Author name cluster

Lei Song

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

20 papers

1 author row

AAAI Conference 2025 Conference Paper

Exploring Rationale Learning for Continual Graph Learning

Lei Song
Jiaxing Li
Qinghua Si
Shihan Guan
Youyong Kong

Catastrophic forgetting poses a significant challenge for graph neural networks in continuously updating their knowledge base with data streams. To address this issue, much of the research has focused on node-level continual learning using parameter regularization or rehearsal-based strategies, while little attention given to graph-level tasks. Furthermore, current paradigms for continual graph learning may inadvertently capture spurious correlations for specific tasks through shortcuts, thereby exacerbating the forgetting of previous knowledge when new tasks are introduced. To tackle these challenges, we propose a novel paradigm, Rationale Learning GNN (RL-GNN), for graph-level continual graph learning. Specifically, we harness the invariant learning principle to incorporate environmental interventions into both the current and historical distributions, aiming to uncover rationales by minimizing empirical risk across all environments. The rationale serves as the sole factor guiding the learning process. Therefore, continual graph learning is redefined as capturing these invariant rationales within task sequences, alleviating catastrophic forgetting caused by spurious features. Extensive experiments on real-world datasets with varying task lengths demonstrate the effectiveness of our RL-GNN in continuous knowledge assimilation and reduction of catastrophic forgetting.

PDF Details DOI

AAAI Conference 2025 Conference Paper

HePa: Heterogeneous Graph Prompting for All-Level Classification Tasks

Jia Jinghong
Lei Song
Jiaxing Li
Youyong Kong

Heterogeneous graphs, which are common in real-world downstream tasks, have recently sparked a wave of research interest. The performance of end-to-end heterogeneous graph neural networks (HGNNs) greatly relies on supervised training for specific tasks. To reduce the labeling cost, the "pretrain-finetune" paradigm has been widely adopted, but it leads to a knowledge gap between the pre-trained model and downstream tasks. In an effort to address this gap, the "pretrain-prompt" paradigm has emerged as a promising approach. This involves fine-tuning randomly initialized learnable vectors in downstream tasks. However, this approach may result in an insufficient representation of downstream task features. Existing techniques for heterogeneous graph prompting restructure the heterogeneous graph to align with the homogeneous graph prompting scheme. This can potentially introduce the same limitations as homogeneous graph prompt learning. In this paper, we propose HePa, short for Heterogeneous Graph Prompting for all-level classification tasks. It not only includes a unified prompt template-graph adapted for heterogeneous graphs but also introduces a novel pre-prompt token optimized during the pre-training phase to convey task information downstream. With these designs, HePa can complete all levels of classification tasks toward few-shot scenarios while activating in-context learning. Finally, we conducted a comprehensive experimental analysis of HePa on three benchmark datasets.

PDF Details DOI

EAAI Journal 2025 Journal Article

Joint depth-segmentation learning with segment priors for non-contact seedling height and stem thickness estimation

Lei Song
Bo Jiang
Huaibo Song

To achieve precise and rapid computation of seedling height and stem diameter — key phenotypic traits for monitoring seedling growth and selecting superior varieties — this study proposes a SAM-Integrated Adaptive Fusion Depth Network (SAFD-Net). SAFD-Net integrates segmentation masks generated by Segment Anything Model (SAM) with an Adaptive Prior Extraction (APE) module to produce priors focused on individual seedling characteristics, and it fuses these priors with deep features through an Adaptive Attention Fusion (AAF) module. A Local Depth Generation (LDG) module refines depth details to improve estimation accuracy, and an Adaptive Multi-scale Fusion (AMF) module merges LDG outputs at different scales to produce high-precision depth maps. From these maps, seedling region depth, pixel height, and pixel stem diameter are extracted to compute actual seedling height and stem diameter. Comparisons with various depth estimation networks demonstrate that SAFD-Net outperforms existing models in both depth estimation and seedling measurement. Experimental evaluations on seedlings from three crops with distinct phenotypic characteristics further show that the method maintains high accuracy under varying shooting distances, lighting conditions, multiple targets, and tilt angles, offering a novel approach for phenotypic monitoring during seedling cultivation. Code is released at https: //github. com/Songlei7664/SAFD-Net.

Details DOI

TMLR Journal 2025 Journal Article

Knowing What Not to Do: Leverage Language Model Insights for Action Space Pruning in Multi-agent Reinforcement Learning

Zhihao Liu
Xianliang Yang
Zichuan Liu
Yifan Xia
Wei Jiang
Yuanyu Zhang
Lijuan Li
Guoliang Fan

Multi-agent reinforcement learning (MARL) is employed to develop autonomous agents that can learn to adopt cooperative or competitive strategies within complex environments. However, the linear increase in the number of agents leads to a combinatorial explosion of the action space, which always results in algorithmic instability, difficulty in convergence, or entrapment in local optima. While researchers have designed a variety of effective algorithms to compress the action space, these methods also introduce new challenges, such as the need for manually designed prior knowledge or reliance on the structure of the problem, which diminishes the applicability of these techniques. In this paper, we introduce \textbf{E}volutionary action \textbf{SPA}ce \textbf{R}eduction with \textbf{K}nowledge (eSpark), an exploration function generation framework driven by large language models (LLMs) to boost exploration and prune unnecessary actions in MARL. Using just a basic prompt that outlines the overall task and setting, eSpark is capable of generating exploration functions in a zero-shot manner, identifying and pruning redundant or irrelevant state-action pairs, and then achieving autonomous improvement from policy feedback. In reinforcement learning tasks involving inventory management and traffic light control encompassing a total of 15 scenarios, eSpark consistently outperforms the combined MARL algorithm in all scenarios, achieving an average performance gain of 34.4% and 9.9% in the two types of tasks respectively. Additionally, eSpark has proven to be capable of managing situations with a large number of agents, securing a 29.7% improvement in scalability challenges that featured over 500 agents. The code can be found in https://github.com/LiuZhihao2022/eSpark.

PDF Details

NeurIPS Conference 2025 Conference Paper

NaDRO: Leveraging Dual-Reward Strategies for LLMs Training on Noisy Data

Haolong Qian
Xianliang Yang
Ling Zhang
Lei Song
Jiang Bian
Chun Yuan

Group Relative Policy Optimization (GRPO) fine-tuning has demonstrated significant enhancements in reasoning tasks. However, it often relies on high quality labeled dataset, which is typically difficult to obtain. To address this challenge, we introduce \textbf{N}oise-\textbf{A}ware \textbf{D}ual-\textbf{R}eward \textbf{O}ptimization (\textbf{NaDRO}) to effectively enhances the training of Large Language Models (LLMs) under noisy or ambiguous supervision. NaDRO operates through two key components: \textbf{(1) Preference-based Outcome Reward (POR)}, which makes a principled bias-variance tradeoff, reducing training variance by learning from robust preference rankings instead of overfitting to single-best estimates; and \textbf{(2) Context Perception Reward (CPR) mechanism}, which ensures that LLMs conduct necessary qualitative assessment of the current problem state to foster deeper situational understanding prior to decision-making. To validate our approach in a realistic decision-making testbed, we model classic combinatorial optimization problems like the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) as Markov Decision Processes, generating training data via cost-limited exploration. Our results demonstrate that the fine-tuned Qwen 7B and Llama 3. 1-8B models achieve statistically robust performance, significantly outperforming leading LLM baselines and standard fine-tuning methods on these complex benchmarks. Code is released at \url{https: //github. com/microsoft/HeurAgenix/tree/NaDRO}.

PDF Details

IJCAI Conference 2025 Conference Paper

Reinforced In-Context Black-Box Optimization

Lei Song
Chen-Xiao Gao
Ke Xue
Chenyang Wu
Dong Li
Jianye Hao
Zongzhang Zhang
Chao Qian

Black-Box Optimization (BBO) has found successful applications in many fields of science and engineering. Recently, there has been a growing interest in meta-learning particular components of BBO algorithms to speed up optimization and get rid of tedious hand-crafted heuristics. As an extension, learning the entire algorithm from data requires the least labor from experts and can provide the most flexibility. In this paper, we propose RIBBO, a method to reinforce-learn a BBO algorithm from offline data in an end-to-end fashion. RIBBO employs expressive sequence models to learn the optimization histories produced by multiple behavior algorithms and tasks, leveraging the in-context learning ability of large models to extract task information and make decisions accordingly. Central to our method is to augment the optimization histories with regret-to-go tokens, which are designed to represent the performance of an algorithm based on cumulative regret over the future part of the histories. The integration of regret-to-go tokens enables RIBBO to automatically generate sequences of query points that are positively correlated to the user-desired regret, verified by its universally good empirical performance on diverse problems, including BBO benchmark, hyper-parameter optimization, and robot control problems.

PDF Details DOI

IJCAI Conference 2024 Conference Paper

Diversification of Adaptive Policy for Effective Offline Reinforcement Learning

Yunseon Choi
Li Zhao
Chuheng Zhang
Lei Song
Jiang Bian
Kee-Eung Kim

Offline Reinforcement Learning (RL) aims to learn policies from pre-collected datasets that capture only a subset of the environment's dynamics. The predominant approach has been to solve a constrained optimization formulation, which ensures that the policy visits state-action pairs within the support of the offline dataset. However, this approach has limited the ability to make decisions when the agent faces unknown parts of the environment at deployment time. To address the challenge of decision-making in out-of-support regions, model-based Bayes-adaptive approaches have been proposed by considering all dynamics models that could potentially be the true environment. Since it is generally infeasible to compute the posterior of all dynamics models based on the offline dataset, these approaches usually approximate the posterior by using a finite ensemble of highly probable dynamics models. Hence, the diversity of these models is the key to obtaining good policies. In this work, we propose MoDAP (Model-based Diverse Adaptive Policy Learning), an algorithm to enable the adaptive policy to make informed decisions in previously unexplored states. MoDAP adopts an iterative strategy that simultaneously training the policy and dynamics models. The policy optimization seeks to maximize expected returns across dynamics models, while the dynamics models are trained to promote policy diversification through the proposed information-theoretic objective. We evaluate MoDAP through experiments on the D4RL and NeoRL benchmarks, showcasing its performance superiority over state-of-the-art algorithms.

PDF Details DOI

TMLR Journal 2024 Journal Article

Mildly Constrained Evaluation Policy for Offline Reinforcement Learning

Linjie Xu
zhengyao jiang
Jinyu Wang
Lei Song
Jiang Bian

Offline reinforcement learning (RL) methodologies enforce constraints on the policy to adhere closely to the behavior policy, thereby stabilizing value learning and mitigating the selection of out-of-distribution (OOD) actions during test time. Conventional approaches apply identical constraints for both value learning and test time inference. However, our findings indicate that the constraints suitable for value estimation may in fact be excessively restrictive for action selection during test time. To address this issue, we propose a Mildly Constrained Evaluation Policy (MCEP) for test time inference with a more constrained target policy for value estimation. Since the target policy has been adopted in various prior approaches, MCEP can be seamlessly integrated with them as a plug-in. We instantiate MCEP based on TD3BC (Fujimoto & Gu, 2021), AWAC (Nair et al., 2020) and DQL (Wang et al., 2023) algorithms. The empirical results on D4RL MuJoCo locomotion, high-dimensional humanoid and a set of 16 robotic manipulation tasks show that the MCEP brought significant performance improvement on classic offline RL methods and can further improve SOTA methods. The codes are open-sourced at \url{https://github.com/egg-west/MCEP}.

PDF Details

NeurIPS Conference 2024 Conference Paper

Monte Carlo Tree Search based Space Transfer for Black Box Optimization

Shukuan Wang
Ke Xue
Lei Song
Xiaobin Huang
Chao Qian

Bayesian optimization (BO) is a popular method for computationally expensive black-box optimization. However, traditional BO methods need to solve new problems from scratch, leading to slow convergence. Recent studies try to extend BO to a transfer learning setup to speed up the optimization, where search space transfer is one of the most promising approaches and has shown impressive performance on many tasks. However, existing search space transfer methods either lack an adaptive mechanism or are not flexible enough, making it difficult to efficiently identify promising search space during the optimization process. In this paper, we propose a search space transfer learning method based on Monte Carlo tree search (MCTS), called MCTS-transfer, to iteratively divide, select, and optimize in a learned subspace. MCTS-transfer can not only provide a well-performing search space for warm-start but also adaptively identify and leverage the information of similar source tasks to reconstruct the search space during the optimization process. Experiments on synthetic functions, real-world problems, Design-Bench and hyper-parameter optimization show that MCTS-transfer can demonstrate superior performance compared to other search space transfer methods under different settings. Our code is available at \url{https: //github. com/lamda-bbo/mcts-transfer}.

PDF Details DOI

EAAI Journal 2024 Journal Article

Multi-granularity siamese transformer-based change detection in remote sensing imagery

Lei Song
Min Xia
Yao Xu
Liguo Weng
Kai Hu
Haifeng Lin
Ming Qian

In recent years, Convolutional Neural Networks (CNNs) have promoted the prosperity of Change Detection (CD). However, due to the intrinsic property of convolution kernel, this method cannot effectively model the long-distance dependency. The emergence of Vision Transformer (ViT) brings a new way to solve the problem. Based on ViT architecture, a novel Multi-Granularity remote sensing image Change Detection model (MGCDT) is proposed in this paper. We cascade several Local–Global Siamese Transformer (LGST) as backbone to extract local and global semantic discriminative features. In order to solve the serious problem of false detection and missing detection of feature boundary, a plug-and-play High Frequency Enhancement Unit (HFE) is proposed to replace the inflexible U-shaped structure to optimize the detection boundary. Considering the problem of multi-scale modeling of ground objects, a Multi-Scale Fusion Attention Unit (MSFA) is proposed, which integrates the flow of multi-scale information into the calculation process of self-attention. Finally, we utilize a Deep Feature Guidance Unit (DFG) to optimize the shallow detailed feature information. Extensive experiments show that, considering multi-granularity information, MGCDT outperforms the existing change detection algorithms on four remote sensing image change detection datasets.

Details DOI

NeurIPS Conference 2024 Conference Paper

Protecting Your LLMs with Information Bottleneck

Zichuan Liu
Zefan Wang
Linjie Xu
Jinyu Wang
Lei Song
Tianchun Wang
Chunlin Chen
Wei Cheng

The advent of large language models (LLMs) has revolutionized the field of natural language processing, yet they might be attacked to produce harmful content. Despite efforts to ethically align LLMs, these are often fragile and can be circumvented by jailbreaking attacks through optimized or manual adversarial prompts. To address this, we introduce the Information Bottleneck Protector (IBProtector), a defense mechanism grounded in the information bottleneck principle, and we modify the objective to avoid trivial solutions. The IBProtector selectively compresses and perturbs prompts, facilitated by a lightweight and trainable extractor, preserving only essential information for the target LLMs to respond with the expected answer. Moreover, we further consider a situation where the gradient is not visible to be compatible with any LLM. Our empirical evaluations show that IBProtector outperforms current defense methods in mitigating jailbreak attempts, without overly affecting response quality or inference speed. Its effectiveness and adaptability across various attack methods and target LLMs underscore the potential of IBProtector as a novel, transferable defense that bolsters the security of LLMs without requiring modifications to the underlying models.

PDF Details DOI

AAAI Conference 2024 Conference Paper

Stochastic Bayesian Optimization with Unknown Continuous Context Distribution via Kernel Density Estimation

Xiaobin Huang
Lei Song
Ke Xue
Chao Qian

Bayesian optimization (BO) is a sample-efficient method and has been widely used for optimizing expensive black-box functions. Recently, there has been a considerable interest in BO literature in optimizing functions that are affected by context variable in the environment, which is uncontrollable by decision makers. In this paper, we focus on the optimization of functions' expectations over continuous context variable, subject to an unknown distribution. To address this problem, we propose two algorithms that employ kernel density estimation to learn the probability density function (PDF) of continuous context variable online. The first algorithm is simpler, which directly optimizes the expectation under the estimated PDF. Considering that the estimated PDF may have high estimation error when the true distribution is complicated, we further propose the second algorithm that optimizes the distributionally robust objective. Theoretical results demonstrate that both algorithms have sub-linear Bayesian cumulative regret on the expectation objective. Furthermore, we conduct numerical experiments to empirically demonstrate the effectiveness of our algorithms.

PDF Details DOI

AAAI Conference 2023 Conference Paper

H-TSP: Hierarchically Solving the Large-Scale Traveling Salesman Problem

Xuanhao Pan
Yan Jin
Yuandong Ding
Mingxiao Feng
Li Zhao
Lei Song
Jiang Bian

We propose an end-to-end learning framework based on hierarchical reinforcement learning, called H-TSP, for addressing the large-scale Traveling Salesman Problem (TSP). The proposed H-TSP constructs a solution of a TSP instance starting from the scratch relying on two components: the upper-level policy chooses a small subset of nodes (up to 200 in our experiment) from all nodes that are to be traversed, while the lower-level policy takes the chosen nodes as input and outputs a tour connecting them to the existing partial route (initially only containing the depot). After jointly training the upper-level and lower-level policies, our approach can directly generate solutions for the given TSP instances without relying on any time-consuming search procedures. To demonstrate effectiveness of the proposed approach, we have conducted extensive experiments on randomly generated TSP instances with different numbers of nodes. We show that H-TSP can achieve comparable results (gap 3.42% vs. 7.32%) as SOTA search-based approaches, and more importantly, we reduce the time consumption up to two orders of magnitude (3.32s vs. 395.85s). To the best of our knowledge, H-TSP is the first end-to-end deep reinforcement learning approach that can scale to TSP instances of up to 10000 nodes. Although there are still gaps to SOTA results with respect to solution quality, we believe that H-TSP will be useful for practical applications, particularly those that are time-sensitive e.g., on-call routing and ride hailing service.

PDF Details DOI

AAAI Conference 2023 Conference Paper

Pointerformer: Deep Reinforced Multi-Pointer Transformer for the Traveling Salesman Problem

Yan Jin
Yuandong Ding
Xuanhao Pan
Kun He
Li Zhao
Tao Qin
Lei Song
Jiang Bian

Traveling Salesman Problem (TSP), as a classic routing optimization problem originally arising in the domain of transportation and logistics, has become a critical task in broader domains, such as manufacturing and biology. Recently, Deep Reinforcement Learning (DRL) has been increasingly employed to solve TSP due to its high inference efficiency. Nevertheless, most of existing end-to-end DRL algorithms only perform well on small TSP instances and can hardly generalize to large scale because of the drastically soaring memory consumption and computation time along with the enlarging problem scale. In this paper, we propose a novel end-to-end DRL approach, referred to as Pointerformer, based on multi-pointer Transformer. Particularly, Pointerformer adopts both reversible residual network in the encoder and multi-pointer network in the decoder to effectively contain memory consumption of the encoder-decoder architecture. To further improve the performance of TSP solutions, Pointerformer employs a feature augmentation method to explore the symmetries of TSP at both training and inference stages as well as an enhanced context embedding approach to include more comprehensive context information in the query. Extensive experiments on a randomly generated benchmark and a public benchmark have shown that, while achieving comparative results on most small-scale TSP instances as state-of-the-art DRL approaches do, Pointerformer can also well generalize to large-scale TSPs.

PDF Details DOI

NeurIPS Conference 2022 Conference Paper

Monte Carlo Tree Search based Variable Selection for High Dimensional Bayesian Optimization

Lei Song
Ke Xue
Xiaobin Huang
Chao Qian

Bayesian optimization (BO) is a class of popular methods for expensive black-box optimization, and has been widely applied to many scenarios. However, BO suffers from the curse of dimensionality, and scaling it to high-dimensional problems is still a challenge. In this paper, we propose a variable selection method MCTS-VS based on Monte Carlo tree search (MCTS), to iteratively select and optimize a subset of variables. That is, MCTS-VS constructs a low-dimensional subspace via MCTS and optimizes in the subspace with any BO algorithm. We give a theoretical analysis of the general variable selection method to reveal how it can work. Experiments on high-dimensional synthetic functions and real-world problems (e. g. , MuJoCo locomotion tasks) show that MCTS-VS equipped with a proper BO optimizer can achieve state-of-the-art performance.

PDF Details

JBHI Journal 2021 Journal Article

Bridging the Gap Between 2D and 3D Contexts in CT Volume for Liver and Tumor Segmentation

Lei Song
Haoqian Wang
Z. Jane Wang

Automatic liver and tumor segmentation remain a challenging topic, which subjects to the exploration of 2D and 3D contexts in CT volume. Existing methods are either only focus on the 2D context by treating the CT volume as many independent image slices (but ignore the useful temporal information between adjacent slices), or just explore the 3D context lied in many little voxels (but damage the spatial detail in each slice). These factors lead an inadequate context exploration together for automatic liver and tumor segmentation. In this paper, we propose a novel full-context convolution neural network to bridge the gap between 2D and 3D contexts. The proposed network can utilize the temporal information along the Z axis in CT volume while retaining the spatial detail in each slice. Specifically, a 2D spatial network for intra-slice features extraction and a 3D temporal network for inter-slice features extraction are proposed separately and then are guided by the squeeze-and-excitation layer that allows the flow of 2D context and 3D temporal information. To address the severe class imbalance issue in the CT volume and meanwhile improve the segmentation performance, a loss function consisting of weighted cross-entropy and jaccard distance is proposed. During the network training, the 2D and 3D contexts are learned jointly in an end-to-end way. The proposed network achieves competitive results on the Liver Tumor Segmentation Challenge (LiTS) and the 3D-IRCADB datasets. This method should be a new promising paradigm to explore the contexts for liver and tumor segmentation.

Details DOI

JBHI Journal 2020 Journal Article

An End-to-End Multi-Task Deep Learning Framework for Skin Lesion Analysis

Lei Song
Jianzhe Lin
Z. Jane Wang
Haoqian Wang

Automatic skin lesion analysis of dermoscopy images remains a challenging topic. In this paper, we propose an end-to-end multi-task deep learning framework for automatic skin lesion analysis. The proposed framework can perform skin lesion detection, classification, and segmentation tasks simultaneously. To address the class imbalance issue in the dataset (as often observed in medical image datasets) and meanwhile to improve the segmentation performance, a loss function based on the focal loss and the jaccard distance is proposed. During the framework training, we employ a three-phase joint training strategy to ensure the efficiency of feature learning. The proposed framework outperforms state-of-the-art methods on the benchmarks ISBI 2016 challenge dataset towards melanoma classification and ISIC 2017 challenge dataset towards melanoma segmentation, especially for the segmentation task. The proposed framework should be a promising computer-aided tool for melanoma diagnosis.

Details DOI

IJCAI Conference 2018 Conference Paper

Model Checking Probabilistic Epistemic Logic for Probabilistic Multiagent Systems

Chen Fu
Andrea Turrini
Xiaowei Huang
Lei Song
Yuan Feng
Lijun Zhang

In this work we study the model checking problem for probabilistic multiagent systems with respect to the probabilistic epistemic logic PETL, which can specify both temporal and epistemic properties. We show that under the realistic assumption of uniform schedulers, i. e. , the choice of every agent depends only on its observation history, PETL model checking is undecidable. By restricting the class of schedulers to be memoryless schedulers, we show that the problem becomes decidable. More importantly, we design a novel algorithm which reduces the model checking problem into a mixed integer non-linear programming problem, which can then be solved by using an SMT solver. The algorithm has been implemented in an existing model checker and experiments are conducted on examples from the IPPC competitions.

PDF Details

IJCAI Conference 2015 Conference Paper

A Simple Probabilistic Extension of Modal Mu-calculus

Wanwei Liu
Lei Song
Ji Wang
Lijun Zhang

Probabilistic systems are an important theme in AI domain. As the specification language, PCTL is the most frequently used logic for reasoning about probabilistic properties. In this paper, we present a natural and succinct probabilistic extension of µcalculus, another prominent logic in the concurrency theory. We study the relationship with PCTL. Surprisingly, the expressiveness is highly orthogonal with PCTL. The proposed logic captures some useful properties which cannot be expressed in PCTL. We investigate the model checking and satisfiability problem, and show that the model checking problem is in UP ∩co-UP, and the satisfiability checking can be decided via reducing into solving parity games. This is in contrast to PCTL as well, whose satisfiability checking is still an open problem.

PDF Details

IJCAI Conference 2015 Conference Paper

Planning for Stochastic Games with Co-Safe Objectives

Lei Song
Yuan Feng
Lijun Zhang

We consider planning problems for stochastic games with objectives specified by a branching-time logic, called probabilistic computation tree logic (PCTL). This problem has been shown to be undecidable if strategies with perfect recall, i. e. , history-dependent, are considered. In this paper, we show that, if restricted to co-safe properties, a subset of PCTL properties capable to specify a wide range of properties in practice including reachability ones, the problem turns to be decidable, even when the class of general strategies is considered. We also give an algorithm for solving robust stochastic planning, where a winning strategy is tolerant to some perturbations of probabilities in the model. Our result indicates that satisfiability of co-safe PCTL is decidable as well.

PDF Details