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.

RL post-training strategies are dataset-dependent and reveal a recurring empirical pattern: capacity parameters accumulate monotonically across stages, while regularization parameters predominantly oscillate in response to shifting training dynamics. This distinction highlights a potential flaw in fixed training schedules: by forcing all parameters along rigid paths, they fail to capture the dynamic exploration-exploitation tradeoffs that regularization must track. We uncover this through LLMZero, an agentic system that optimizes training trajectories via tree search by diagnosing pathologies at each checkpoint and proposing coordinated multi-parameter transitions. Across four diverse GRPO tasks, LLMZero discovers strategies that improve over the base model by 9% to 140% and over grid search by 6% to 15% (relative), consistently outperforming random search and a skill-based agent under a matched compute budget. The capacity–regularization asymmetry is consistent across all four tasks, offering a candidate design heuristic for multi-stage training.

Tabular data is frequently captured in image form across a wide range of real-world scenarios such as financial reports, handwritten records, and document scans. These visual representations pose unique challenges for machine understanding, as they combine both structural and visual complexities. While recent advances in Multimodal Large Language Models (MLLMs) show promising results in table understanding, they typically assume the relevant table is readily available. However, a more practical scenario involves identifying and reasoning over relevant tables from large-scale collections to answer user queries. To address this gap, we propose , a framework that enables MLLMs to answer queries over large collections of table images. Our approach first retrieves candidate tables using jointly trained visual-text foundation models, then leverages MLLMs to perform fine-grained reranking of these candidates, and finally employs MLLMs to reason over the selected tables for answer generation. Through extensive experiments on a newly constructed dataset comprising 88,161 training and 9,819 testing samples across 8 benchmarks with 48,504 unique tables, we demonstrate that our framework significantly outperforms existing methods by 7.0% in retrieval recall and 6.1% in answer accuracy, offering a practical solution for real-world table understanding tasks.