Coverage, Not Targeting: A Structural Regime in Multi-Turn Agent Credit Assignment
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Chenyu Zhou, Qiliang Jiang, Shuning Wu, Xu Zhou
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Multi-turn agentic RL increasingly treats credit assignment as a targeting problem: given a terminal verifiable reward, per-turn methods localize credit onto the turns that mattered. We identify the structural quantity that predicts when this is the right move, the verifier information density V_d = k/C (the fraction of an agent's C-step causal chain whose per-turn correctness the verifier exposes), and show that terminal-state verifiers sit deep in a low-V_d regime where targeting is the wrong axis. In controlled shared-rollout comparisons on tau^2-bench that separate reward density from credit geometry, a continuous dense reward spread uniformly beats the sparse binary outcome reward (net-harmful on 4/5 seeds), while concentrating the same advantage on progress turns or on random turns is equally harmful: targeting is second-order. The mechanism is coverage: terminal-state verification collapses the observable signal to a single final-write turn (k=1 in 98% of rollouts) while success requires a 5-8 step chain of prerequisite tool calls. A synthetic phase boundary places the crossover at V_d* ~ 0.8, whereas measured V_d is ~0.15 on tau^2-bench and ~0.4 on BFCL V3; uniform also wins on BFCL, where a matched-concentration shuffled control is negative on 8/8 seeds. The effect reproduces across model families on ToolACE-2-8B (Delta = -0.048 over 32 pre-registered seeds; an independent 20-seed replication is itself significant), and a pre-registered matched-budget breadth sweep traces a monotone dose-response whose deficit vanishes only at full chain coverage, with a reward-to-go arm reaching full-coverage parity. Uniform redistribution is the zero-information coverage default that per-turn schemes must beat; we contribute the matched-concentration shuffled control that any targeting claim should clear.
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