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1,248篇论文匹配“Deep RL”
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Jianting Tang, Dongshuai Li, Tao Wen 0018, Fuyu Lv, Dan Ou, Linli Xu 0002

In modern e-commerce search systems, dense retrieval has become an indispensable component. By computing similarities between query and item (product) embeddings, it efficiently selects candidate products from large-scale repositories. With the breakthroughs in large language models (LLMs), mainstream embedding models have gradually shifted from BERT to LLMs for more accurate text modeling. However, these models still adopt direct-embedding methods, and the semantic accuracy of embeddings remains inadequate. Therefore, contrastive learning is heavily employed to achieve tight semantic alignment between positive pairs. Consequently, such models tend to capture statistical co-occurrence patterns in the training data, biasing them toward shallow lexical and semantic matches. For difficult queries exhibiting notable lexical disparity from target items, the performance degrades significantly. In this work, we propose the Large Reasoning Embedding Model (LREM), which novelly integrates reasoning processes into representation learning. For difficult queries, LREM first conducts reasoning to achieve a deep understanding of the original query, and then produces a reasoning-augmented query embedding for retrieval. This reasoning process effectively bridges the semantic gap between original queries and target items, significantly improving retrieval accuracy. Specifically, we adopt a two-stage training process: the first stage optimizes the LLM on carefully curated Query-CoT-Item triplets with SFT and InfoNCE losses to establish preliminary reasoning and embedding capabilities, and the second stage further refines the reasoning trajectories via reinforcement learning (RL). Extensive offline and online experiments validate the effectiveness of LREM, leading to its deployment on China's largest e-commerce platform since August 2025.

Guanting Dong 0001, Licheng Bao, Zhongyuan Wang 0006, Kangzhi Zhao, Xiaoxi Li 0005, Jiajie Jin, Jinghan Yang, Hangyu Mao, Fuzheng Zhang, Kun Gai 等

Recently, Agentic Reinforcement Learning (Agentic RL) has made significant progress in incentivizing the multi-turn, long-horizon tool-use capabilities of web agents. While mainstream agentic RL algorithms autonomously explore high-uncertainty tool-call steps under the guidance of entropy, excessive reliance on such signals leads to the training collapse. In this paper, we delve into the challenges caused by entropy and propose the Agentic Entropy-Balanced Policy Optimization (AEPO), an agentic RL algorithm designed to balance entropy in both the rollout and policy update phases. AEPO comprises two core components: (1) a dynamic entropy-balanced rollout mechanism that adaptively allocates global and branch sampling budget through entropy pre-monitoring, while imposing a branch penalty on consecutive high-entropy tool-call steps to prevent over-branching issues; and (2) Entropy-Balanced Policy Optimization that inserts a stop-gradient operation into the high-entropy clipping term to preserve and properly rescale gradients on high-entropy tokens, while incorporating entropy-aware advantage estimation to prioritize learning on high-uncertainty tokens. Results across 14 challenging datasets show that AEPO consistently outperforms 7 mainstream RL algorithms. Further analysis reveals that AEPO improves rollout sampling diversity while maintaining stable policy entropy, facilitating scalable training of general web agents. The code is available at https://github.com/RUC-NLPIR/ARPO.

Mohammad Pivezhandi, Mahdi Banisharif, Saeed Bakhshan, Abusayeed Saifullah, Ali Jannesari

Autonomous AI agents on embedded platforms require real-time, risk-aware scheduling under resource and thermal constraints. Classical heuristics struggle with workload irregularity, tabular regressors discard structural information, and model-free reinforcement learning (RL) risks overheating. We introduce GraphPerf-RT, an AI technology achieving deep learning accuracy at heuristic speeds (2-7ms). GraphPerf-RT is, to our knowledge, the first graph-grounded infrastructure unifying task DAG topology, CFG-derived code semantics, and runtime context (per-core DVFS, thermal state, utilization) in a heterogeneous graph with typed edges encoding precedence, placement, and contention. The architecture supports multi-task evidential heads with Normal-Inverse-Gamma uncertainty; we validate on makespan prediction for risk-aware scheduling. Experiments on three ARM platforms (Jetson TX2, Orin NX, RUBIK Pi) achieve R^2 = 0.81 on log-transformed makespan with Spearman rho = 0.95 and conservative uncertainty calibration (PICP = 99.9% at 95% confidence). Integration with four RL methods demonstrates that multi-agent model-based RL with GraphPerf-RT as the world model achieves 66% makespan reduction and 82% energy reduction versus model-free baselines, with zero thermal violations.

Yiwei Shi, Mengyue Yang, Qi Zhang, Cunjia Liu, Weinan Zhang, Weiru Liu

Active inverse source localization and characterization (ISLC) in dynamic fields requires sequential decision making under partial observability, where a mobile sensor must infer latent source parameters from sparse, noisy readings. We introduce a belief-contraction-driven approach that unifies inference, stopping, and control. An attention-augmented particle filter stabilizes Bayesian belief updates through ESS-based resampling, feature-aware sparse attention smoothing, and Metropolis–Hastings rejuvenation that preserves the filtering posterior. Belief contraction (posterior dispersion) defines both a termination rule and a goal-aligned intrinsic reward, enabling reinforcement learning without distance-to-source shaping. Across seven field modalities, spatial out-of-distribution tests, and nonstationary source shifts, our agent (ATT-PFRL) achieves higher completion, faster convergence, and more accurate localization than planning and RL+Bayes baselines under similar computation. Fixed-trajectory studies also show improved ESS and lower RMSE, isolating the benefit of the inference layer.

Guojun Xiong, Mauricio Tec, Haichuan Wang, Francesca Dominici, Joseph Ngonzi, Adeline Boatin, Milind Tambe

Reducing preventable maternal mortality remains a global health priority. Under Sustainable Development Goal (SDG) target 3.1, the WHO emphasizes timely and equitable allocation of limited maternal health resources. Motivated by Department of Obstetrics and Gynecology at several important hospitals in Uganda and Ghana, we study the problem of sequential allocation of wearable vital sign monitoring devices among maternal mothers. While deep reinforcement learning (RL) has shown promise for sequential resource allocation, its limited interpretability hinders adoption in such high-stakes settings. In contrast, large language model (LLM) agents provide human-readable reasoning but often struggle with effective long-term decision making. To bridge this gap, we introduce Rule-Bottleneck RL (RBRL), the first LLM agent framework for resource allocation problems that jointly optimizes language-based decision policy and explainability. At each step within RBRL, an LLM first generates candidate rules---language statements capturing decision priorities tailored to the current state. RL then optimizes rule selection to maximize environmental rewards and explainability, with the LLM acting as a judge. Finally, an LLM chooses the action (optimal allocation) based on the rule. We provide conditions for RBRL performance guarantees as well as the finite-horizon evaluation gap of the learned RBRL policy. Experiments in maternal health show that RBRL outperforms baseline LLM agents and approaches the performance of deep RL, while producing clearer, policy-relevant explanations. Human evaluations further confirm improved trust and usability, demonstrating RBRL as a practical AI approach aligned with SDG target 3.1.

Soumyajit Dev, Malay Bhattacharyya

Dismantling interdependent directed networks to obtain the largest mutually strongly connected component (MSCC) is an NP-hard problem. To address this, we propose a novel method, Disassembling Directed Interdependent Networks (DDIN), by synergizing Reinforcement Learning (RL) and Graph Neural Networks (GNN). We introduce asymmetric GNNs to capture the asymmetry of in/out-degree and multi-relational attention to model directed inter-layer dependencies, integrated with prioritized RL for efficient node selection in large action spaces. Our contributions include (i) a directed GraphSAGE encoder separating in/out aggregations for asymmetry, (ii) multi-relational attention fusing layer semantics, and (iii) sum-tree prioritized n-step Deep Q-Network (DQN) for efficient policy search. DDIN is evaluated on 5 directed multiplexes from biological, social, and economic domains, achieving 16-23% lower AUDC compared to known baseline heuristics.

Zijian Zhao

Recently, deep Reinforcement Learning (RL) methods have been widely used in labor management within transportation gig markets, such as ride-hailing, food delivery, and express delivery. Compared to traditional rule-based and optimization-based methods, RL can capture more information about long-term uncertainty and environmental dynamics, leading to better and non-myopic strategies. However, deep learning methods have long been criticized for their low interpretability, raising concerns about algorithmic discrimination in gig markets. Currently, most works focus on this issue from the perspective of statistical analysis and surveys. However, the underlying reasons related to the algorithms remain unclear, as most companies do not disclose their algorithms. This lack of transparency can hinder governments from designing efficient management policies to address these problems. To fill this research gap, this thesis proposal aims to develop appropriate RL methods to mimic the labor management behavior of transportation gig platforms and to propose effective policies that protect the rights of gig workers.

Benedikt Schlereth-Groh, Sakir Furkan Yöndem, Ramin Tavakoli Kolagari

Reinforcement Learning (RL) has shown significant promise in developing autonomous navigation algorithms for complex environments. However, the direct application of RL policies trained in simulation to real-world scenarios often faces challenges due to the reality gap. This paper proposes a two-stage system incorporating a segmentation strategy and a bird’s-eye-view (BEV) representation to mitigate the domain gap between simulation and reality. In the first stage, the segmentation transforms sensor data into a simplified and interpretable representation of the surrounding area, facilitating transferability across different deployments. In the second stage, the agent navigates through the BEV map, which can be trained using a vectorized simulation environment---a setup that runs multiple parallel instances of the environment to provide a wide range of training scenarios. This vectorization enables rapid exposure to varied environmental conditions, thereby accelerating and diversifying the training of a deep RL agent to achieve optimal navigation behaviors while maintaining high-speed, in-bound trajectories. The segmentation is crucial because it supports generalization of the learned policy across different robotic platforms. The contribution of this paper lies in combining real-time semantic segmentation with a bird’s-eye-view navigation policy, resulting in a transferable and scalable framework for real-world deployment of RL-based navigation agents. Experimental results demonstrate that agents trained with this methodology exhibit robust navigation performance and adaptability in both simulated and real-world environments, validating the efficacy of combining vectorized simulation with real-world segmentation for practical robotic navigation.

Yue Fang, Yuxin Guo, Jiaran Gao, Hongxin Ding, Xinke Jiang, Weibin Liao, Yongxin Xu, Yinghao Zhu, Zhibang Yang, Liantao Ma 等

Improving large language models (LLMs) for electronic health record (EHR) reasoning is essential for enabling accurate and generalizable clinical predictions. While LLMs excel at medical text understanding, they underperform on EHR-based prediction tasks due to challenges in modeling temporally structured, high-dimensional data. Existing approaches often rely on hybrid paradigms, where LLMs serve merely as frozen prior retrievers while downstream deep learning (DL) models handle prediction, failing to improve the LLM’s intrinsic reasoning capacity and inheriting the generalization limitations of DL models. To this end, we propose EAG-RL, a novel two-stage training framework designed to intrinsically enhance LLMs’ EHR reasoning ability through expert attention guidance, where expert EHR models refer to task-specific DL models trained on EHR data. Concretely, EAG-RL first constructs high-quality, stepwise reasoning trajectories using expert-guided Monte Carlo Tree Search to effectively initialize the LLM’s policy. Then, EAG-RL further optimizes the policy via reinforcement learning by aligning the LLM’s attention with clinically salient features identified by expert EHR models. Extensive experiments on two real-world EHR datasets show that EAG-RL improves the intrinsic EHR reasoning ability of LLMs by an average of 14.62%, while also enhancing robustness to feature perturbations and generalization to unseen clinical domains. These results demonstrate the practical potential of EAG-RL for real-world deployment in clinical prediction tasks.

Yiming Wang, Kaiyan Zhao, Borong Zhang, Yan Li, Leong Hou U

Reinforcement learning (RL) has achieved promising results in continuous control tasks, where efficient exploration of the state space is crucial for success. However, many recent RL approaches still struggle with sample inefficiency and insufficient exploration for long-horizon tasks, particularly in environments characterized by high-dimensional and complex state spaces. To address these challenges, we propose a novel exploration framework, Latent State Predictive Exploration (LSPE). The core idea behind LSPE is to endow the agent with a form of ``foresight" to enhance exploration in long-horizon settings. Specifically, LSPE employs a state encoder to learn compact latent representations from high-dimensional visual observations, effectively filtering out irrelevant or noisy information. To further enrich and stabilize these representations, we incorporate a diffusion-based self-predictive module that enforces temporal consistency by predicting future states, thereby improving both exploration and downstream predictive control. Additionally, we introduce an Exploration Reward Function (ERF) that explicitly encourages the agent to visit novel latent states. This reward signal promotes more efficient and scalable exploration in complex environments. We evaluate LSPE across a diverse set of challenging long-horizon navigation and manipulation tasks, spanning simulation environments such as Habitat and Robosuite, as well as deployment on a real robot in a **physical indoor environment**. Experimental results show that LSPE substantially enhances exploration efficiency and scales effectively to complex, high-dimensional tasks.

Alonso Granados, Jason Pacheco

Model-free deep reinforcement learning (RL) algorithms have achieved tremendous success on a range of challenging tasks. However, safety concerns remain when these methods are deployed on real-world applications, necessitating risk-aware agents. A common utility for learning such risk-aware agents is the entropic risk measure, but current policy gradient methods optimizing this measure must perform high-variance and numerically unstable updates. As a result, existing risk-sensitive model-free approaches are limited to simple tasks and tabular settings. In this paper, we provide a comprehensive theoretical justification for policy gradient methods on the entropic risk measure, including on- and off-policy gradient theorems for the stochastic and deterministic policy settings. Motivated by theory, we propose risk-sensitive exponential actor-critic (rsEAC), an off-policy model-free approach that incorporates novel procedures to avoid the explicit representation of exponential value functions and their gradients, and optimizes its policy w.r.t. the entropic risk measure. In this way, we show that rsEAC produces more numerically stable updates compared to existing approaches and reliably learns risk-sensitive policies in challenging risky variants of continuous tasks in MuJoCo.

Jiejun Tan, Zhicheng Dou, Yan Yu, Jiehan Cheng, Lifeng Liu, Jian Xie, Jirong Wen

Recently, large reasoning models have demonstrated strong mathematical and coding abilities, and deep search leverages their reasoning capabilities in challenging information retrieval tasks. Existing deep search works are generally limited to a single knowledge source, either local or the Web. However, enterprises often require private deep search systems that can leverage search tools over both local and the Web corpus. Simply training an agent equipped with multiple search tools using flat reinforcement learning (RL) is a straightforward idea, but it has problems such as low training data efficiency and poor mastery of complex tools. To address the above issue, we propose a hierarchical agentic deep search framework, HierSearch, trained with hierarchical RL. At the low level, a local deep search agent and a Web deep search agent are trained to retrieve evidence from their corresponding domains. At the high level, a planner agent coordinates low-level agents and provides the final answer. Moreover, to prevent direct answer copying and error propagation, we design a knowledge refiner that filters out hallucinations and irrelevant evidence returned by low-level agents. Experiments show that HierSearch achieves better performance compared to flat RL, and outperforms various deep search and multi-source retrieval-augmented generation baselines in six benchmarks across general, finance, and medical domains.

Jiancong Xie, Wentao Wei, Chi Zhang, Jiahua Rao, Yuedong Yang

Drug-drug interaction (DDI) prediction is pivotal for drug safety and clinical decision-making. Recently, subgraph-based methods utilizing knowledge graphs (KGs) and domain information have achieved promising results by extracting informative subgraphs for DDI prediction. However, existing subgraph extraction methods are typically coarse-grained and nonspecific, facing two key limitations: First, they are constrained by the vast and noisy nature of real-world KGs, making it challenging to identify the most informative substructures from the massive space of candidate subgraphs. Second, current methods often fail to exploit the molecular structural specificity of drugs to selectively extract relevant subgraphs, lacking effective integration of molecular structure information with knowledge graph context. To address these challenges, we propose RISE-DDI, a novel framework for Reinforced-based Informative Subgraph Extraction approach for drug-drug interaction prediction. Specifically, RISE-DDI formulates the subgraph extraction as a Markov Decision Process (MDP) and leverages a deep reinforcement learning (RL) agent to dynamically and adaptively extract the most informative and context-specific subgraphs for each drug pair. The agent is guided by a learnable structure-aware reward model that considers both the topological context from the knowledge graph and the molecular features of the drug pairs, thereby encouraging the selection of subgraphs that are both structurally relevant and biologically informative. Extensive experiments on DDI benchmark datasets demonstrate that our method outperforms state-of-the-art baselines in both transductive and inductive scenarios, achieving improvements of up to 20%. Furthermore, visualization analyses of the extracted subgraphs highlight the interpretability of our model, providing insights into the underlying mechanisms of drug interactions.

Xiaodong Wang, Zhirong Wu, Langling Huang, Yuxi Zheng, Peixi Peng

Multimodal Large Language Models (MLLMs) have made great progress in video understanding tasks. However, when it comes to understanding complex or lengthy videos, MLLMs tend to overlook details or produce hallucinations. To alleviate these issues, recent work has attempted to leverage reinforcement learning (RL) to boost models' deep linguistic reasoning of complex videos. But these methods have two main problems: First, the RL framework they used has unstable training, high training costs, and is difficult to train satisfactory video reasoning models; Second, the linguistic reasoning process is difficult to guarantee the reliability of visual information. To alleviate these problems, we propose to use multimodal elements for reasoning, and we design a novel framework to build and enhance versatile video reasoning capabilities on MLLMs. We carefully design a multi-task cold start and multi-task reinforcement learning to improve the model's visual perception and proficiency in multiple capabilities. In the inference phase, we leverage multimodal reasoning and dynamic sampling to further improve the performance. We verified the efficiency of the framework on a base MLLM (Qwen2-VL-7B-Base). Through cold-start with 3k data and reinforcement learning training with 5k data, combined with inference design, our final model significantly outperforms the base model on seven public video benchmarks, even surpassing and approaching the state-of-the-art Instruct Models such as Qwen2.5-VL-7B-Instruct trained with large-scale data. Our code will be available at https://github.com/Wang-Xiaodong1899/VideoReasoner.

Alexis Jensen, Pei Xu, Ioannis Karamouzas, Charles Pontonnier, Julien Pettré

We present a physics-based method for simulating full-body agents that recover balance by stepping or applying contact forces after being perturbed in dense crowds. While traditional 2D crowd simulations focus on navigation and social interactions in moderately dense settings, interactions in highly dense environments are predominantly physical, leading to push propagation, falls, and potential hazards. Existing models cannot capture how forces are transmitted through the body at the limb level. To address this, we use physics-based anthropomorphic simulations combined with a two-stage deep reinforcement learning framework. In the first stage, a policy is pre-trained using reference motion data and general balance rewards, enabling agents to handle a wide range of perturbations. In the second stage, an adaptive phase refines the policy to allow socially aware interactions, using hand contacts for stabilization guided by an online heuristic targeting neighbors' shoulders based on mechanical efficiency and collision risk. Ablation studies validate the training framework and reward components, and simulations reproduce trends observed in empirical studies of push propagation. Our method scales to large populations, offering new opportunities to study safety and collective behavior in dense crowds.

Yuan Wang, Xiang Li, Yali Li, Xuege Hou, Shengjin Wang

Unified interpreting and synthesizing human behaviors within 3D environments is vital for advancing spatial intelligence and humanoid robotics. Despite recent advancements (e.g., HSI-GPT), two fundamental capabilities expected of a unified model--understanding and generation--still lag behind specialist models. This is primarily due to 1) single-granularity codebook overemphasizes low-frequency motion details while neglecting motion semantics, 2) limited decoding capacity of the motion detokenizer which restricts the fidelity of human-scene interactions, 3) only relying on supervised fine-tuning (SFT) failing to capture high-level motion semantics and logical reasoning with an end-to-end mapping. To this issue, we develop HSI-GPT2--a reasoning-enhanced, dual-granularity motion-representational large Scene-Motion-Language model, powered by reinforcement learning (RL) with Chain-of-Thought (CoT) reasoning. First, HSI-GPT2 introduces a Dual-granularity Motion Tokenizer, DMoTok, which jointly preserves both fine-grained motion details and text-aligned motion semantics for various HSI-related tasks. Further, a motion diffusion decoder functions as a motion detokenizer, translating deep semantics and detailed features of LLMs into physically grounded human motions. Finally, we curate a Motion Chain-of-Thought (MoCoT) data engine and extend a Group Relative Policy Optimization (GRPO) paradigm to execute long-horizon and compositionallyrich commands. Results on standard HSI benchmarks confirm the clear superiority of HSI-GPT2 in enhancing interaction quality, semantic alignment, behavioral diversity, and generalization to unseen 3D scenes.

Uddin Md. Borhan, Arif Raza, Zhiliang Lin, Lu Wang, Jianqiang Li, Jie Chen

End-to-End (E2E) Reinforcement Learning (RL) for autonomous driving still struggles with safety and generalization under distribution shift, as perception-heavy encoders, sparse rewards, and ad hoc uncertainty handling yield brittle closed-loop behavior. This work introduces a unified Deep RL (DRL) framework built around a control-layer reliability interface where the same uncertainty signal informs relational attention, gates policy entropy, and regularizes transfer alignment. An ego-centric relational graph encodes agent influence via uncertainty-weighted attention over kinematics, lane geometry, and semantics, producing a compact control state. A multi-objective differentiable reward shapes safety, progress, and comfort with an uncertainty term. Aleatoric and epistemic uncertainty, captured through per-edge heteroscedastic variance and a critic ensemble, modulate policy entropy for risk-aware exploration. A causal-semantic transfer objective aligns actions, attention, and uncertainty statistics across domains with meta-learned initialization for few-shot adaptation. In closed-loop urban driving across varied towns, traffic, and weather, the framework improves success rate, reduces infractions, and achieves higher time-to-conflict combined with lower lateral deviation over strong baselines.

Sitong Wu, Haoru Tan, Bin Xia, Xichen Zhang, Jingyao Li, Shaofeng Zhang, Xiaojuan Qi, Bei Yu, Jiaya Jia

In this paper, we propose an extremely efficient, training-free method to extract token-level reward signals directly from an existing deep reward model. Our core idea is to attribute the overall process reward to individual tokens by estimating each token's influence. This influence is defined as the change in the final macroscopic reward (e.g., the process reward) when a token is replaced with a semantically null token. Naively calculating this influence is computationally infeasible, requiring N forward passes through the PRM for an N-token sequence. We overcome this bottleneck by proposing a highly efficient gradient-based estimator. Specifically, we use a first-order Taylor approximation, which simplifies the influence calculation to the inner product of the difference between the token embedding and the null token embedding, and the gradient of the reward with respect to the token embedding. This requires only a single forward and backward pass. The resulting token-level rewards enable standard RL algorithms to perform precise credit assignment without requiring additional reward model training. Experiments on challenging reasoning benchmarks demonstrate that our method substantially improves policy optimization efficiency and enhances the generalization of LLM reasoning capabilities. Our P2T outperforms the outcome reward by +4.9% on MathVista for Qwen2.5-VL-7B-Instruct, and +11.5% on AIME24 for Qwen2.5-Math-7B. The code is available at: https://github.com/JIA-Lab-research/P2T.

Qingfei Zhao, Ruobing Wang, Dingling Xu, Daren Zha, Ma Bowen, Zhichun Wang, Shijie Jia, Limin Liu, Xin Wang

Large language models (LLMs) have notably progressed in multi-step and long-chain reasoning. However, extending their reasoning capabilities to encompass deep interactions with search remains a non-trivial challenge, as models often fail to identify optimal reasoning–search interaction trajectories, resulting in suboptimal responses. We propose R-Search, a novel reinforcement learning framework for Reasoning–Search integration, designed to enable LLMs to autonomously execute multi-step reasoning with deep search interaction, and learn optimal reasoning–search interaction trajectories via multi-reward signals, improving response quality in complex logic- and knowledge-intensive tasks. R-Search guides the LLM to dynamically decide when to search or reason, while globally integrating key evidence to enhance deep knowledge interaction between reasoning and search. During RL training, R-Search provides multi-type rewards to jointly optimize the reasoning–search trajectory. Experiments on seven datasets show that R-Search significantly outperforms mainstream RAG baselines.

Shilin Tang, Zunyi Yin, Xuefeng Liang, Guanghui Shi, Song Tong, Chen Guangyu

LLMs have shown promise in mental health counseling, but existing models are limited to surface-level empathy or predefined therapeutic procedures and lack the ability to actively explore the root causes of psychological distress. Inspired by case conceptualization, we formalize counseling as the online reconstruction of a client’s underlying causal graph through multi-turn dialogue. To this end, we propose TRACE, a two-phase reinforcement learning framework. It implements a causal-graph-driven reward scheme across two phases: an exploration phase that rewards the causal graph reconstruction following a surface-to-deep path, and an intervention phase that rewards targeted restructuring of irrational beliefs. Extensive experiments show that TRACE outperforms existing models, enabling causal-chain-aware psychological intervention beyond surface-level empathy.