Multi-task offline safe reinforcement learning (RL) promises to learn a shared optimal safe policy from offline data across multiple tasks. This paradigm provides an effective means for the widespread application of RL in multi-task scenarios with high risk and interaction costs. However, the triple challenges of multi-tasking, safety constraints, and out-of-distribution (OOD) actions pose a significant hurdle for existing methods to ensure safety while maximizing reward returns. In this work, we propose a Conditional Diffusion model with Contextual Prompts (CDCP) to address these challenges. Concretely, we first rethink the requirements and challenges in current multi-task decision-making and control scenarios and establish the objectives of multi-task offline safe RL. Subsequently, we transform the multi-task constrained optimization problem into a conditional generation problem using the diffusion model. Based on this, we design a classifier-free guided cost-constraint strategy to provide flexible cost constraints and eliminate extrapolation errors from OOD actions via supervised learning. Additionally, we introduce a novel contextual prompting method to enhance multi-task representation accuracy and adaptability to unseen tasks. A gradient loss synchronization strategy is also introduced to eliminate gradient interference, improving training stability. Finally, extensive experiments demonstrate that the CDCP algorithm exhibits higher performance and safety in multi-task scenarios than the current state-of-the-art baseline methods. It meets different cost constraints without further training, providing a more flexible cost-constraint solution for the multi-task safe RL.

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