Trust Regions Sell, But Who's Buying? Overlap Geometry as an Alternative Trust Region for Policy Optimization

Standard trust-region methods constrain policy updates via Kullback-Leibler (KL) divergence. However, KL controls only an average divergence and does not directly prevent rare, large likelihood-ratio excursions that destabilize training--precisely the failure mode that motivates heuristics such as PPO's clipping. We propose overlap geometry as an alternative trust region, constraining distributional overlap via the Bhattacharyya coefficient (closely related to the Hellinger/Renyi-1/2 geometry). This objective penalizes separation in the ratio tails, yielding tighter control over likelihood-ratio excursions without relying on total variation bounds that can be loose in tail regimes. We derive Bhattacharyya-TRPO (BTRPO) and Bhattacharyya-PPO (BPPO), enforcing overlap constraints via square-root ratio updates: BPPO clips the square-root ratio q = sqrt(r), and BTRPO applies a quadratic Hellinger/Bhattacharyya penalty. Empirically, overlap-based updates improve robustness and aggregate performance as measured by RLiable under matched training budgets, suggesting overlap constraints as a practical, principled alternative to KL for stable policy optimization.

Actionable Advice from Reviews via Mixture of LoRA Experts: A Two-LLM Pipeline for Issue Extraction and Business Recommendations

Customer reviews contain detailed, domain specific signals about service failures and user expectations, but converting this unstructured feedback into actionable business decisions remains difficult. We study review-to-action generation: producing concrete, implementable recommendations grounded in review text. We propose a modular two-LLM framework in which an Issue model extracts salient issues and assigns coarse themes, and an Advice model generates targeted operational fixes conditioned on the extracted issue representation. To enable specialization without expensive full fine-tuning, we adapt the Advice model using a mixture of LoRA experts strategy: multiple low-rank adapters are trained and a lightweight gating mechanism performs token-level expert mixing at inference, combining complementary expertise across issue types. We construct synthetic review-issue-advice triples from Yelp reviews (airlines and restaurants) to supervise training, and evaluate recommendations using an eight dimension operational rubric spanning actionability, specificity, feasibility, expected impact, novelty, non-redundancy, bias, and clarity. Across both domains, our approach consistently outperforms prompting-only and single-adapter baselines, yielding higher actionability and specificity while retaining favorable efficiency-quality trade-offs.

A Multi-Agent System for Generating Actionable Business Advice

Customer reviews contain rich signals about product weaknesses and unmet user needs, yet existing analytic methods rarely move beyond descriptive tasks such as sentiment analysis or aspect extraction. While large language models (LLMs) can generate free-form suggestions, their outputs often lack accuracy and depth of reasoning. In this paper, we present a multi-agent, LLM-based framework for prescriptive decision support, which transforms large scale review corpora into actionable business advice. The framework integrates four components: clustering to select representative reviews, generation of advices, iterative evaluation, and feasibility based ranking. This design couples corpus distillation with feedback driven advice refinement to produce outputs that are specific, actionable, and practical. Experiments across three service domains and multiple model families show that our framework consistently outperform single model baselines on actionability, specificity, and non-redundancy, with medium sized models approaching the performance of large model frameworks.

HAEPO: History-Aggregated Exploratory Policy Optimization

Exploration is essential in modern learning, from reinforcement learning environments with small neural policies to large language models (LLMs). Existing work, such as DPO, leverages full sequence log-likelihoods to capture an entire trajectory of the model's decisions, while methods like GRPO aggregate per-token ratios into a trajectory-level update. However, both often limit exploration on long-horizon tasks. We introduce History-Aggregated Exploratory Policy Optimization (HAEPO), a history-aware exploratory loss to combat these shortcomings. HAEPO compresses each trajectory into the sum of its logarithmic probabilities (a cumulative logarithmic likelihood), and applies a Plackett-Luce softmax across trajectories to obtain normalized weights proportional to their returns, thus encouraging broader exploration. We add entropy regularization to stabilize the aggressive updates to prevent premature collapse and a soft KL penalty relative to a frozen copy of the previous (reference) policy. Empirically, HAEPO converges fast, explores thoroughly, aligns closely with true rewards, and demonstrates robust learning behavior better or at par with PPO, GRPO, and DPO across diverse tasks. Thus, HAEPO provides a stable and interpretable framework by explicitly leveraging full-trajectory history while balancing exploration and stability.