CostAda is introduced, a cost-calibrated adaptive controller built around a cost-calibrated frontier utility that reaches the strongest baseline's full-budget quality with at most half the budget on twelve of sixteen benchmark--backbone pairs while achieving the strongest mean final quality on all eight benchmarks under GLM-5 and GPT-5.
Abstract
Large language models increasingly support scientific and algorithmic discovery through inference-time search over evaluated candidates. Existing adaptive discovery controllers assign credit based only on score progress, even though prompt length, retries, and guidance calls cause search actions to incur different token costs. We prove that cost-blind credit can forfeit all but a vanishing fraction of attainable quality as frontiers multiply and costs diverge. Under a fixed search-side token budget, the controller must decide which frontier is improving and whether its gain justifies the realized cost before the budget is exhausted. We introduce \textbf{CostAda}, a cost-calibrated adaptive controller built around \emph{cost-calibrated frontier utility}. The utility values frontier progress relative to realized action cost and conditions that credit on the remaining budget. CostAda uses this signal to control local exploration intensity, frontier allocation, and budgeted tactic intervention. Cost and remaining budget therefore shape the search rather than serving only as accounting variables or a stopping rule. CostAda reaches the strongest baseline's full-budget quality with at most half the budget on twelve of sixteen benchmark--backbone pairs while achieving the strongest mean final quality on all eight benchmarks under GLM-5 and GPT-5.4.
Budget-constrained agentic search arises when an LLM agent must refine candidates under a small evaluation budget, because validation is expensive, generation requires multiple model calls, or both. In this regime, standard MCTS allocates budget poorly: exploration bonuses dominate at low visit counts, unpromising siblings are expanded before promising chains can deepen, and branching is independent of node quality. We introduce ExTS, a tree-search policy that treats expansion itself as a value-of-information decision. ExTS combines three mechanisms: discriminative reward shaping to separate candidates under narrow score distributions, a stochastic virtual child that estimates the value of creating a new branch from the parent's reward history, and quality-conditioned branching that expands only when a node's score justifies the budget cost. Across prompt optimization, code generation, molecular structure elucidation, and agentic workflow optimization, ExTS is competitive with or improves over task-specific tree-search baselines, with an average relative gain of +5.5% using a single fixed configuration. We further introduce pilot-run diagnostics that characterize what makes budget-constrained agentic search problems structurally different from one another, providing both understanding of the problem space and practical guidance for adaptation.
Many algorithms spend an internal resource before returning a decision and are evaluated only by the quality of that terminal output. We formalize such procedures as terminal computation-allocation problems: costly computations produce observations, update beliefs about a latent environment, and matter only through terminal decision loss. Bellman equations characterize optimal allocation under fixed budgets, priced computation, and exact certification. We then relate value of computation (VOC) to information. Mutual information equals myopic VOC under log loss, whereas under simple regret VOC is a knowledge-gradient quantity; moreover, information gain can rank computations arbitrarily poorly, although it gives a one-sided upper bound on VOC. Bandit pulls, tree simulations, and node expansions illustrate the same model under different computation topologies. Finally, under an explicit frontier-resolution and heuristic-error model, maximizing approximate VOC recovers weighted A*, with A* and greedy best-first search as limiting cases. The theory identifies a shared decision problem without asserting that one acquisition rule is universally optimal.
Active RAG systems decide when to retrieve external knowledge during generation, making them a budget-sensitive case of agentic RAG and self-adaptive retrieval. Yet evaluations often leave the operating point underspecified: two systems may both claim a 50% evidence-usage budget while realizing different held-out usage rates, so higher accuracy can reflect a looser budget rather than a better retrieval policy. We study budget-aware evaluation for Active RAG by recasting active retrieval as utility estimation, where retrieval is valuable only through its marginal correctness change over a no-retrieval answer. This view separates three questions that single-point evaluations conflate: whether trigger scores rank useful retrieval decisions, whether thresholds calibrated on past data meet future budgets, and how trigger-side computation changes deployment cost. We operationalize these questions with exact top-k utility frontiers, deployable threshold frontiers, conservative budget frontiers, harm audits, and cost decompositions. Across knowledge-intensive multi-hop QA datasets and open instruction models, retrieval harm is non-negligible, router rankings change across datasets and budgets, nominal thresholds can miss target usage, and simple uncertainty or retrieval-score baselines often rival learned utility routers. Budget-aware Active RAG evaluations should therefore report frontiers, realized usage, threshold-transfer error, harm rates, and cost decompositions alongside accuracy.
Pinyan Qian, Su Wang, Chong Peng et al.· arXiv.org· 1 citation
While reinforcement learning has enabled LLM-based search agents to invoke external tools, existing methods train under fixed budgets and cannot adapt when constraints vary at deployment. We propose AnySearch, a framework that enables a single policy to perform budget-aware search under any budget constraint through a training scaffold and curriculum reinforcement learning. In the first phase, we train the agent with explicit budget state injection and structured reasoning prompts that guide efficient allocation under linearly decaying budgets. In the second phase, the scaffold is removed and the agent learns to operate autonomously under adaptively sampled budget constraints, matching inference conditions. Both phases are optimized with a composite reward that couples answer accuracy with budget efficiency through absolute and relative signals, where an adaptive weight amplifies the efficiency signal for high-accuracy queries and attenuates it for low-accuracy ones. Extensive experiments on seven general and multi-hop QA benchmarks show that our method outperforms baselines across all budget scales, generalizes to unseen constraints beyond the training range, and achieves superior tool productivity without excessive token overhead. Our code is available at https://github.com/xwsun01/AnySearch.
Xiaowei Sun, Jin Li, Yi-Li Hong et al.· 0 citations
EcoAgent-Bench is introduced, in which every task specifies priced actions and an explicit budget, and results show that completion under a budget and economical action selection are distinct properties.
Jie Wu, Ming Gong, Feixiang Cheng et al.· 0 citations
Inference-time search with large language models (LLMs) often concentrates on a small set of structurally or semantically similar trajectories, leaving alternatives underexplored---a failure mode we call \textit{reasoning basin collapse}. We introduce BASIN, a training-free, structure-aware selection method that groups reasoning states into basins and penalizes repeated visits to the same strategy, thereby reallocating search across genuinely distinct reasoning paths under a fixed compute budget. Under matched inference budgets, BASIN improves over Tree of Thoughts (ToT) by up to $+22$pp on Game of 24 and $+6.7$pp on MuSR. A quality-aware variant, QA-BASIN, further improves robustness by preserving high-quality basins when unconditional diversification over-explores. To explain when basin-aware selection helps, we introduce the redundancy gap $\Delta$, which measures how differently search concentrates for correct versus incorrect predictions: standard ToT often operates near $\Delta \approx 0$, while BASIN consistently shifts $\Delta$ positive. More broadly, BASIN suggests structure-aware selection as a simple and general approach to improving inference-time reasoning. Code can be found at https://github.com/GitHubLuCheng/basin.
Lu Cheng· 0 citations
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