CARP: Continuous Latent Routing for Mixture-of-LoRA under Non-Stationary Opponents

Specialising LoRA adapters to non-stationary opponents is commonly done by hard-routing each forward pass through the adapter selected by a predicted cluster label. We show this interface is structurally fragile: the predicted-cluster map is non-Lipschitz, so a small error in the inferred context can flip the cluster and silently swap adapters. We propose CARP, which instead routes through a soft mixture of LoRA prototypes indexed by a continuous latent c, with weights softmax(−‖c−μ_k‖²/τ) trained by an EMA teacher–student on the realised context. The map is L_w-Lipschitz, so context error β enters the regret as O(L_w β) rather than as a 0–1 flip. We prove a two-sided guarantee: a Lipschitz upper bound for CARP and an Ω(1) per-round lower bound for any hard router under non-zero predictor noise. Empirically the separation appears exactly where the theory places it. On a controlled strategic game (30 seeds, 6 baselines) CARP beats hard routing by +2.6 LTR out-of-distribution and is 5–9× less sensitive to predictor noise; a c-conditioned linear gate recovers most of the gain, so the interface, not the kernel, carries it. On MovieLens-1M, Last.fm-1K and Amazon-Books the predicted cross-over materialises: CARP wins on drifting or noisy-boundary splits, hard routing wins on cleanly partitioned ones, and all routers tie where the context geometry is near-linear. At LM scale (Qwen2.5 0.5B–3B) hard routing on the inferred context is worse than no routing, and an oracle-context control confirms the mechanism: given the true context the hard router's penalty vanishes. The Lipschitz gain is therefore robustness to context-inference error—which also locates the LM-scale bottleneck in context inference, not routing.