SIPO: Selective-Inference Policy Optimization for Tree-Structured Agentic RL

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) has become a dominant paradigm for improving the reasoning capabilities of large language models (LLMs). Recent tree-based methods such as TreeRPO extend flat trajectory sampling with tree-structured rollouts to obtain dense, step-level reward signals without a separate process reward model. However, not all trees are equally informative: trees where all leaves succeed, all leaves fail, or the policy already predicts the reward distribution contribute little to gradient updates, wasting compute. We introduce CATPO (Critique-Augmented Tree Policy Optimization), which diagnoses and addresses this waste at the tree level. CATPO first scores each tree via a tree informativeness score, F(T), combining leaf-outcome diversity with policy-reward decorrelation at zero extra compute. For dead-wrong trees where all branches fail, CATPO applies critique-guided healing: it locates the shallowest failure point, generates a natural-language critique, and grafts refined continuations to recover training signal. Finally, an informativeness-weighted loss scales each tree's gradient contribution by its normalized score, concentrating parameter updates on the most informative trees while preserving overall gradient magnitude. Experiments on Qwen2.5-Math-1.5B trained with the MATH dataset show that CATPO achieves 37.5% macro accuracy across four benchmarks (AIME24, MATH-500, OlympiadBench, and MinervaMath), improving over TreeRPO by 1.9% and GRPO by 4.8%.

Reinforcement learning has emerged as the dominant paradigm for training large language model (LLM) agents that interact with executable sandboxes. State-of-the-art algorithms such as PPO, RLOO, and GRPO inherit their rollout topology from RLHF: for each prompt, N independent trajectories are sampled from the initial state, and an advantage is computed by subtracting a group baseline. This design ignores a defining property of agent sandboxes. They are deterministic, snapshottable, and resumable from any intermediate state. We argue that this property enables a fundamentally different rollout topology: rather than N independent trees of depth T, one can construct a single tree of N leaves whose siblings share prefixes, and therefore share variance. We instantiate this idea as Branching Policy Optimization (BPO), a sandbox-native RL algorithm that (i) adaptively snapshots the sandbox at high-entropy decision points along a backbone trajectory, (ii) forks K alternative actions per branch point and rolls out each to termination, and (iii) computes per-step advantages from sibling returns rather than from independent prompts. We prove this estimator is unbiased and has strictly lower variance than the trajectory-level baseline, with the reduction equal to the prefix-explained portion of return variance. On WebShop, ALFWorld, and SWE-bench Verified with Qwen2.5-7B and Llama-3.1-8B backbones, BPO improves success by 3.6--6.1 absolute points over GRPO and RLOO at matched compute, halves gradient-norm variance, and matches the best baseline using 38% fewer policy updates.