Which LLM for Which Work? Budgeted Model Allocation under Uncertain Evaluation

A company with a fixed artificial intelligence (AI) budget must decide which large language model (LLM) handles each recurring workload. What it lacks is the quality table, how well each model performs on each workload. Given that table, the decision is a multiple-choice knapsack problem and is routine to solve, so estimating it is the difficulty, and that estimation fails in two ways. Models are rarely compared on the same work, and the recorded score is usually a proxy rather than the outcome the company values. Causal and off-policy methods repair the first but condition on the second, while evaluator-validation methods estimate the second but stop short of the decision. Worse, buying more re-evaluation cannot settle the second: randomization governs which requests are scored, not how a score is produced, so the table stays uncertain however much evaluation is purchased. Yet the deployment decision may still be determined even when the table is not. We therefore ask whether one assignment stays optimal across every quality table consistent with the evidence. For the fixed-budget problem, this admits an exact two-solve certificate: solve once at the estimated table and once at a least-favourable table. Agreement certifies the assignment; disagreement identifies the model-workload pairs where further evidence can matter. We propose CASE (causal active sequential experimentation), which targets evaluation to those pairs and repeats the test as evidence accumulates. On a production log, the measurement failure is the larger of the two: correcting assignment exactly still leaves most of the loss, and randomized re-evaluation does not remove it. In our experiments, the available evidence often does not determine the assignment. On paid software tasks, better information about model quality yields more savings than further optimization of the assignment on the same estimates.

Thinking Hard, Not Smart: Reasoning Models Fail to Ration Test-Time Compute Across Questions

Reasoning language models increasingly use test-time compute to improve performance, but existing evaluations typically study this compute one question at a time. Yet when multiple problems share an end-to-end cost or latency constraint, models must decide how to divide limited inference compute among them. We introduce an exam-style evaluation framework for studying this setting, in which a model must distribute one shared token budget across questions with different difficulty and point values to maximize its total score. Across several open and frontier reasoning models, we find that models fail to allocate a shared budget strategically across questions of varying difficulties and values. Models behave largely as greedy sequential solvers: they prioritize questions by presentation order, front-load effort on early questions, and remain insensitive to value, with these tendencies becoming more pronounced as the number of questions grows. Explicit planning prompts spread compute more evenly but do not produce value- or difficulty-aware prioritization. The same behavioral pattern extends from mathematical to code reasoning. These findings establish global budget allocation as a distinct capability that is not captured by conventional per-question evaluation and remains a challenge for current reasoning models.

Relay, Don't Route: Adaptive Population Handoff for Cost-Efficient LLM-Driven Evolution

Large language model (LLM)-driven evolution has shown promise for program search and algorithm discovery, but relying on strong models throughout long evolutionary runs is costly. A natural alternative is to combine cheap and strong models under a fixed inference budget. However, existing approaches typically allocate models at the level of individual queries or mutation steps, overlooking that evolutionary search is \textit{stateful}: each generated candidate changes the population from which subsequent mutations are produced. We empirically analyze LLM-driven evolutionary trajectories and find that search progress is strongly front-loaded, early trajectory performance is informative but noisy, and cheap models recover much of the early progress achieved by strong models at lower cost. Motivated by these findings, we propose \textbf{\model}, a training-free framework that shifts budget allocation from individual calls to evolving populations through adaptive \textit{population handoff}. A cheap model explores multiple trajectories in short blocks allocated by a bandit scheduler. Relay Gain, defined as the marginal improvement of a compact, quality-diverse candidate bank constructed for handoff, serves as the scheduler reward and determines when to hand off. The curated candidates initialize a shared strong model population for refinement. Across four benchmarks and three budgets, \model achieves the highest mean score in 11 of 12 settings, outperforming competitive baselines. Our results suggest that in stateful search, budget allocation should be organized around the population, not the individual call.

One Human, $N$ Agents: Audit-Budget Allocation for LLM Agent Fleets under Miscalibrated, Correlated Confidence

A single human must audit $N$ LLM agents under a budget of $B \ll N$ audits per round, guided by self-reported confidence that may be adversarially miscalibrated and by correlated errors. We model this as budgeted noisy inspection over a two-level Gaussian copula and locate the miscalibration threshold $δ^*$ past which confidence-ranked auditing is \emph{worse} than random. Two a-priori expectations reverse: $δ^*$ \emph{rises} as the budget shrinks, and cross-family correlation is not low---shared difficulty dominates lineage. Five open-weight LLMs show operationally useless (near-constant) confidence, point estimates at or beyond the flip though CIs straddle it; a proprietary model is informative and lands below it. We give a quantitative criterion for \emph{vacuous} oversight, and replaying policies on recorded traces confirms the ordering.

Resample or Reroute? Budget-Aware Test-Time Model Selection for Large Language Models

Routing among large language models (LLMs) trades response quality against serving cost, motivated by the reported gap between deployed routers and a per-instance oracle. Recent analysis shows that test-time resampling can recover per-instance selection headroom that no single-commit router captures; however, that guarantee holds only under an idealized oracle equipped with correctness labels and an unconstrained budget, neither of which a deployed system has. To the best of our knowledge, no previous work treats resampling the committed model and rerouting to an alternative model as competing uses of a single per-query cost budget. Therefore, this work formulates budget-aware test-time model selection: given a per-query budget and an imperfect verifier, allocate each unit of budget between resampling and rerouting so that expected correctness is maximized. An online resample-or-reroute (RoR) allocation policy driven by estimated marginal correctness per unit cost is proposed, and its behavior is grounded in the recoverability asymmetry between selection and sampling. Replay experiments on newly regenerated multi-draw correctness tensors from an eleven-model open-weight pool over four benchmarks of differing difficulty show that the proposed RoR policy attains a favorable cost-quality Pareto front relative to single-route, one-commit-router, budget-aware best-of-K, cascade, and random-allocation baselines for the tested pools, with the largest gains on the most heterogeneous benchmark; an ablation further shows the gains are verifier-gated, shrinking as verifier quality degrades, and robustness replays under a provider price vector and a label-free agreement verifier delineate where the conclusions carry over.

A Few Teacher Steps Go a Long Way: Cost-Efficient On-Policy Data Augmentation for Agent Post-Training

For LLM agents, supervised fine-tuning is not only about teacher labels' quality, but also about which interaction contexts those labels condition on. Pure behavioral cloning uses full teacher demonstrations, creating a mismatch between teacher-induced contexts seen in training and student-induced contexts encountered at test time. Recent work addresses this mismatch by querying a teacher at contexts reached by the student, often with increasingly elaborate filtering of the teacher's continuations. We instead frame on-policy data construction as a budget-allocation problem: under matched supervision resources, should teacher output be spent on more start-to-finish demos, longer continuations, outcome filtering, or broader coverage of learner-induced contexts? We formalize this design space through the rollout policy, switch-time distribution, continuation horizon, filtering rules, and two complementary costs: teacher inference generated before filtering and teacher supervision retained for SFT. Across HotpotQA, ALFWorld, and Terminal-Bench-Dev, bounded unfiltered teacher continuations at learner-induced contexts improve over pure behavioral cloning at matched budgets. On HotpotQA and ALFWorld, where we run the full comparison, few-step continuations match or exceed success-filtered and critical-context-filtered alternatives. Our findings suggest that a few teacher steps, placed at learner-induced contexts, can be a more cost-efficient supervision allocation than longer or more heavily curated teacher completions.

Where Does Harness-Optimization Value Live? Localized Gains and the Budget-Splitting Trap in Self-Evolving LLM Agents

A growing body of work improves frozen large language models (LLMs) as agents by evolving their harness: the textual scaffolding around the model, including persona, strategy, format rules, and control heuristics. Existing reflective prompt-evolution methods usually optimize this harness as one flat string. We instead ask where the optimization value actually resides. We introduce HARNESSEVO, which decomposes the harness into four separately evolvable slots: role, task-strategy, tool/format-rules, and reflection/control. Using the same reflective optimizer under an iso-budget setting, we pair this decomposition with leave-one-in and leave-one-out attribution to measure the contribution of each slot. On ALFWorld with a frozen 7B backbone, HARNESSEVO does not significantly improve the overall binary success rate over either the stock harness or flat-string evolution: 0.657 versus 0.642 and 0.642, respectively. However, the slot-level analysis reveals that nearly all useful optimization value is localized in the reflection/control slot, which achieves a leave-one-in gain of +0.119. The other slots are individually null. We further show that uniform budget splitting is harmful: allocating 64 rollouts across four slots leaves only 16 per slot, below the optimizer's effective search floor, causing every slot to freeze at its empty seed. Concentrating the budget on the high-credit control slot recovers the lost gain, reaching 0.761 with half the split budget. The effect is task-contingent. On WebShop, all slots freeze empty and all methods tie, indicating a genuine absence of recurrent, verbalizable control failures rather than budget starvation. Overall, our results suggest that harness value is localized, uniform budget splitting can be actively harmful, and credit assignment should precede structured agent-evolution.

The Shadow Price of Reasoning: Economic Perspective on Optimal Budget Allocation for LLMs

Inference-time scaling has emerged as a critical avenue for enhancing Large Language Models' performance, yet real-world deployment is constrained by strict computational budgets. In this work, we formulate inference budget allocation as a global constrained optimization problem governed by economic principles. By modeling per-query reasoning utility with a shifted-surge function, we derive an optimal allocation policy based on a global shadow price that equilibrates marginal utility under resource scarcity. Based on this theory, we propose Constrained Latent-utility Equilibrium Allocation for Reasoning (CLEAR). It performs rational abandonment and reallocates resources from insolvent queries to solvable queries near their emergence thresholds. Extensive experiments on several reasoning tasks with different traffic streams demonstrate that CLEAR significantly improves the Pareto frontier of total token cost versus mean accuracy. In resource-scarce regimes, CLEAR achieves up to a 3x improvement in global accuracy compared to uniform allocation.