Canopy: Exploiting Piecewise Smooth Tree Priors for Multi-Fidelity Bandits
cs.LG, cs.AI
Submitted: 2026-09-24
Updated: 2026-09-24
License: http://creativecommons.org/licenses/by/4.0/
The gist: Many LLM inference problems, including model routing, prefix-cache management, prompt trimming, and test-time search, can be viewed as optimization over a tree.
Terminology
Abstract
Many LLM inference problems, including model routing, prefix-cache management, prompt trimming, and test-time search, can be viewed as optimization over a tree. This structure arises naturally from autoregressive generation: every prefix defines a node, and its continuations form a subtree below it. Internal nodes of the tree provide cheap but biased estimates of a region's value, while leaf evaluations are expensive but accurate. Hierarchical bandit methods can exploit this structure, but typically require a specific smoothness schedule to be specified in advance, even though real objectives are often only piecewise smooth and their optima may lie near sharp boundaries. We introduce CANOPY, a multi-fidelity tree bandit that learns where the smoothness prior is valid rather than assuming it globally. CANOPY uses cheap random-path probes to construct an online certificate of local aggregation bias, then directs expensive leaf evaluations toward cells where the certificate detects a smoothness violation. We prove fixed-budget and regret guarantees whose additional cost is additive in the number of discontinuities, recovering the smooth-tree rate when no violations are present and approaching structure-blind search as violations become dense. Across routing, top- k identification, test-time search, caching, and prompt trimming, CANOPY consistently improves matched-budget performance, including 2.9 times higher top-10 recall on a 1000-model pool, 1.6 times more SWE-bench Verified issues resolved than best-of- N, and 3.6 times lower median time-to-first-token with prefix caching.
Sources
- Program Synthesis with Large Language Models
- LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding
- Large Language Monkeys: Scaling Inference Compute with Repeated Sampling
- Evaluating Large Language Models Trained on Code
- Training Verifiers to Solve Math Word Problems
- The Llama 3 Herd of Models
- RouterBench: A Benchmark for Multi-LLM Routing System
- RouterEval: A Comprehensive Benchmark for Routing LLMs to Explore Model-level Scaling Up in LLMs
- LLMLingua: Compressing Prompts for Accelerated Inference of Large Language Models
- LLMRouterBench: A Massive Benchmark and Unified Framework for LLM Routing
- RouteLLM: Learning to Route LLMs with Preference Data
- Mooncake: A KVCache-centric Disaggregated Architecture for LLM Serving
- GPQA: A Graduate-Level Google-Proof Q&A Benchmark
- Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters
- Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them
- From Decoding to Meta-Generation: Inference-time Algorithms for Large Language Models
- Qwen2.5 Technical Report
- Tree of Thoughts: Deliberate Problem Solving with Large Language Models
- $\tau$-bench: A Benchmark for Tool-Agent-User Interaction in Real-World Domains
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