We propose DPLoRA (Dual-Pruning Low-Rank Adaptation), a framework that optimizes rank allocation via two stages: (1) an initial pruning stage (OPLoRA; Optimal Pruning LoRA) that uses Integer Linear Programming (ILP) to determine optimal layer-wise ranks without manual tuning; and (2) a progressive pruning stage that further reduces ranks adaptively during training using importance scores smoothed by Exponential Moving Average (EMA). Experiments demonstrate that OPLoRA consistently outperforms existing PEFT baselines on GLUE and instruction-following tasks, while the full DPLoRA framework establishes a new state-of-the-art among compared PEFT baselines on GLUE at high-performance settings (p=0.4). At efficiency-focused settings (p=0.8), our method reduces trainable parameters by over 80% and training time by 46% compared to standard LoRA, offering a highly efficient solution for deploying large-scale models in resource-constrained environments.

Retrieval-Augmented Generation enhances Large Language Models by grounding responses in external knowledge, but multi-hop reasoning remains vulnerable to error propagation, where early retrieval failures confound subsequent steps. Standard outcome-based optimization only rewards the final answer, leaving intermediate retrieval and reasoning errors undetected. While existing process-based methods introduce step-level signals, they still score each step against the final answer, rewarding spurious successes where flawed retrieval coincidentally produces the correct answer. Step-level supervision in RAG requires evaluating both logical validity and evidential grounding at each step. We introduce PRO-STEP: we train a generative PRM that evaluates both dimensions, employ PRM-guided value tree search to construct preference pairs contrasting valid steps against flawed ones, and optimize the policy via step-level Direct Preference Optimization. Experiments on single- and multi-hop QA datasets demonstrate that PRO-STEP mitigates error propagation and outperforms existing outcome- and process-based RAG baselines.