Maximizing Rollout Informativeness under a Fixed Budget: A Submodular View of Tree Search for Tool-Use Agentic Reinforcement Learning
Authors: Yuelin Hu, Zhenbo Yu, Zhengxue Cheng, Wei Liu, Li Song
Organizations: Shanghai Jiao Tong University · Shanghai Maritime University
Abstract
We formalize Rollout Informativeness under a Fixed Budget (RIFB) as the expected non-vanishing policy-gradient mass that a tool-use rollout set injects into Group Relative Policy Optimization (GRPO). We prove that any budget-agnostic independent sampler suffers a collapse rate bounded away from zero for hard prompts regardless of the budget. Motivated by this, we recast intermediate state selection as a monotone submodular maximization problem, where a greedy one-step selector enjoys a 1 minus 1/e approximation guarantee. Our Uncertainty-aware Upper Confidence Bound (UUCB) terms arise as closed-form marginal gains of this objective. This turns the token-level entropy bonus from an empirical trick into an analytic consequence of the formulation. We present InfoTree, a training-time tree-search framework coupling UUCB with a learned Adaptive Budget Allocator (ABA) and an asynchronous Speculative Expansion scheme. ABA rescues prompts whose initial tree is wasted on uniform outcomes, lifting the mixed-outcome ratio from 58.1 percent to 76.3 percent with less than 5 percent budget overhead. Speculative Expansion reduces wall-clock overhead from 14.3 percent to 4.8 percent by tolerating bounded staleness in UUCB scores. Across nine benchmarks spanning math reasoning (AIME 2024 and 2025, MATH-500, OlympiadBench, USAMO), web-search agents (GAIA, HLE-100, BrowseComp-lite), and tool-rich coding and OS agents (APPS-verified, AgentBench-OS), InfoTree outperforms flat GRPO, DeepSearch, Tree-GRPO, AT2PO, CW-GRPO, and RC-GRPO. Head-to-head compositions with Tree-GRPO prefix sharing and CW-GRPO contribution weights deliver further gains, confirming that our selector operates orthogonally to rollout reuse and trajectory re-weighting. A 5 by 5 by 5 robustness grid reveals that over three quarters of the hyperparameter space lies on a performance plateau, confirming UUCB robustness.
Reinforcement learning with verifiable rewards (RLVR) is a promising approach for enhancing reasoning and agentic behavior in large language models. However, rollout-intensive policy optimization is often limited by insufficient reward contrast, arising when overly simple or complex prompts generate low-variance feedback and when outcome-only rewards assign the same terminal assessment to every decision in a multi-turn rollout. Past efforts have focused on allocating available rollout resources to promising prompts, yet they only leverage sample informativeness at the prompt level and neglect variation in prefix-level informativeness across turns within the same rollout. This work targets multi-turn agentic RL by modeling each ReAct-style thought-action-observation turn as a semantically distinct node, allowing budget allocation to extend from prompt roots to turn-level prefixes with further continuations, which naturally forms tree-structured rollouts. We introduce Tree Rollout Allocation for Contrastive Exploration (TRACE), a unified rollout allocation framework that enhances reward contrast within a fixed sampling budget. Technically, TRACE allocates rollout budget to both prompt roots and intermediate prefixes that are most likely to yield mixed terminal rewards. A shared generalizable predictor estimates conditional success probability at these anchors from prefix histories to guide this allocation. The resulting adaptive tree structure enriches outcome-only feedback and amplifies the policy-update signal. Empirically, TRACE achieves competitive performance and efficiency gains on typical agentic benchmarks, e.g., improving Qwen3-14B Multi-Hop QA average accuracy by 2.8 points over competitive baselines at equal sampling cost.
Reinforcement learning has become a promising paradigm for improving large language model (LLM) agents on long-horizon search tasks, where the agent must make a sequence of intermediate decisions before receiving a final outcome. However, existing methods still face a key limitation: the rollout budget is often allocated without explicitly assessing the utility of intermediate states. As a result, substantial computation may be spent on low-value states, even though different branches can vary drastically in their informativeness. In this paper, we propose Information Gain-based Rollout Policy Optimization (IGRPO), a policy optimization framework that treats intermediate-state informativeness as the organizing principle of rollout collection. Specifically, IGRPO performs budget-aware tree-structured rollouts by allocating expansion budget according to node-level informativeness, so that more informative branches are expanded more frequently while unpromising branches are progressively suppressed. We further demonstrate that the information gain-based rollout induces an explicit limiting teacher distribution over trajectories, which naturally yields a clear policy optimization target, thereby unifying adaptive tree-structured exploration with principled policy learning under a single framework. Experiments on seven challenging search-augmented QA benchmarks demonstrate that IGRPO consistently outperforms strong baselines under the same rollout budget constraints, validating the effectiveness of leveraging the induced teacher distribution to guide policy optimization for long-horizon search agents.
LLM post-training often relies on reinforcement learning methods that sample multiple rollouts per prompt, yet most existing approaches use a fixed rollout budget for every prompt, despite large differences in the training signal different prompts provide. In this paper, we study adaptive rollout allocation under a fixed global budget and formulate the problem as online resource allocation with prompt-level diminishing returns. Our method, CERO, maintains a Beta posterior over each prompt's success probability and uses the posterior expected Bernoulli variance as a Bayesian estimate of the value of additional rollouts. We use this estimate to construct a concave, saturating utility over cumulative allocations, yielding an objective in which decisions across prompts and epochs are coupled by the global budget. Since the resulting objective is temporally nonseparable, we derive a Fenchel-dual reformulation and update both prompt-level and budget-level dual variables via projected online gradient descent. Under fixed prompt utilities, we prove an O(K) regret bound against the offline allocation benchmark. Experiments on mathematical-reasoning problems show that CERO consistently outperforms GRPO across multiple open-weight LLMs and benchmarks, demonstrating that adaptive rollout budgeting can improve sample efficiency.