Authors:Yann Pernot (1 and 2), Vi Retault (2) ((1) Mila - Québec AI Institute, (2) Polytechnique Montréal)
Abstract:Multi-turn agents interleave consequential decisions with routine execution: some actions change the downstream return distribution, while others are necessary but reward-equivalent. The cost of trajectory-level credit assignment, often attributed to long horizons, is in fact governed by decision density $\rho$: the fraction of turns whose actions affect the return. When decision density is low, routine turns create signal dilution: they add gradient variance to trajectory-level estimators such as GRPO without adding expected signal. Under explicit assumptions, the resulting turn-level to trajectory-level signal-to-noise ratio scales as $\rho^{-1/2}$, provided critic error remains controlled. The same analysis identifies the complementary regime: at high decision density, trajectory-level methods can remain competitive while avoiding the cost of a critic. In a controlled environment where $\rho$ is exactly tunable, the predicted scaling is recovered with $R^2 = 0.999$, and the training-step gap widens significantly as $\rho \to 0$.
From: Yann Pernot [view email]
[v1]
Sat, 20 Jun 2026 17:55:10 UTC (1,076 KB)
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