Reducing hallucinations in abstractive summarization remains a critical challenge for deploying language models (LMs) in real-world settings. In this work, we introduce a rewarddriven fine-tuning framework that explicitly optimizes for Entity Hallucination Index (EHI), a metric designed to quantify the presence, correctness, and grounding of named entities in generated summaries. Given a corpus of meeting transcripts, we first generate baseline summaries using a pre-trained LM and compute EHI scores via automatic entity extraction and matching. We then apply reinforcement learning to fine-tune the model parameters, using EHI as a reward signal to bias generation toward entity-faithful outputs. Our approach does not rely on human-written factuality annotations, enabling scalable fine-tuning. Experiments demonstrate consistent improvements in EHI across datasets, with qualitative analysis revealing a significant reduction in entity-level hallucinations without degradation in fluency or informativeness. We release a reproducible Colab pipeline, facilitating further research on hallucination-aware model fine-tuning using lightweight, hallucintion metrics like EHI.

Dense embedding-based retrieval is now the industry standard for semantic search and ranking problems, like obtaining relevant web documents for a given query. Such techniques use a two-stage process: (a) contrastive learning to train a dual encoder to embed both the query and documents and (b) approximate nearest neighbor search (ANNS) for finding similar documents for a given query. These two stages are disjoint; the learned embeddings might be ill-suited for the ANNS method and vice-versa, leading to suboptimal performance. In this work, we propose End-to-end Hierarchical Indexing -- EHI -- that jointly learns both the embeddings and the ANNS structure to optimize retrieval performance. EHI uses a standard dual encoder model for embedding queries and documents while learning an inverted file index (IVF) style tree structure for efficient ANNS. To ensure stable and efficient learning of discrete tree-based ANNS structure, EHI introduces the notion of dense path embedding that captures the position of a query/document in the tree. We demonstrate the effectiveness of EHI on several benchmarks, including de-facto industry standard MS MARCO (Dev set and TREC DL19) datasets. For example, with the same compute budget, EHI outperforms state-of-the-art (SOTA) in by 0.6% (MRR@10) on MS MARCO dev set and by 4.2% (nDCG@10) on TREC DL19 benchmarks.

Optimizing nonlinear systems involving expensive (computer) experiments with regard to conflicting objectives is a common challenge. When the number of experiments is severely restricted and/or when the number of objectives increases, uncovering the whole set of optimal solutions (the Pareto front) is out of reach, even for surrogate-based approaches. As non-compromising Pareto optimal solutions have usually little point in applications, this work restricts the search to relevant solutions that are close to the Pareto front center. The article starts by characterizing this center. Next, a Bayesian multi-objective optimization method for directing the search towards it is proposed. A criterion for detecting convergence to the center is described. If the criterion is triggered, a widened central part of the Pareto front is targeted such that sufficiently accurate convergence to it is forecasted within the remaining budget. Numerical experiments show how the resulting algorithm, C-EHI, better locates the central part of the Pareto front when compared to state-of-the-art Bayesian algorithms.