NeurIPS 2025 论文列表

Conference on Neural Information Processing Systems

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5,812篇论文

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主题: 强化学习 · 784 篇论文 · 重置筛选

On Evaluating Policies for Robust POMDPs

Merlijn Krale, Eline M. Bovy, Maris F. L. Galesloot, Thiago D. Simão, Nils Jansen

展开摘要

Robust partially observable Markov decision processes (RPOMDPs) model sequential decision-making problems under partial observability, where an agent must be robust against a range of dynamics. RPOMDPs can be viewed as a two-player game between an agent, who selects actions, and nature, who adversarially selects the dynamics. Evaluating an agent policy requires finding an adversarial nature policy, which is computationally challenging. In this paper, we advance the evaluation of agent policies for RPOMDPs in three ways. First, we discuss suitable benchmarks. We observe that for some RPOMDPs, an optimal agent policy can be found by considering only subsets of nature policies, making them easier to solve. We formalize this concept of solvability and construct three benchmarks that are only solvable for expressive sets of nature policies. Second, we describe a new method to evaluate agent policies for RPOMDPs by solving an equivalent MDP. Third, we lift two well-known upper bounds from POMDPs to RPOMDPs, which can be used to efficiently approximate the optimality gap of a policy and serve as baselines. Our experimental evaluation shows that (1) our proposed benchmarks cannot be solved by assuming naive nature policies, (2) our method of evaluating policies is accurate, and (3) the upper bounds provide solid baselines for evaluation

Poster
Planning without Search: Refining Frontier LLMs with Offline Goal-Conditioned RL

Joey Hong, Anca Dragan, Sergey Levine

展开摘要

Large language models (LLMs) excel in tasks like question answering and dialogue, but complex tasks requiring interaction, such as negotiation and persuasion, require additional long-horizon reasoning and planning. Reinforcement learning (RL) fine-tuning can enable such planning in principle, but suffers from drawbacks that hinder scalability. In particular, multi-turn RL training incurs high memory and computational costs, which are exacerbated when training LLMs as policies. Furthermore, the largest LLMs do not expose the APIs necessary to be trained in such manner. As a result, modern methods to improve the reasoning of LLMs rely on sophisticated prompting mechanisms rather than RL fine-tuning. To remedy this, we propose a novel approach that uses goal-conditioned value functions to guide the reasoning of LLM agents, that scales even to large API-based models. These value functions predict how a task will unfold given an action, allowing the LLM agent to evaluate multiple possible outcomes, both positive and negative, to plan effectively. In addition, these value functions are trained over reasoning steps rather than full actions, to be a concise and light-weight module that facilitates decision-making in multi-turn interactions. We validate our method on tasks requiring interaction, including tool use, social deduction, and dialogue, demonstrating superior performance over both RL fine-tuning and prompting methods while maintaining efficiency and scalability.

Poster
MisoDICE: Multi-Agent Imitation from Mixed-Quality Demonstrations

The Viet Bui, Tien Anh Mai, Thanh Hong Nguyen

展开摘要

We study offline imitation learning (IL) in cooperative multi-agent settings, where demonstrations have unlabeled mixed quality - containing both expert and suboptimal trajectories. Our proposed solution is structured in two stages: trajectory labeling and multi-agent imitation learning, designed jointly to enable effective learning from heterogeneous, unlabeled data. In the first stage, we combine advances in large language models and preference-based reinforcement learning to construct a progressive labeling pipeline that distinguishes expert-quality trajectories. In the second stage, we introduce MisoDICE, a novel multi-agent IL algorithm that leverages these labels to learn robust policies while addressing the computational complexity of large joint state-action spaces. By extending the popular single-agent DICE framework to multi-agent settings with a new value decomposition and mixing architecture, our method yields a convex policy optimization objective and ensures consistency between global and local policies. We evaluate MisoDICE on multiple standard multi-agent RL benchmarks and demonstrate superior performance, especially when expert data is scarce.

Poster
Improving LLM General Preference Alignment via Optimistic Online Mirror Descent

Yuheng Zhang, Dian Yu, Tao Ge, Linfeng Song, Zhichen Zeng, Haitao Mi, Nan Jiang, Dong Yu

展开摘要

Reinforcement learning from human feedback (RLHF) has demonstrated remarkable effectiveness in aligning large language models (LLMs) with human preferences. Many existing alignment approaches rely on the Bradley-Terry (BT) model assumption, which assumes the existence of a ground-truth reward for each prompt-response pair. However, this assumption can be overly restrictive when modeling complex human preferences. In this paper, we drop the BT model assumption and study LLM alignment under general preferences, formulated as a two-player game. Drawing on theoretical insights from learning in games, we integrate optimistic online mirror descent into our alignment framework to approximate the Nash policy. Theoretically, we demonstrate that our approach achieves an $\mathcal{O}(T^{-1})$ bound on the duality gap, improving upon the previous $\mathcal{O}(T^{-1/2})$ result. Meanwhile, it enjoys a linear convergence rate in the last iterate, a property not achieved by previous methods. More importantly, we implement our method and show through experiments that it outperforms state-of-the-art RLHF algorithms across multiple representative benchmarks.

Spotlight
Near-Optimal Sample Complexity for Online Constrained MDPs

Chang Liu, Yunfan Li, Lin Yang

展开摘要

Safety is a fundamental challenge in reinforcement learning (RL), particularly in real-world applications such as autonomous driving, robotics, and healthcare. To address this, Constrained Markov Decision Processes (CMDPs) are commonly used to enforce safety constraints while optimizing performance. However, existing methods often suffer from significant safety violations or require a high sample complexity to generate near-optimal policies. We address two settings: relaxed feasibility, where small violations are allowed, and strict feasibility, where no violation is allowed. We propose a model-based primal-dual algorithm that balances regret and bounded constraint violations, drawing on techniques from online RL and constrained optimization. For relaxed feasibility, we prove that our algorithm returns an $\varepsilon$-optimal policy with $\varepsilon$-bounded violation with arbitrarily high probability, requiring $\tilde{O}\left(\frac{SAH^3}{\varepsilon^2}\right)$ learning episodes, matching the lower bound for unconstrained MDPs. For strict feasibility, we prove that our algorithm returns an $\varepsilon$-optimal policy with zero violation with arbitrarily high probability, requiring $\tilde{O}\left(\frac{SAH^5}{\varepsilon^2\zeta^2}\right)$ learning episodes, where $\zeta$ is the problem-dependent Slater constant characterizing the size of the feasible region. This result matches the lower bound for learning CMDPs with access to a generative model. Episodic tabular CMDPs serve as a crucial benchmark for safe RL, providing a structured environment for theoretical analysis and algorithmic validation. Our results demonstrate that learning CMDPs in an online setting is as easy as learning with a generative model and is no more challenging than learning unconstrained MDPs when small violations are allowed.

Poster
Agentic RL Scaling Law: Spontaneous Code Execution for Mathematical Problem Solving

Xinji Mai, Haotian Xu, Xing W, Weinong Wang, Yingying Zhang, Wenqiang Zhang

展开摘要

Large Language Models (LLMs) often struggle with mathematical reasoning tasks requiring precise, verifiable computation. While Reinforcement Learning (RL) from outcome-based rewards enhances text-based reasoning, understanding how agents autonomously learn to leverage external tools like code execution remains crucial. We investigate RL from outcome-based rewards for Tool-Integrated Reasoning, ZeroTIR, training base LLMs to spontaneously generate and execute Python code for mathematical problems without supervised tool-use examples. Our central contribution is we demonstrate that as RL training progresses, key metrics scale predictably. Specifically, we observe strong positive correlations where increased training steps lead to increases in the spontaneous code execution frequency, the average response length, and, critically, the final task accuracy. This suggests a quantifiable relationship between computational effort invested in training and the emergence of effective, tool-augmented reasoning strategies. We implement a robust framework featuring a decoupled code execution environment and validate our findings across standard RL algorithms and frameworks. Experiments show ZeroTIR significantly surpasses non-tool ZeroRL baselines on challenging math benchmarks. Our findings provide a foundational understanding of how autonomous tool use is acquired and scales within Agent RL, offering a reproducible benchmark for future studies. Code is released at \href{https://github.com/yyht/openrlhf_async_pipline}{https://github.com/yyht/openrlhf\_async\_pipline}.

Poster
Teaching Language Models to Reason with Tools

Chengpeng Li, Zhengyang Tang, Ziniu Li, Mingfeng Xue, Keqin Bao, Tian Ding, Ruoyu Sun, Benyou Wang, Xiang Wang, Junyang Lin, Dayiheng Liu

展开摘要

Large reasoning models (LRMs) like OpenAI-o1 have shown impressive capabilities in natural language reasoning. However, these models frequently demonstrate inefficiencies or inaccuracies when tackling complex mathematical operations. While integrating computational tools such as Code Interpreters (CIs) offers a promising solution, it introduces a critical challenge: a conflict between the model's internal, probabilistic reasoning and the external, deterministic knowledge provided by the CI, which often leads models to unproductive deliberation. To overcome this, we introduce CoRT (Code-Optimized Reasoning Training), a post-training framework designed to teach LRMs to effectively utilize CIs. We propose **Hint-Engineering**, a new data synthesis strategy that strategically injects diverse hints at optimal points within reasoning paths. This approach generates high-quality, code-integrated reasoning data specifically tailored to optimize LRM-CI interaction. Using this method, we have synthesized 30 high-quality samples to post-train models ranging from 1.5B to 32B parameters through supervised fine-tuning. CoRT further refines the multi-round interleaving of external CI usage and internal thinking by employing rejection sampling and reinforcement learning. Our experimental evaluations demonstrate CoRT's effectiveness, yielding absolute improvements of 4\% and 8\% on DeepSeek-R1-Distill-Qwen-32B and DeepSeek-R1-Distill-Qwen-1.5B, respectively, across five challenging mathematical reasoning datasets. Moreover, CoRT significantly enhances efficiency, reducing token usage by approximately 30\% for the 32B model and 50\% for the 1.5B model compared to pure natural language reasoning baselines. The models and code are available at: [this url](https://github.com/ChengpengLi1003/CoRT).

Poster
R1-ShareVL: Incentivizing Reasoning Capabilities of Multimodal Large Language Models via Share-GRPO

Huanjin Yao, Qixiang Yin, Jingyi Zhang, Min Yang, Yibo Wang, Wenhao Wu, Fei Su, Li Shen, Minghui Qiu, Dacheng Tao, Jiaxing Huang

展开摘要

In this work, we aim to incentivize the reasoning ability of Multimodal Large Language Models (MLLMs) via reinforcement learning (RL) and develop an effective approach that mitigates the sparse reward and advantage vanishing issues during RL. To this end, we propose Share-GRPO, a novel RL approach that tackle these issues by exploring and sharing diverse reasoning trajectories over expanded question space. Specifically, Share-GRPO first expands the question space for a given question via data transformation techniques, and then encourages MLLM to effectively explore diverse reasoning trajectories over the expanded question space and shares the discovered reasoning trajectories across the expanded questions during RL. In addition, Share-GRPO also shares reward information during advantage computation, which estimates solution advantages hierarchically across and within question variants, allowing more accurate estimation of relative advantages and improving the stability of policy training. Extensive evaluations over 6 widely-used reasoning benchmarks showcase the superior performance of our method. Code is available at https://github.com/HJYao00/R1-ShareVL.

Poster
Right Question is Already Half the Answer: Fully Unsupervised LLM Reasoning Incentivization

Qingyang Zhang, Haitao Wu, Changqing Zhang, Peilin Zhao, Yatao Bian

展开摘要

Existing methods to enhance the reasoning capability of large language models predominantly rely on supervised fine-tuning (SFT) followed by reinforcement learning (RL) on reasoning-specific data. These approaches critically depend on external supervisions--such as labeled reasoning traces, verified golden answers, or pre-trained reward models. In this work, we propose Entropy Minimized Policy Optimization (EMPO), which makes an early attempt at fully unsupervised LLM reasoning incentivization. By minimizing the semantic entropy of LLMs on unlabeled questions, EMPO achieves competitive performance compared to supervised counterparts. Specifically, without any supervised signals, EMPO boosts the accuracy of Qwen2.5-Math-7B Base from 33.7\% to 51.6\% on math benchmarks and improves the accuracy of Qwen2.5-7B Base from 32.1\% to 50.1\% on MMLU-Pro. Primary analysis are also provided to interpret the effectiveness of EMPO. Code is available at https://github.com/QingyangZhang/EMPO.

Spotlight
Explainable Reinforcement Learning from Human Feedback to Improve Alignment

Shicheng Liu, Siyuan Xu, Wenjie Qiu, Hangfan Zhang, Minghui Zhu

展开摘要

A common and effective strategy for humans to improve an unsatisfactory outcome in daily life is to find a cause of this outcome and correct the cause. In this paper, we investigate whether this human improvement strategy can be applied to improving reinforcement learning from human feedback (RLHF) for alignment of language models (LMs). In particular, it is observed in the literature that LMs tuned by RLHF can still output unsatisfactory responses. This paper proposes a method to improve the unsatisfactory responses by correcting their causes. Our method has two parts. The first part proposes a post-hoc explanation method to explain why an unsatisfactory response is generated to a prompt by identifying the training data that lead to this response. We formulate this problem as a constrained combinatorial optimization problem where the objective is to find a set of training data closest to this prompt-response pair in a feature representation space, and the constraint is that the prompt-response pair can be decomposed as a convex combination of this set of training data in the feature space. We propose an efficient iterative data selection algorithm to solve this problem. The second part proposes an unlearning method that improves unsatisfactory responses to some prompts by unlearning the training data that lead to these unsatisfactory responses and, meanwhile, does not significantly degrade satisfactory responses to other prompts. Experimental results demonstrate that our algorithm can improve RLHF.

Poster
Heterogeneous Graph Transformers for Simultaneous Mobile Multi-Robot Task Allocation and Scheduling under Temporal Constraints

Batuhan Altundas, Shengkang Chen, Shivika Singh, Shivangi Deo, Minwoo Cho, Matthew Craig Gombolay

展开摘要

Coordinating large teams of heterogeneous mobile agents to perform complex tasks efficiently has scalability bottlenecks in feasible and optimal task scheduling, with critical applications in logistics, manufacturing, and disaster response. Existing task allocation and scheduling methods, including heuristics and optimization-based solvers, often fail to scale and overlook inter-task dependencies and agent heterogeneity. We propose a novel Simultaneous Decision-Making model for Heterogeneous Multi-Agent Task Allocation and Scheduling (HM-MATAS), built on a Residual Heterogeneous Graph Transformer with edge and node-level attention. Our model encodes agent capabilities, travel times, and temporospatial constraints into a rich graph representation and is trainable via reinforcement learning. Trained on small-scale problems (10 agents, 20 tasks), our model generalizes effectively to significantly larger scenarios (up to 40 agents and 200 tasks), enabling fast, one-shot task assignment and scheduling. Our simultaneous model outperforms classical heuristics by assigning 164.10\% more feasible tasks given temporal constraints in 3.83\% of the time, metaheuristics by 201.54\% in 0.01\% of the time and exact solver by 231.73\% in 0.03\% of the time, while achieving $20\times$-to-$250\times$ speedup from prior graph-based methods across scales.

Poster
Actial: Activate Spatial Reasoning Ability of Multimodal Large Language Models

Xiaoyu Zhan, Wenxuan Huang, Hao Sun, Xinyu Fu, Changfeng Ma, Shaosheng Cao, Bohan Jia, Shaohui Lin, Zhenfei Yin, Lei Bai, Wanli Ouyang, Yuanqi Li, Jie Guo, Yanwen Guo

展开摘要

Recent advances in Multimodal Large Language Models (MLLMs) have significantly improved 2D visual understanding, prompting interest in their application to complex 3D reasoning tasks. However, it remains unclear whether these models can effectively capture the detailed spatial information required for robust real-world performance, especially cross-view consistency, a key requirement for accurate 3D reasoning. Considering this issue, we introduce Viewpoint Learning, a task designed to evaluate and improve the spatial reasoning capabilities of MLLMs. We present the Viewpoint-100K dataset, consisting of 100K object-centric image pairs with diverse viewpoints and corresponding question-answer pairs. Our approach employs a two-stage fine-tuning strategy: first, foundational knowledge is injected to the baseline MLLM via Supervised Fine-Tuning (SFT) on Viewpoint-100K, resulting in significant improvements across multiple tasks; second, generalization is enhanced through Reinforcement Learning using the Group Relative Policy Optimization (GRPO) algorithm on a broader set of questions. Additionally, we introduce a hybrid cold-start initialization method designed to simultaneously learn viewpoint representations and maintain coherent reasoning thinking. Experimental results show that our approach significantly activates the spatial reasoning ability of MLLM, improving performance on both in-domain and out-of-domain reasoning tasks. Our findings highlight the value of developing foundational spatial skills in MLLMs, supporting future progress in robotics, autonomous systems, and 3D scene understanding.

Poster
RLVR-World: Training World Models with Reinforcement Learning

Jialong Wu, Shaofeng Yin, Ningya Feng, Mingsheng Long

展开摘要

World models predict state transitions in response to actions and are increasingly developed across diverse modalities. However, standard training objectives such as maximum likelihood estimation (MLE) often misalign with task-specific goals of world models, i.e., transition prediction metrics like accuracy or perceptual quality. In this paper, we present RLVR-World, a unified framework that leverages reinforcement learning with verifiable rewards (RLVR) to directly optimize world models for such metrics. Despite formulating world modeling as autoregressive prediction of tokenized sequences, RLVR-World evaluates metrics of decoded predictions as verifiable rewards. We demonstrate substantial performance gains on both language- and video-based world models across domains, including text games, web navigation, and robot manipulation. Our work indicates that, beyond recent advances in reasoning language models, RLVR offers a promising post-training paradigm for enhancing the utility of generative models more broadly. Code, datasets, models, and video samples are available at the project website: https://thuml.github.io/RLVR-World.

Poster
Reinforced Context Order Recovery for Adaptive Reasoning and Planning

Long Ma, fangwei zhong, Yizhou Wang

展开摘要

Modern causal language models, followed by rapid developments in discrete diffusion models, can now produce a wide variety of interesting and useful content. However, these families of models are predominantly trained to output tokens with a fixed (left-to-right) or random order, which may deviate from the logical order in which tokens are generated originally. In this paper, we observe that current causal and diffusion models encounter difficulties in problems that require adaptive token generation orders to solve tractably, which we characterize with the $\mathcal{V}$-information framework. Motivated by this, we propose Reinforced Context Order Recovery (ReCOR), a reinforcement-learning-based framework to extract adaptive, data-dependent token generation orders from text data without annotations. Self-supervised by token prediction statistics, ReCOR estimates the hardness of predicting every unfilled token and adaptively selects the next token during both training and inference. Experiments on challenging reasoning and planning datasets demonstrate the superior performance of ReCOR compared with baselines, sometimes outperforming oracle models supervised with the ground-truth order.

Poster
Guiding Cross-Modal Representations with MLLM Priors via Preference Alignment

Pengfei Zhao, Rongbo Luan, Wei Zhang, Peng Wu, Sifeng He

展开摘要

Despite Contrastive Language–Image Pre-training (CLIP)'s remarkable capability to retrieve content across modalities, a substantial modality gap persists in its feature space. Intriguingly, we discover that off-the-shelf MLLMs (Multimodal Large Language Models) demonstrate powerful inherent modality alignment properties. While recent MLLM-based retrievers with unified architectures partially mitigate this gap, their reliance on coarse modality alignment mechanisms fundamentally limits their potential. In this work, We introduce MAPLE (Modality-Aligned Preference Learning for Embeddings), a novel framework that leverages the fine-grained alignment priors inherent in MLLM to guide cross-modal representation learning. MAPLE formulates the learning process as reinforcement learning with two key components: (1) Automatic preference data construction using off-the-shelf MLLM, and (2) a new Relative Preference Alignment (RPA) loss, which adapts Direct Preference Optimization (DPO) to the embedding learning setting. Experimental results show that our preference-guided alignment achieves substantial gains in fine-grained cross-modal retrieval, underscoring its effectiveness in handling nuanced semantic distinctions.

Poster
LaRes: Evolutionary Reinforcement Learning with LLM-based Adaptive Reward Search

Pengyi Li, Hongyao Tang, Jinbin Qiao, Yan Zheng, Jianye Hao

展开摘要

The integration of evolutionary algorithms (EAs) with reinforcement learning (RL) has shown superior performance compared to standalone methods. However, previous research focuses on exploration in policy parameter space, while overlooking the reward function search. To bridge this gap, we propose **LaRes**, a novel hybrid framework that achieves efficient policy learning through reward function search. LaRes leverages large language models (LLMs) to generate the reward function population, guiding RL in policy learning. The reward functions are evaluated by the policy performance and improved through LLMs. To improve sample efficiency, LaRes employs a shared experience buffer that collects experiences from all policies, with each experience containing rewards from all reward functions. Upon reward function updates, the rewards of experiences are relabeled, enabling efficient use of historical data. Furthermore, we introduce a Thompson sampling-based selection mechanism that enables more efficient elite interaction. To prevent policy collapse when improving reward functions, we propose the reward scaling and parameter constraint mechanisms to efficiently coordinate reward search with policy learning. Across both initialized and non-initialized settings, LaRes consistently achieves state-of-the-art performance, outperforming strong baselines in both sample efficiency and final performance. The code is available at https://github.com/yeshenpy/LaRes.

Poster
Greedy Sampling Is Provably Efficient For RLHF

Di Wu, Chengshuai Shi, Jing Yang, Cong Shen

展开摘要

Reinforcement Learning from Human Feedback (RLHF) has emerged as a key technique for post‑training large language models. Despite its empirical success, the theoretical understanding of RLHF is still limited, as learning the KL-regularized target with only preference feedback poses additional challenges compared with canonical RL. Existing works mostly study the reward-based Bradley-Terry (BT) preference model, and extend classical designs utilizing optimism or pessimism. This work, instead, considers the general preference model (whose practical relevance has been observed recently) and obtains performance guarantees with major, order-wise improvements over existing ones. Surprisingly, these results are derived from algorithms that directly use empirical estimates (i.e., greedy sampling), as opposed to constructing optimistic or pessimistic estimates in previous works. This insight has a deep root in the unique structural property of the optimal policy class under the KL-regularized target, and we further specialize it to the BT model, highlighting the surprising sufficiency of greedy sampling in RLHF.

Poster
Value-Guided Search for Efficient Chain-of-Thought Reasoning

Kaiwen Wang, Jin Peng Zhou, Jonathan Daniel Chang, Zhaolin Gao, Nathan Kallus, Kianté Brantley, Wen Sun

展开摘要

In this paper, we propose a simple and efficient method for value model training on long-context reasoning traces. Compared to existing process reward models (PRMs), our method does not require a fine-grained notion of ``step,'' which is difficult to define for long-context reasoning models. By collecting a dataset of 2.5 million reasoning traces, we train a 1.5B token-level value model and apply it to DeepSeek models for improved performance with test-time compute scaling. We find that block-wise value-guided search (\texttt{VGS}) with a final weighted majority vote achieves better test-time scaling than standard methods such as majority voting or best-of-$n$. Moreover, \texttt{VGS} significantly reduces the inference FLOPs required to achieve the same performance of majority voting. Our dataset, model and codebase are open-sourced at \codeurl.

Poster
Optimizing Anytime Reasoning via Budget Relative Policy Optimization

Penghui Qi, Zichen Liu, Tianyu Pang, Chao Du, Wee Sun Lee, Min Lin

展开摘要

Scaling test-time compute is crucial for enhancing the reasoning capabilities of large language models (LLMs). Existing approaches typically employ reinforcement learning (RL) to maximize a verifiable reward obtained at the end of reasoning traces. However, such methods optimize only the final performance under a large and fixed token budget, which hinders efficiency in both training and deployment. In this work, we present **AnytimeReasoner**, a novel framework for optimizing reasoning performance under varying thinking budget constraints. To achieve this, we truncate the complete thinking process to fit within sampled token budgets from a prior distribution, compelling the model to summarize the optimal answer for each truncated thinking for verification. This introduces verifiable dense rewards into the reasoning process, facilitating more effective credit assignment in RL optimization. We then optimize the thinking and summary policies in a decoupled manner to maximize the cumulative reward. Additionally, we introduce a novel variance reduction technique, **Budget Relative Policy Optimization (BRPO)**, to enhance the robustness and efficiency of the learning process when reinforcing the thinking policy. Empirical results in mathematical reasoning tasks demonstrate that our method consistently outperforms GRPO across all thinking budgets under various prior distributions, enhancing both training and token efficiency.

Poster
Contextual Online Pricing with (Biased) Offline Data

Yixuan Zhang, Ruihao Zhu, Qiaomin Xie

展开摘要

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.

Poster