You Cannot Pick a Provider From the Price List: Market-Aware Routing for Open-Weight LLM Inference

Liang He; Jingbo Wen; Yixiong Chen; Yue Yang; Qizhen Lan; Kangning Cui; Xilu Wang

cs.AISep 29, 2026

You Cannot Pick a Provider From the Price List: Market-Aware Routing for Open-Weight LLM Inference

Authors: Liang He, Jingbo Wen, Yixiong Chen, Yue Yang, Qizhen Lan, Kangning Cui, Xilu Wang

Organizations: University of Sydney · Johns Hopkins University · Stanford University · City University of Hong Kong

Abstract

Existing LLM routers choose among models using static per-model costs. We show that open-weight inference markets introduce a second, largely ignored decision axis: after choosing a model, a client must still choose which provider serves it. Measuring live endpoints across [nummodels] open models, competing providers, multiple task types, and three measurement waves, we find that provider choice cannot be inferred from the price list. The same model can vary sharply in quality, latency, availability, and price across providers; higher-priced providers are consistently faster, but price does not reliably predict quality or availability; and provider feasibility is task-selective, with one deployment nearly normal on knowledge tasks but catastrophically degraded on multi-step reasoning. We formulate same-model provider selection as a price-taker market-aware routing problem. A simple measured-map policy routes to the cheapest provider that is both quality-equivalent and healthy, yielding matched-quality savings while avoiding degraded endpoints. Because the map drifts, we introduce FACET, an online provider router that certifies per-(provider x task) feasibility facets and fails safe to an anchor before serving uncertified arms. Across relaxed deployment assumptions, FACET tolerates imperfect task assignment and sparse feedback, while systematic evaluator bias exposes a quality-signal trust boundary that can be mitigated with ground-truth probes or audits. Live provider runs further confirm that certification can move real traffic from a premium anchor to a substantially cheaper certified endpoint. Our results suggest that market-aware LLM routing must measure not only which model to use, but also who serves it.

Figures & tables

Price vs.	Median Spearman	Interpretation
Accuracy	$+0.05$	no stable price–quality relation
Latency	$\mathbf{-0.61}$	higher-priced providers are faster
Availability	$0.00$	no stable price–availability relation

Table 2: Benchmark-scale within-(model

\times

task) Spearman correlations between provider price and metrics. Price is strongly associated with lower latency, but not with accuracy or availability.

	Catastrophic exposure
Scenario	Facet (full)	No anchor	Context-blind
S1: Cheap mine from start	$\mathbf{0.0\%}$	8.3%	6.7%
S2: Certified arm slips mid-run	$\mathbf{0.4\%}$	5.6%	3.2%
S3: No cheap catastrophic mine	1.2%	0.0%	—

Table 3: Ablation experiments isolating fail-safe anchoring and task-conditioned certification. Values report catastrophic exposure (below-floor served queries).

Periodic re-measurement				facet
$P$	Probe cost ($)	Below-floor	Total cost ($)	$r$	Probe cost ($)	Below-floor	Total cost ($)
100	1740.2	3.70%	2361	0.10	16.7	$\mathbf{0.17\%}$	1255
400	487.2	$\mathbf{14.30\%}$	$\mathbf{1089}$	0.25	22.9	$\mathbf{0.67\%}$	$\mathbf{1110}$
1600	139.2	38.60%	709	1.00	27.6	$\mathbf{0.28\%}$	1130

Table 4: Periodic re-measurement versus facet . A certified provider can slip between measurement rounds. Periodic re-probing reduces exposure by probing more frequently, while facet continuously monitors served facets and uses probes only for certification (10 seeds).

Label corruption (known tasks)			OOD traffic
Perturbation	Facet	Reference	Perturbation	Facet	Reference
$0\%$ error	$\mathbf{0.00\%}$	$6.72\%$ (context-blind)	$10\%$ OOD	$\mathbf{0.00\%}$	$3.41\%$ (nearest facet)
$10\%$ error	$\mathbf{2.23\%}$	$6.72\%$	$25\%$ OOD	$\mathbf{0.00\%}$	$1.03\%$
$20\%$ error	$\mathbf{3.54\%}$	$6.72\%$	$50\%$ OOD	$\mathbf{0.00\%}$	$0.24\%$
$33\%$ error	$\mathbf{4.72\%}$	$\mathbf{6.72\%}$

Table 5: Robustness to imperfect task assignment. Left: corruption of known task labels. Right: OOD traffic treated as uncertified or mapped to the nearest known facet. Values report catastrophic exposure (below-floor served queries; 10 seeds).

Metric	Value	Metric	Value
Deployment scale
Served queries	$538$	Certification probes	$130$
Failed calls	$4$	Aggregate served accuracy	$\mathbf{88.3\%}$
Serving behavior
Avg. price, queries 1–100	$\mathbf{\$ 0.924/M}$	Avg. price, queries 301–500	$\mathbf{\$ 0.210/M}$
Anchor price	$1.04 / M

Table 6: Live facet deployment: 36-hour run on Llama-3.3-70B across 12 providers. Validates cold-start certification and migration; no quality slip occurred during the window.

Appendix figures & tables23 assets

Supplementary material from the paper’s appendix.

Appendix

	Decision axis	Cost model	Cross-provider quality
FrugalGPT / RouteLLM
CARROT / MixLLM	which model	static list price	—
PriLLM (provider-side)	sets its own price	endogenous	—
Token Arena (measurement)	— (leaderboard)	—	static snapshot
Ours	which provider	live, exogenous	measured, live

Appendix

Table 7: Positioning against representative routing and measurement work. Prior client-side routers select among models; our layer selects among providers serving the same selected open-weight model.

	Cost premium	Below-floor rate		Quality-regret
Policy	vs. oracle	Median	Worst	Median	Worst
Static-argmin	$-6\%$	$33.0\%$	$33.0\%$	$49.50$	$49.50$
Cost-Thompson	$+4\%$	$6.5\%$	$47.6\%$	$9.08$	$20.45$
SW-UCB	$+13\%$	$2.4\%$	$56.6\%$	$3.33$	$6.26$
M-UCB (change-detect)	$+14\%$	$2.5\%$	$53.2\%$	$3.71$	$6.17$
facet core	$+59\%$	$\mathbf{1.3\%}$	$42.6\%$	$\mathbf{1.78}$	$\mathbf{4.41}$

Appendix

Table 8: facet ’s detector core versus non-stationary bandit baselines. Results cover 12 benchmark cells against a clairvoyant cheapest-feasible oracle. Each safety metric is shown at the median and at each policy’s own worst cell. Cost premium is relative to the oracle; quality-regret is the summed below-floor shortfall

\sum_{t}\max(0,\theta-q_{a_{t}})

per

10^{3}

serves.

	Policy outcome		Break-even threshold
Baseline	Cost ($)	Below-floor serves	$\lambda^{\star}$ ($)	Query-price equiv.
Frozen map	$1015$	$990$	$0.78$	$1.5\times$
Periodic $P{=}400$	$1448$	$595$	$0.40$	$0.8\times$
M-UCB	$1241$	$314$	$6.02$	$11\times$
SW-UCB	$1230$	$296$	$9.08$	$17\times$

Appendix

Table 9: Break-even cost of avoiding one below-floor serve. facet is preferred whenever the deployment-level loss associated with one below-floor answer exceeds

\lambda^{\star}

. The final column expresses the threshold in units of the mean price of an ordinary served query.

	Latency		Accuracy		Availability
Run selection	Median $\rho$	Negative cells	Median $\rho$	Negative cells	Median $\rho$	Negative cells
Latest	$\mathbf{-0.610}$	$\mathbf{21/21}$	$+0.049$	$10/21$	$+0.000$	$9/21$
Earliest	$\mathbf{-0.610}$	$\mathbf{21/23}$	$-0.224$	$14/23$	$+0.000$	$10/23$
Across-run mean	$\mathbf{-0.566}$	$\mathbf{22/23}$	$-0.063$	$13/23$	$+0.000$	$11/23$

Appendix

Table 11: Robustness of within-cell price correlations to measurement-run selection. The correlation direction and the number of cells with negative correlation are reported for each service metric.

Latency component	Median $\rho$ with price	Negative cells
Seconds per generated token	$\mathbf{-0.675}$	$\mathbf{21/21}$
Fixed request overhead	$+0.274$	$7/21$

Appendix

Table 12: Decomposition of the price–latency relationship. Correlations are computed across providers within each model–task cell.

Statistic	Value
Evaluation set
Cells with at least two feasible providers	$17$
Latency consequence
Median normalized speed rank of cheapest feasible provider	$1.00$
Cheapest feasible provider is strictly slowest	$\mathbf{9/17}$
Median p95-latency penalty vs. fastest feasible provider	$\mathbf{7.8\times}$

Appendix

Table 13: Latency consequence of choosing the cheapest quality-feasible provider.

	Routing outcome
Latency deadline	Feasible cells	Relative cost	Route changes
$30$ s	$12/12$	$1.00\times$	$0\%$
$10$ s	$\mathbf{12/12}$	$\mathbf{1.19\times}$	$58\%$
$5$ s	$12/12$	$1.31\times$	$58\%$
$2$ s	$10/12$	$2.03\times$	$70\%$
$1$ s	$\mathbf{6/12}$	$\mathbf{2.62\times}$	$\mathbf{100\%}$

Appendix

Table 14: Latency-constrained measured-map routing. Relative cost is normalized to the unconstrained cheapest quality-feasible route. Route changes report the fraction of feasible cells whose selected provider changes after imposing the deadline.

	Safety outcome		Monitoring cost
Probe rate	Below-floor median	IQR	Probe spend median ($)
$0.10$	$0.00\%$	[ $0.00$ , $0.80$ ]%	$17.0$
$0.25$	$0.44\%$	[ $0.00$ , $0.80$ ]%	$17.6$
$0.50$	$0.60\%$	[ $0.00$ , $0.88$ ]%	$28.2$
$1.00$	$0.14\%$	[ $0.00$ , $0.96$ ]%	$29.8$
$2.00$	$0.92\%$	[ $0.52$ , $1.36$ ]%	$48.9$

Appendix

Table 15: Run-to-run variability of the facet probe-rate sweep. Results are computed over 20 seeds. The overlapping interquartile ranges at low probe rates show that the ordering of nearby point estimates should not be interpreted as a tuning effect.

		Measured-map router		OOS baselines
Health threshold	Cells	In-sample	OOS	Cheapest	Premium
Quality margin: 2 points
$80\%$	$9$	$0.0\%$	$22.2\%$	$44.4\%$	$55.6\%$
$90\%$	$9$	$0.0\%$	$22.2\%$	$44.4\%$	$55.6\%$
Quality margin: 5 points
$80\%$	$9$	$0.0\%$	$11.1\%$	$22.2\%$	$33.3\%$

Appendix

Table 16: Out-of-sample sensitivity to the quality margin and health threshold. Results cover nine benchmark cells. The earlier wave determines the route and the later wave evaluates it. Values are below-floor rates.

	facet core		Best baseline
Drift regime	Below-floor	q-regret	Below-floor	q-regret
Abrupt-change regimes
Abrupt, spaced (assumed)	$1.3\%$	$1.9$	$1.4\%$	$2.9$
Frequent (sub-recovery)	$1.3\%$	$2.0$	$2.5\%$	$4.5$
Correlated cohort slip	$3.3\%$	$3.9$	$16.4\%$	$21.0$
Outside the abrupt-change assumption

Appendix

Table 17: facet ’s detector core across drift shapes. Values report below-floor rate and quality-regret on the flagship cell. The detector is robust to frequent and correlated drift, but the advantage does not hold under gradual ramps or multiple concurrent mines, which are outside its abrupt-change assumption.

Policy	Mean acc.	Rel. cost ∗	Below-floor	Mean avail.
Single-best (quality-first)	$\mathbf{95\%}$	$1.66\times$	$\mathbf{0\%}$	$96\%$
Premium (most expensive)	$92\%$	$3.67\times$	$17\%$	$95\%$
Random	$92\%$	$2.19\times$	$22\%$	$98\%$
Cheapest (price-blind)	$91\%$	$\mathbf{1.00\times}$	$28\%$	$97\%$
Ours	$94\%$	$\mathbf{1.57\times}$	$\mathbf{0\%}$	$\mathbf{99\%}$

Appendix

Table 18: Routing policy comparison over all measured model–task cells. Relative cost normalizes each cell to its cheapest provider. Below-floor is the fraction of cells whose selected provider falls below the cell’s quality floor.

	In-sample			Out-of-sample
Policy	Accuracy	Below-floor	q-regret	Accuracy	Below-floor	q-regret
Single-best	$87\%$	$0\%$	$0.0$	$87\%$	$0\%$	$0.0$
Router (ours)	$85\%$	$0\%$	$0.0$	$86\%$	$11\%$	$0.0$
Cheapest	$84\%$	$22\%$	$0.1$	$85\%$	$22\%$	$0.1$
Premium	$79\%$	$44\%$	$4.3$	$80\%$	$33\%$	$4.0$

Appendix

Table 19: Out-of-sample routing. Providers are selected using an earlier measurement wave and evaluated on a later wave with

n{\geq}100

benchmark accuracy.

Cell subset	Cells	Median saving
All cells	$18$	$56.5\%$
Saturated cells only	$9$	$56.5\%$
Non-saturated cells only	$9$	$\mathbf{50.0\%}$

Appendix

Table 20: Matched-quality savings after separating saturated and non-saturated model–task cells.

Model	Task	Saving	Providers
llama-3.1-8b-instruct	extraction	$\mathbf{84.1\%}$	$5$
	math	$\mathbf{84.1\%}$	$5$
llama-3.3-70b-instruct	extraction	$79.8\%$	$10$
	math	$79.2\%$	$11$
llama-4-maverick	extraction	$50.0\%$	$4$
	math	$50.0\%$	$4$

Appendix

Table 21: Complete per-cell results for the nine non-saturated cells. Saving is the reduction of the selected measured-equivalent healthy route relative to the premium provider.

	Cost outcome	Safety outcome
Policy	Cost ($)	Below-floor	Catastrophic	q-regret / $10^{3}$
S1: Cheap mine from the start
Periodic $P=200$	$1834.8$	$2.78\%$	$2.78\%$	$8.33$
Periodic $P=500$	$1212.8$	$0.00\%$	$0.00\%$	$0.00$
Periodic $P=1000$	$1004.2$	$0.00\%$	$0.00\%$	$0.00$
SW-UCB	$1040.3$	$1.79\%$	$1.79\%$	$5.52$

Appendix

Table 22: Periodic re-probing under three drift regimes. S1 contains a cheap mine from the start; S2 lets a certified provider slip mid-run; S3 contains repeated measured-style changes.

Cell	Route before	Route after	Driver
Interval 1 (days 0–13)
deepseek-v3.1 / extraction	AtlasCloud	DeepInfra	availability recovery
deepseek-v3.1 / math	AtlasCloud	DeepInfra	availability recovery
llama-3.3-70B / extraction	DeepInfra	Nebius	quality slip below floor
mistral-small / classification	Venice	DeepInfra	rate limiting
Interval 2 (days 13–43)

Appendix

Table 25: Decision changes across three measurement waves. Despite mostly stable prices, the cheapest feasible provider changes because of health, availability, provider churn, and quality drift.

	Catastrophic exposure
Task-label error	facet	Context-blind
$0\%$	$0.00\%$	$6.72\%$
$5\%$	$1.06\%$	$6.72\%$
$10\%$	$2.23\%$	$6.72\%$
$20\%$	$3.54\%$	$6.72\%$
$33\%$	$\mathbf{4.72\%}$	$\mathbf{6.72\%}$

Appendix

Table 26: Task-label corruption. Exposure rises gradually as the task label becomes less reliable.

	Catastrophic exposure
OOD share	Unknown $\rightarrow$ fail-safe	Nearest known facet
$10\%$	$\mathbf{0.00\%}$	$3.41\%$
$25\%$	$\mathbf{0.00\%}$	$1.03\%$
$50\%$	$\mathbf{0.00\%}$	$0.24\%$

Appendix

Table 27: Unknown-task traffic. Fail-safe routing avoids borrowing certification from an unrelated known task.

	Safety outcome	Cost outcome
Judge-label error	Below-floor	Total cost ($)
$0\%$	$0.28\%$	$1130$
$20\%$	$\mathbf{0.00\%}$	$2868$
$30\%$	$\mathbf{0.00\%}$	$2942$

Appendix

Table 28: Symmetric quality-label noise. Random label flips primarily raise fallback cost rather than below-floor exposure. Results average over 10 seeds.

	Below-floor exposure
Observed-feedback fraction	facet	Reference
$100\%$	$0.28\%$	—
$50\%$	$1.26\%$	—
$20\%$	$1.47\%$	—
$5\%$	$\mathbf{4.57\%}$	SW-UCB: $\mathbf{13.32\%}$

Appendix

Table 30: Sparse quality feedback. Safety degrades as labeled traffic becomes rare, but remains substantially better than the comparison policies at the lowest label rate. Results average over 10 seeds.

	Below-floor exposure
Setting	facet	Periodic	SW-UCB	Static
Clean	$0.28\%$	$14.30\%$	$2.16\%$	—
$20\%$ noise $+$ $20\%$ labels	$\mathbf{0.14\%}$	$17.00\%$	$10.52\%$	$65.00\%$
$20\%$ noise $+$ $20\%$ labels $+$ probe rate $0.25$	$\mathbf{0.00\%}$	$17.00\%$	$10.52\%$	$65.00\%$

Appendix

Table 31: Joint information stress test. The combination of noisy and sparse feedback sharply reduces cost efficiency, but does not produce a comparable collapse in safety.

	Cost outcome	Quality and safety outcome
Provider policy	Cost ($)	Accuracy	Below-floor	Catastrophic
GSM8K
Dearest	$1435.7$	$85.4\%$	$24.6\%$	$24.6\%$
Cheapest	$222.6$	$92.5\%$	$0.0\%$	$0.0\%$
Ours	$222.6$	$\mathbf{92.5\%}$	$\mathbf{0.0\%}$	$\mathbf{0.0\%}$
MMLU

Appendix

Table 32: Provider routing underneath model routing. Cost is reported over 3000 replayed queries. When the cheapest provider is already safe, our layer leaves the route unchanged. When it is degraded, provider-aware selection trades a small cost increase over the cheapest default for substantially lower below-floor exposure.

		Market dynamics
Model	Providers	Price changes	Re-elections	Re-elections/day
deepseek-chat-v3.1	$8$	$0$	$0$	$0.0$
llama-3.3-70b-instruct	$12$	$0$	$0$	$0.0$
deepseek-v4-pro-0813	$15$	$\mathbf{2}$	$\mathbf{2}$	$\mathbf{2.0}$
deepseek-v4-flash-0731	$30$	$\mathbf{14}$	$\mathbf{3}$	$\mathbf{3.0}$

Appendix

Table 33: High-frequency price monitoring over 24 hours at 15-minute resolution. A re-election is a change in the identity of the cheapest provider for that model. Price movement and re-election frequency both increase with the number of competing providers.

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Sep 23, 2026, cs.AIJ/K move · Enter open · S save

Learning the Cost of Reliable Inference

Dimitrios Rontogiannis, Ander Artola Velasco, Manuel Gomez Rodriguez

Max Planck Institute for Software Systems Kaiserslautern, Germany

Question-Answering Benchmarks

Open paper AskPDF arXiv

Benchmarking and routing platforms increasingly act as intermediaries connecting large language model providers with end-users. However, providers on these platforms typically use a fixed price per token, preventing users from achieving the most competitive price for their tasks. In this work, we design a procurement platform where token prices for each task are driven by provider competition, enabling users to secure competitive pricing for guaranteed quality levels. To this end, the platform sequentially routes queries via a reverse second-price auction that incentivizes model providers to truthfully bid their best estimate of the average cost to serve a user's query. As it routes queries, the platform learns the quality offered by each provider and progressively routes queries to the most cost-competitive provider among those meeting a desired quality threshold. To validate our design, we conduct experiments with multiple LLMs from the Llama and Qwen families on popular mathematical reasoning and question-answering benchmarks. The results show that the pricing margin of the most cost-competitive provider on our platform varies significantly---from

10\%

71\%

---depending on the task and quality threshold. This suggests a substantial inefficiency in the current fixed-price market, and it demonstrates that our platform may enable users to capture maximum savings whenever competitive market conditions permit.

Abstract

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