In this work, we study the problem of offline safe imitation learning (IL). In many real-world settings, online interactions can be risky, and accurately specifying the reward and the safety cost information at each timestep can be difficult. However, it is often feasible to collect trajectories reflecting undesirable or risky behavior, implicitly conveying the behavior the agent should avoid. We refer to these trajectories as non-preferred trajectories. Unlike standard IL, which aims to mimic demonstrations, our agent must also learn to avoid risky behavior using non-preferred trajectories. In this paper, we propose a novel approach, SafeMIL, to learn a parameterized cost that predicts if the state-action pair is risky via Multiple Instance Learning. The learned cost is then used to avoid non-preferred behaviors, resulting in a policy that prioritizes safety. We empirically demonstrate that our approach can learn a safer policy that satisfies cost constraints without degrading the reward performance, thereby outperforming several baselines.

Hard negatives are essential for training effective retrieval models. Hard-negative mining typically relies on ranking documents using cross-encoders or static embedding models based on similarity metrics such as cosine distance. Hard negative mining becomes challenging for biomedical and scientific domains due to the difficulty in distinguishing between source and hard negative documents. However, referenced documents naturally share contextual relevance with the source document but are not duplicates, making them well-suited as hard negatives. In this work, we propose BiCA: Biomedical Dense Retrieval with Citation-Aware Hard Negatives, an approach for hard-negative mining by utilizing citation links in 20,000 PubMed articles for improving a domain-specific small dense retriever. We fine-tune the GTE_small and GTE_Base models using these citation-informed negatives and observe consistent improvements in zero-shot dense retrieval using nDCG@10 for both in-domain and out-of-domain tasks on BEIR and outperform baselines on long-tailed topics in LoTTE using Success@5. Our findings highlight the potential of leveraging document link structure to generate highly informative negatives, enabling state-of-the-art performance with minimal fine-tuning and demonstrating a path towards highly data-efficient domain adaptation.