Drift-Aware LLM Routing with Sparse Contexts and Shared Budgets
A multi-model language service must route each request while preserving workload-level budgets for compute, latency, memory, or monetary cost. Two features make this problem materially harder than static model selection. Prompt representations are high dimensional, so only a small subset of embedding directions may predict the incremental value of a model, and both the request mix and the model frontier drift after launches, fine-tunes, quantization changes, and system updates. We formulate nonstationary sparse contextual routing with multiple knapsack constraints and an optional shadow-audit stream that evaluates a small fraction of prompts on several models. We propose Drift-Aware Sparse Routing (DRS). The policy estimates reward and resource use from a rolling audit window, routes using pessimistic reward and optimistic cost estimates, updates resource shadow prices online, and applies a hard meter before commitment. The analysis separates control from statistics. On any event with uniform prediction radii $\{\beta_t\}$, regret against a paced dynamic fluid benchmark is bounded by the sum of the radii, a capacity-buffer term, and an $O(\sqrt{T})$ pacing term. Under a sparse linear model and bounded drift $V_T$, rolling estimation gives \[ \widetilde O\left( T\sqrt{\frac{s}{\rho W}}+WV_T+\sqrt{T} \right), \] where $s$ is sparsity, $\rho$ is the audit rate, and $W$ is the window length. Optimizing $W$ yields the usual stationary $O(\sqrt{sT/\rho})$ rate when $V_T=0$ and a $O(T^{2/3}(s/\rho)^{1/3}V_T^{1/3})$ adaptation term under drift.