Policy Regret for Embedding Model Routing: Contextual Bandits with Low-Rank Experts

The rapid development of large language models, each with distinct capabilities and inference costs, raises a practical deployment question: given an incoming request, which model should handle it? We present OrcaRouter, a production-oriented LLM router that combines a LinUCB-based contextual bandit over lexical and sentence-embedding features with a hybrid offline-online learning protocol. Offline, OrcaRouter obtains full-information feedback by evaluating each candidate model on a curated set of routing prompts, yielding a reward matrix used to fit one ridge regressor per arm. At deployment time, it initializes from these parameters and can optionally continue learning from bandit feedback, updating only the selected model's arm after observing its reward. At the time of our RouterArena submission (May 20, 2026), OrcaRouter-Adaptive ranked second on the public RouterArena leaderboard with an arena score of 72.08, achieving 75.54% accuracy at a cost of USD 1.00 per 1,000 queries.

Early ranking stages in recommendation systems precompute item embeddings and cache them in-model for scoring within strict latency constraints. Because this cache exists only at serving time, outside the training loop, training and serving use different item representations, a structural discrepancy that limits quality and adds operational fragility. We show that co-designing the training and serving paths removes this representation discrepancy at its source. We introduce the memory layer, an in-model key-value embedding cache co-trained with the model: the item tower writes embeddings during training and the model reads them at serving, one source of truth for item representations by construction. Always-on embeddings cover items not yet cached, so every item receives a prediction, and the design consolidates three separate trainer-to-predictor update paths into a single self-contained pipeline. Deployed in production on Instagram Reels, the memory layer raises prediction coverage from 96% to 100%, improves embedding freshness from $O(5\text{ min})$ to $O(20\text{ s})$, and narrows the training-serving Normalized Entropy (NE) gap by up to 86%, yielding over $2\times$ recall for the freshest content and a 5-6% cold start engagement lift. Because embeddings are produced during training, the system needs no separate bulk-evaluation or publish-time recomputation, cutting training-and-publish computational cost by 30% at neutral serving computational cost.

Model routing balances solution accuracy and computational cost by selecting among models of varying capabilities. While recent multi-round frameworks interleave reasoning and planning, we identify a structural failure mode termed Trust Region Collapse. We demonstrate that the deep coupling of reasoning and routing, exacerbated by the dominance of strong pre-training priors under sparse supervision, leads to degenerate local optima where capable experts are systematically suppressed. To decouple these processes, we propose $\textbf{EntroRouter}$, a single-round routing framework that treats entropy regulation as a core objective. We first initialize the policy via Soft Supervision, fitting a distribution of suitable models to establish a high-entropy prior for exploration. Subsequently, we stabilize Reinforcement Learning using a Soft Anchor, which utilizes offline capability estimates to orchestrate controlled entropy contraction within a safe trust region. Extensive experiments demonstrate that EntroRouter retains 98.3% of the strongest expert's accuracy while reducing computational costs by 48.25%.