and exhibits high robustness to policy collapse, offering a general, scalable path toward building more powerful and broadly applicable reasoning systems.

Optimization · Large Scale, Parallel and Distributed

Jingyi Zhao, Linxin Yang, Haohua Zhang, Qile He, Tian Ding

Dynamic programming (DP) is central to combinatorial optimization, optimal control, and reinforcement learning, yet its perceived sequentiality has long hindered scalability. We introduce a general-purpose GPU framework that reformulates broad classes of forward DP recursions as batched min--plus matrix--vector products over layered DAGs, collapsing actions into masked state-to-state transitions that map directly to GPU kernels. This approach removes a major bottleneck in scenario-based stochastic programming (SP), where the use of DP has traditionally restricted the number of scenarios due to excessive computational cost. Our framework exposes massive parallelism across scenarios, transition layers, and, when applicable, route or action options, via self-designed GPU kernels that implement Bellman updates with warp-/block-level reductions and numerically safe masking. In a single GPU pass, these kernels can process over $10^6$ uncertainty realizations, far beyond the capacity of prior scenario-based methods. We demonstrate the approach in two canonical SP applications: (i) a vectorized split operator for the capacitated vehicle routing problem with stochastic demand, exploiting **2D** parallelism (scenarios $\times$ transitions); and (ii) a forward inventory reinsertion DP under an order-up-to policy, exploiting **3D** parallelism (scenarios $\times$ inventory transitions $\times$ route options). Across benchmarks, the implementation scales nearly linearly in the number of scenarios and achieves one to three orders of magnitude speedups over multithreaded CPU baselines, yielding tighter SAA estimates and consistently stronger first-stage decisions under identical wall-clock budgets. Viewed as hardware-aware software primitives, our min--plus DP kernels offer a drop-in path to scalable, GPU-accelerated stochastic discrete optimization.

Reinforcement Learning · Online

Hao Liang, Jiayu Cheng, Sean Sinclair, Yali Du

Exogenous MDPs (Exo-MDPs) capture sequential decision-making where uncertainty comes solely from exogenous inputs that evolve independently of the learner’s actions. This structure is especially common in operations research applications such as inventory control, energy storage, and resource allocation, where exogenous randomness (e.g., demand, arrivals, or prices) drives system behavior. Despite decades of empirical evidence that greedy, exploitation-only methods work remarkably well in these settings, theory has lagged behind: all existing regret guarantees for Exo-MDPs rely on explicit exploration or tabular assumptions. We show that exploration is unnecessary. We propose Pure Exploitation Learning ($\texttt{PEL}$) and prove the first general finite-sample regret bounds for exploitation-only algorithms in Exo-MDPs. In the tabular case, PEL achieves $\widetilde{O}(H^2|\Xi|\sqrt{K})$. For large, continuous endogenous state spaces, we introduce $\texttt{LSVI-PE}$, a simple linear-approximation method whose regret is polynomial in the feature dimension, exogenous state space, and horizon, independent of the endogenous state and action spaces. Our analysis introduces two new tools: counterfactual trajectories and Bellman-closed feature transport, which together allow greedy policies to have accurate value estimates without optimism. Experiments on synthetic and resource-management tasks show $\texttt{PEL}$ consistently outperforming baselines. Overall, our results overturn the conventional wisdom that exploration is required, demonstrating that in Exo-MDPs, pure exploitation is enough.

Reinforcement Learning · Planning

Kai Zhang, Jingjing Gu, Qiuhong Wang

Dynamic Path Planning (DPP) in urban road networks faces fundamental challenges, as traffic conditions change rapidly over time and often render planned routes ineffective. Reinforcement Learning (RL) provides an effective way to adaptively handle such uncertainties by incorporating traffic dynamics into state, but its performance crucially depends on how these dynamics are represented. Existing approaches either rely on global traffic information, which ensures decision completeness but suffers from redundancy and high computational cost, or oversimplified local features, which are efficient but often omit critical dynamics and lead to suboptimal paths. To address this, we propose a Dynamics Feature Representation (DFR) framework that progressively refines global traffic dynamics into compact features for RL-based DPP. Specifically, we introduce a policy attention mechanism that identifies a core subset of global dynamics by extracting the top-k shortest paths, and further constructs node-related local features by intersecting with n-hop neighborhoods, enabling near-optimal policy learning. Theoretical analysis demonstrates that DFR guarantees state completeness, while empirical results confirm that, compared to classical baselines and standard RL methods, DFR significantly improves path planning performance and accelerates convergence. This work highlights the central role of feature representation in RL-based DPP and proposes a general framework that balances information sufficiency with computational efficiency, paving the way for scalable dynamic decision-making in real-world transportation systems.

Theory · Probabilistic Methods

Linye Li, Yufei Chen, Xiaodong Yue, Xujing Zhou, Qunjie Chen

Evidential Deep Learning (EDL) has emerged as a promising framework for uncertainty estimation in classification tasks by modeling predictive uncertainty with a Dirichlet prior. Despite its empirical success, prior work has primarily focused on the probabilistic properties of the Dirichlet distribution, leaving the role of optimization dynamics during training underexplored. In this paper, we revisit EDL through the lens of optimization and establish a non-trivial connection: minimizing the expected cross-entropy loss over the Dirichlet prior implicitly encourages solutions akin to multi-class Support Vector Machines, maximizing decision margins. Motivated by this observation, we introduce the \emph{optimization-consistency principle}, which deems an uncertainty measure valid if its value decreases as samples approach the global optimum of the training objective. This principle provides a new criterion for evaluating and designing uncertainty measures that are consistent with the optimization dynamics. Building on this foundation, we further propose a novel measure, \emph{Margin-aware Predictive Uncertainty (MPU)}, which directly captures the separation between target and non-target evidence. Extensive experiments on out-of-distribution detection and classification-with-rejection benchmarks demonstrate the effectiveness of our propositions.

Computer Vision · Vision Models & Multimodal

Xiangqi Li, Libo Huang, Jiarui Zhao, Weilun Feng, Chuanguang Yang, Zhulin An, Yongjun Xu

3D few-shot class-incremental learning (3D FSCIL) requires effectively integrating novel classes from limited samples while preserving base-class knowledge, without succumbing to catastrophic forgetting the learned knowledge or overfitting the novel ones. Current 3D FSCIL approaches predominantly focus on fine-tuning feature representations yet retain static decision boundaries. This leads to a critical trade-off: excessive adaptation to new samples tends to erase previously learned knowledge, while insufficient adaptation hinders novel-class recognition. We argue that the key to effective incremental learning lies not only in feature enhancement but also in adaptive decision-making. To this end, we introduce **Point-UQ**, an incremental training-free paradigm for 3D **point** clouds based on **u**ncertainty **q**uantification, which shifts the focus from feature tuning to dynamic decision optimization. Point-UQ comprises two co-designed modules: *Attention-driven Adaptive Enhancement (AAE)* and *Uncertainty-quantification Decision Decoupling (UDD)*. The former module fuses multi-scale features into calibrated representations, where prediction entropy serves as a reliable measure of per-sample epistemic uncertainty while preserving original feature semantics. Building on AAE-derived calibrated entropy, the UDD module dynamically arbitrates between semantic classifiers and geometric prototypes—enabling robust base-class knowledge retention and accurate novel-class recognition in 3D FSCIL without retraining. Extensive experiments on ModelNet, ShapeNet, ScanObjectNN, and CO3D demonstrate that our approach outperforms state-of-the-art methods by 4% in average accuracy, setting a new standard for robust 3D incremental learning.

Optimization · Learning for Optimization

Prince Wang, Shuyi Chen, Jinhao Liang, Ferdinando Fioretto, Shixiang Zhu

Decision-focused learning (DFL) integrates predictive models with downstream optimization, directly training machine learning models to minimize decision errors. While DFL has been shown to provide substantial advantages when compared to a counterpart that treats the predictive and prescriptive models separately, it has also been shown to struggle in high-dimensional and risk-sensitive settings, limiting its applicability in real-world settings. To address this limitation, this paper introduces Decision-Focused Generative Learning (Gen-DFL), a novel framework that leverages generative models to adaptively model uncertainty and improve decision quality. Instead of relying on fixed uncertainty sets, Gen-DFL learns a structured representation of the optimization parameters and samples from the tail regions of the learned distribution to enhance robustness against worst-case scenarios. This approach mitigates over-conservatism while capturing complex dependencies in the parameter space. The paper shows, theoretically, that Gen-DFL achieves improved worst-case performance bounds compared to traditional DFL. Empirically, it evaluates Gen-DFL on various scheduling and logistics problems, demonstrating its strong performance against existing DFL methods.

Optimization · Optimization and Learning under Uncertainty

Yang Hu, Jieren Tan, Changliang Zou, Yajie Bao, Haojie Ren

Robust decision-making is crucial in numerous risk-sensitive applications where outcomes are uncertain and the cost of failure is high. Conditional Robust Optimization (CRO) offers a framework for such tasks by constructing prediction sets for the outcome that satisfy predefined coverage requirements and then making decisions based on these sets. Many existing approaches leverage conformal prediction to build prediction sets with guaranteed coverage for CRO. However, since coverage is a *sufficient but not necessary* condition for robustness, enforcing such constraints often leads to overly conservative decisions. To overcome this limitation, we propose a novel framework named Conformal Robustness Control (CRC), that directly optimizes the prediction set construction under explicit robustness constraints, thereby enabling more efficient decisions without compromising robustness. We develop efficient algorithms to solve the CRC optimization problem, and also provide theoretical guarantees on both robustness and optimality. Empirical results show that CRC consistently yields more effective decisions than existing baselines while still meeting the target robustness level.

Reinforcement Learning · Deep RL

yueheng li, Guangming Xie, Zongqing Lu

Reinforcement Learning (RL) in partially observable environments poses significant challenges due to the complexity of learning under uncertainty. While additional information, such as that available in simulations, can enhance training, effectively leveraging it remains an open problem. To address this, we introduce Guided Policy Optimization (GPO), a framework that co-trains a guider and a learner. The guider takes advantage of privileged information while ensuring alignment with the learner's policy that is primarily trained via imitation learning. We theoretically demonstrate that this learning scheme achieves optimality comparable to direct RL, thereby overcoming key limitations inherent in existing approaches. Empirical evaluations show strong performance of GPO across various tasks, including continuous control with partial observability and noise, and memory-based challenges, significantly outperforming existing methods.

Computer Vision · Classification and Understanding

Yuan Dong, Zhe Zhao, Liheng Yu, Di Wu, Pengkun Wang

Long-Tailed Recognition (LTR) remains a significant challenge in deep learning. While multi-expert architectures are a prominent paradigm, we argue that their efficacy is fundamentally limited by a series of deeply entangled problems at the levels of representation, policy, and optimization. These entanglements induce homogeneity collapse among experts, suboptimal dynamic adjustments, and unstable meta-learning. In this paper, we introduce GUIDE, a novel framework conceived from the philosophy of Hierarchical Disentanglement. We systematically address these issues at three distinct levels. First, we disentangle expert representations and decisions through competitive specialization objectives to foster genuine diversity. Second, we disentangle policy-making from ambiguous signals by using online uncertainty decomposition to guide a dynamic expert refinement module, enabling a differentiated response to model ignorance versus data ambiguity. Third, we disentangle the optimization of the main task and the meta-policy via a two-timescale update mechanism, ensuring stable convergence. Extensive experiments on five challenging LTR benchmarks, including ImageNet-LT, iNaturalist 2018, CIFAR-100-LT, CIFAR-10-LT and Places-LT, demonstrate that GUIDE establishes a new state of the art, validating the efficacy of our disentanglement approach. Code is available at Supplement.

Social Aspects · Trustworthy Machine Learning

Xinyu Zhou, Chang Jin, Carsten Eickhoff, Zhijiang Guo, Seyed Ali Bahrainian

Large language models (LLMs) rarely admit uncertainty, often producing fluent but misleading answers, rather than abstaining (i.e., refusing to answer). This weakness is even evident in temporal question answering (QA), where models frequently ignore time-sensitive evidence and conflate facts across different time-periods. In this paper, we present the first empirical study of training LLMs with abstention ability while reasoning about temporal QA. Existing approaches such as calibration might be unreliable in capturing uncertainty in complex reasoning. We instead frame abstention as a teachable skill and introduce pipelines including one that couples Chain-of-Thought (CoT) supervision with Reinforcement Learning (RL) guided by abstention-aware rewards. Our goal is to systematically analyze how different information types and training techniques affect temporal reasoning with abstention behavior in LLMs. Through extensive experiments studying various methods, we find that RL yields strong empirical gains on reasoning: a model initialized by Qwen2.5-1.5B-Instruct surpasses GPT-4o by 3.46% and 5.80% in Exact Match on TimeQA-Easy and -Hard, respectively. Moreover, it improves the True Positive rate on unanswerable questions by 20% over a pure supervised fine-tuned (SFT) variant. Beyond performance, our analysis shows that SFT induces overconfidence and harms reliability, while RL improves prediction accuracy but exhibits similar risks. Finally, by comparing implicit reasoning cues (e.g., original context, temporal sub-context, knowledge graphs) with explicit CoT supervision, we find that implicit information provides limited benefit for reasoning with abstention. Our study presents new insights into how abstention and reasoning can be jointly optimized, providing a foundation for building more reliable LLMs. Dataset and code is publicly released https://github.com/Blackzxy/AbstentionTemporalQA.

Zhongjian Qiao, Jiafei Lyu, Boxiang Lyu, Yao Shu, Siyang Gao, Shuang Qiu

Model-based offline reinforcement learning (RL) aims to enhance offline RL with a dynamics model that facilitates policy exploration. However, model exploitation could occur due to inevitable model errors, which degrades algorithm performance. Adversarial model learning offers a theoretical framework to mitigate model exploitation by solving a maximin formulation, and RAMBO provides a practical implementation with model gradient. However, we empirically observe that severe Q-value underestimation and gradient explosion can occur in RAMBO with only slight hyperparameter tuning, suggesting that it tends to be overly conservative and suffers from unstable model updates. To address these issues, we propose RObust value-aware Model learning via Implicitly differentiable adaptive weighting (ROMI). Instead of updating the dynamics model with model gradient, ROMI introduces a novel robust value-aware model learning approach. This approach requires the dynamics model to predict future states with values close to the minimum Q-value within a scale-adjustable state uncertainty set, enabling controllable conservatism and stable model updates. To further improve out-of-distribution (OOD) generalization during multi-step rollouts, we propose implicitly differentiable adaptive weighting, a bi-level optimization scheme that adaptively achieves dynamics- and value-aware model learning. Empirical results on D4RL and NeoRL datasets show that ROMI significantly outperforms RAMBO and achieves competitive or superior performance compared to state-of-the-art methods on datasets where RAMBO typically underperforms.

General Machine Learning · Probabilistic Methods

Zihang Zeng, Jiaquan Zhang, Pengze Li, Yuan Qi, Xi Chen

Large Language Models (LLMs) demonstrate potentials for automating scientific code generation but face challenges in reliability, error propagation in multi-agent workflows, and evaluation in domains with ill-defined success metrics. We present a Bayesian adversarial multi-agent framework specifically designed for AI for Science (AI4S) tasks in the form of a Low-code Platform (LCP). Three LLM-based agents are coordinated under the Bayesian framework: a Task Manager that structures user inputs into actionable plans and adaptive test cases, a Code Generator that produces candidate solutions, and an Evaluator providing comprehensive feedback. The framework employs an adversarial loop where the Task Manager iteratively refines test cases to challenge the Code Generator, while prompt distributions are dynamically updated using Bayesian principles by integrating code quality metrics: functional correctness, structural alignment, and static analysis. This co-optimization of tests and code reduces dependence on LLM reliability and addresses evaluation uncertainty inherent to scientific tasks. LCP also streamlines human-AI collaboration by translating non-expert prompts into domain-specific requirements, bypassing the need for manual prompt engineering by practitioners without coding backgrounds. Benchmark evaluations demonstrate LCP’s effectiveness in generating robust code while minimizing error propagation. The proposed platform is also tested on an Earth Science cross-disciplinary task and demonstrates strong reliability, outperforming competing models.

Deep Learning · Generative Models and Autoencoders

Minyoung Kim

The famous Schr\"{o}dinger bridge (SB) has gained renewed attention in the generative machine learning field these days for its successful applications in various areas including unsupervised image-to-image translation and particle crowd modeling. Recently, a promising algorithm dubbed GSBM was proposed to solve the generalized SB (GSB) problem, an extension of SB to deal with additional path constraints. Therein the SB is formulated as a minimal kinetic energy conditional flow matching problem, and an additional task-specific stage cost is introduced as the conditional stochastic optimal control (CondSOC) problem. The GSB is a new emerging problem with considerable room for research contributions, and we introduce a novel Gaussian process pinned marginal path posterior inference as a meaningful contribution in this area. Our main motivation is that the stage cost in GSBM, typically representing task-specific obstacles in the particle paths and other congestion penalties, can be potentially noisy and uncertain. Whereas the current GSBM approach regards this stage cost as a noise-free deterministic quantity in the CondSOC optimization, we instead model it as a stochastic quantity. Specifically, we impose a Gaussian process (GP) prior on the pinned marginal path, view the CondSOC objective as a (noisy) likelihood function, and infer the posterior path via sparse variational free-energy GP approximate inference. The main benefit is more flexible marginal path modeling that takes into account the uncertainty in the stage cost such as more realistic noisy observations. On some image-to-image translation and crowd navigation problems under noisy scenarios, we show that our proposed GP-based method yields more robust solutions than the original GSBM.