Coverage, Not Targeting: A Structural Regime in Multi-Turn Agent Credit Assignment

TL;DR - This paper argues that when verifiers reveal little about which steps in a multi-turn agent trajectory were correct, broad reward coverage matters more than targeting selected turns. Uniform credit redistribution consistently outperformed concentrated schemes across several agent benchmarks and model families.

• Defines verifier information density, (V_d=k/C), as the fraction of a causal chain whose per-turn correctness is exposed by the verifier.
• Terminal-state verification produced low information density—about 0.15 on (\tau^2)-bench and 0.4 on BFCL V3—while the estimated targeting crossover was roughly 0.8.
• Uniform dense rewards beat sparse outcomes and targeted or randomly concentrated alternatives; shuffled controls were also consistently harmful.
• A breadth sweep showed a monotonic improvement as more of the causal chain received credit, with the deficit disappearing only at full coverage.