arXiv subjects

Aniruddha Roy

Publications and source records attributed to Aniruddha Roy.

6 recordsLinked to original sources

arXiv2026

Output Feedback Guaranteed Cost Equilibrium in Networked Multi-Agent Linear-Quadratic Difference Games

In this paper, we study infinite-horizon deterministic linear-quadratic difference games with an output feedback information structure. We consider linear time-invariant dynamics and quadratic cost functionals defined over an infinite horizon. We first demonstrate that computing an output feedback Nash equilibrium (OF-NE) in difference games is challenging, even for low-dimensional games. To address this difficulty, we introduce an output feedback guaranteed cost equilibrium (OF-GCE) for difference games. In an OF-GCE, each player seeks a feedback strategy that guarantees its cost remains below a prescribed bound while satisfying an equilibrium condition. We derive necessary and sufficient conditions for the existence of an OF-GCE in terms of the solvability of a set of coupled bilinear matrix inequalities. We provide a linear matrix inequality-based iterative algorithm for synthesizing OF-GCE strategies. We further show that the state feedback GCE (SF-GCE) is a special case of the OF-GCE when players have complete state information. Numerical examples illustrate the effectiveness of the proposed approach.

math.OC↗

arXiv2026

Guaranteed cost structured control in infinite-horizon linear-quadratic cooperative differential games

In this paper, we consider the infinite-horizon linear-quadratic cooperative differential games with output feedback information structure. We first show that computing Pareto optimal controls under output feedback is difficult even for low-dimensional games. To address this, we introduce the concept of feedback guaranteed cost structured control (GCSC). At a feedback GCSC, the total weighted team cost remains below a prescribed threshold while satisfying the structural constraint. We derive monotonicity properties of the feedback GCSC set and the admissible weight set, respectively. Further, we show that Pareto optimal controls (if they exist) belong to the class of feedback GCSCs. We provide performance measures of the Pareto optimal controls and the proposed GCSC relative to the output feedback optimal control. We also establish verification and synthesis conditions for a feedback GCSC using linear matrix inequalities, where the synthesis formulation is convex and requires no semi-definite programming relaxation. Finally, we illustrate the effectiveness of the proposed approach through numerical examples, including a microgrid tracking synchronization case study.

math.OC↗

arXiv2025

AlignMerge - Alignment-Preserving Large Language Model Merging via Fisher-Guided Geometric Constraints

Merging large language models (LLMs) is a practical way to compose capabilities from multiple fine-tuned checkpoints without retraining. Yet standard schemes (linear weight soups, task vectors, and Fisher-weighted averaging) can preserve loss while quietly destroying alignment. We argue that merging is not a numerical trick but a geometry-constrained operation around an already-aligned anchor: fusion must be steered to respect safety geometry, not validated post hoc. We introduce AlignMerge, a geometry-aware merging framework that makes alignment an explicit invariant. In a local Fisher chart around an instruction-tuned base, we estimate an alignment subspace with projector P_A and optimize: L_AlignMerge = L_geo + lambda_align * L_align + lambda_bud * L_bud, where L_geo keeps the merge close to its experts in Fisher-Rao geometry, L_align penalizes motion along alignment-sensitive directions, and L_bud enforces a soft alignment budget. As the alignment functional we use the decoding-invariant Alignment Quality Index (AQI), a latent-space criterion that captures how cleanly aligned and misaligned behaviors separate in representation space. Across five model families (LLaMA-3 8B, Mistral 7B, Qwen 2, Phi-3.5, Gemma 2), merging safety anchors with task experts, AlignMerge improves alignment metrics (AQI, toxicity, LLM-judge alignment) while matching or exceeding the best expert on instruction-following, reasoning, and helpfulness. It also exhibits smaller alignment-subspace drift and fewer budget violations than Fisher soups, TIES, SafeMerge, and MergeAlign. These results make alignment-preserving merging a first-class design goal and suggest a path to geometry-aware composition of future foundation models.

cs.AI↗

arXiv2025

REFINE-AF: A Task-Agnostic Framework to Align Language Models via Self-Generated Instructions using Reinforcement Learning from Automated Feedback

Instruction-based Large Language Models (LLMs) have proven effective in numerous few-shot or zero-shot Natural Language Processing (NLP) tasks. However, creating human-annotated instruction data is time-consuming, expensive, and often limited in quantity and task diversity. Previous research endeavors have attempted to address this challenge by proposing frameworks capable of generating instructions in a semi-automated and task-agnostic manner directly from the model itself. Many of these efforts have relied on large API-only parameter-based models such as GPT-3.5 (175B), which are expensive, and subject to limits on a number of queries. This paper explores the performance of three open-source small LLMs such as LLaMA 2-7B, LLama 2-13B, and Mistral 7B, using a semi-automated framework, thereby reducing human intervention, effort, and cost required to generate an instruction dataset for fine-tuning LLMs. Furthermore, we demonstrate that incorporating a Reinforcement Learning (RL) based training algorithm into this LLMs-based framework leads to further enhancements. Our evaluation of the dataset reveals that these RL-based frameworks achieve a substantial improvements in 63-66% of the tasks compared to previous approaches.

cs.CL↗

arXiv2024

Soft-constrained output feedback guaranteed cost equilibria in infinite-horizon uncertain linear-quadratic differential games

In this paper, we study infinite-horizon linear-quadratic uncertain differential games with an output feedback information structure. We assume linear time-invariant nominal dynamics influenced by deterministic external disturbances, and players' risk preferences are expressed by a soft-constrained quadratic cost criterion over an infinite horizon. We demonstrate that the conditions available in the literature for the existence of a soft-constrained output feedback Nash equilibrium (SCONE) are too stringent to satisfy, even in low-dimensional games. To address this issue, using ideas from suboptimal control, we introduce the concept of a soft-constrained output feedback guaranteed cost equilibrium (SCOGCE). At an SCOGCE, the players' worst-case costs are upper-bounded by a specified cost profile while maintaining an equilibrium property. We show that SCOGCE strategies form a larger class of equilibrium strategies; that is, whenever an SCONE exists, it is also an SCOGCE. We demonstrate that sufficient conditions for the existence of SCOGCE are related to the solvability of a set of coupled bi-linear matrix inequalities. Using semi-definite programming relaxations, we provide linear matrix inequality-based iterative algorithms for the synthesis of SCOGCE strategies. Finally, we illustrate the performance of SCOGCE controllers with numerical examples.

math.OC↗

arXiv2024

Enhancing Low-Resource NMT with a Multilingual Encoder and Knowledge Distillation: A Case Study

Neural Machine Translation (NMT) remains a formidable challenge, especially when dealing with low-resource languages. Pre-trained sequence-to-sequence (seq2seq) multi-lingual models, such as mBART-50, have demonstrated impressive performance in various low-resource NMT tasks. However, their pre-training has been confined to 50 languages, leaving out support for numerous low-resource languages, particularly those spoken in the Indian subcontinent. Expanding mBART-50's language support requires complex pre-training, risking performance decline due to catastrophic forgetting. Considering these expanding challenges, this paper explores a framework that leverages the benefits of a pre-trained language model along with knowledge distillation in a seq2seq architecture to facilitate translation for low-resource languages, including those not covered by mBART-50. The proposed framework employs a multilingual encoder-based seq2seq model as the foundational architecture and subsequently uses complementary knowledge distillation techniques to mitigate the impact of imbalanced training. Our framework is evaluated on three low-resource Indic languages in four Indic-to-Indic directions, yielding significant BLEU-4 and chrF improvements over baselines. Further, we conduct human evaluation to confirm effectiveness of our approach. Our code is publicly available at https://github.com/raypretam/Two-step-low-res-NMT.

cs.CL↗