Dynamic Budget Allocation for LLM Evaluation under Hard Resource Constraints

Evaluating and predicting the performance of large language models (LLMs) in multi-turn conversational settings is critical yet computationally expensive; key events -- e.g., jailbreaks or successful task completion by an agent -- often emerge only after repeated interactions. These events might be rare, and under any feasible computational budget, remain unobserved. Recent conformal survival frameworks construct reliable lower predictive bounds (LPBs) on the number of iterations to trigger the event of interest, but rely on static budget allocation that is inefficient in multi-turn setups. To address this, we introduce \emph{Dynamic Allocation via PRojected Optimization} (DAPRO), the first theoretically valid dynamic budget allocation framework for bounding the time-to-event in multi-turn LLM interactions. We prove that DAPRO satisfies the budget constraint and provides distribution-free, finite-sample coverage guarantees without requiring the conditional independence between censoring and event times assumed by prior conformal survival approaches. A key theoretical contribution is a novel coverage bound that scales with the square root of the mean censoring weight rather than the worst-case weight, yielding provably tighter guarantees than prior work. Furthermore, DAPRO can be employed to obtain unbiased, low-variance estimates of population-level evaluation metrics, such as the jailbreak rate, under limited computing resources. Comprehensive experiments across agentic task success, adversarial jailbreaks, toxic content generation, and RAG hallucinations using LLMs such as Llama 3.1 and Qwen 2.5 demonstrate that DAPRO consistently achieves coverage closer to the nominal level with lower variance than static baselines, while satisfying the budget constraint.

Test-time compute scaling, the practice of spending extra computation during inference via repeated sampling, search, or extended reasoning, has become a powerful lever for improving large language model performance. Yet deploying these techniques under finite inference budgets requires a decision that current systems largely ignore: which inputs deserve more compute, and which can be answered cheaply? We formalize this as a constrained optimization problem (maximize expected accuracy subject to an average compute budget) and solve it with a two-stage Solve-then-Learn pipeline. In the solve stage, Lagrangian relaxation decomposes the global constraint into per-instance sub-problems, each admitting a closed-form oracle action that optimally prices accuracy against cost. We prove that the induced cost is monotone in the dual variable, enabling exact budget targeting via binary search. In the learn stage, a lightweight classifier is trained to predict oracle actions from cheap input features, amortizing the allocation rule for real-time deployment. We establish that the task-level regret of the learned policy is bounded by its imitation error times the worst-case per-instance gap, yielding a clean reduction from constrained inference to supervised classification. Experiments on MATH and GSM8K with three LLMs (DeepSeek-V3, GPT-4o-mini, Qwen2.5-7B) show that our method consistently outperforms uniform and heuristic allocation baselines, achieving up to 12.8% relative accuracy improvement on MATH under matched budget constraints, while closely tracking the Lagrangian oracle upper bound with over 91% imitation accuracy.

Large language model (LLM) configuration evaluation is challenging due to limited evaluation budgets, varying costs, and multiple competing objectives. In this paper, we formulate LLM configuration evaluation as a cost-aware multi-objective bandit problem, where each configuration evaluation incurs a configuration-dependent cost and yields a noisy vector-valued outcome. Under this framework, we study two fundamental problems: online configuration selection and Pareto configuration identification. For online configuration selection, we propose a hypervolume-based UCB algorithm that optimizes an optimistic hypervolume-per-cost index. We establish a budgeted regret bound of order $O\bigl(\sum_{i\ne i^\star}\frac{\log B}{Δ_i}\bigr)$, where $B$ is the evaluation budget, $i^\star$ is the optimal configuration in terms of hypervolume efficiency, and $Δ_i$ is the corresponding efficiency gap of configuration $i$. This bound retains the logarithmic budget dependence of classical single-objective budgeted bandits. For fixed-budget Pareto identification, we develop a cost-aware empirical gap elimination algorithm and prove that its error probability is of order $O\bigl(\exp(-\frac{B}{H_{μ,c}})\bigr)$, where $H_{μ,c}$ is a cost-aware Pareto identification complexity depending on configuration costs and Pareto classification gaps. This error probability decays exponentially with the evaluation budget and recovers the standard Pareto set identification guarantee when all configuration costs are identical. Experiments on LLM configuration evaluation tasks demonstrate that the proposed framework enables efficient online decision-making and accurate cost-aware Pareto identification under limited budgets.