[Submitted on 22 Sep 2026]
Title:Marginally Correct Tool Caches Can Reverse Group-Normalized Policy Updates
View a PDF of the paper titled Marginally Correct Tool Caches Can Reverse Group-Normalized Policy Updates, by Shivam Gupta
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Abstract:Tool-result caching reduces repeated execution in agent training, but also couples rollout randomness. We study a two-action model in which independent and shared execution preserve every rollout's conditional reward distribution. Despite this marginal agreement, sharing one stochastic result per group can reverse the expected group-normalized policy update. We derive an exact finite-group expression: against a constant alternative, the shared update follows the probability of winning minus the probability of losing, rather than the difference in expected reward. A Bernoulli specialization yields a wrong-direction region and a non-vanishing update-variance floor as group size grows. Centering without group standard-deviation scaling preserves the expected-return direction in this model, using an existing estimator control. Exhaustive finite sums verify 540 configurations and 3,240 estimator evaluations, with a separate ordered-sequence checker. An implementation audit reproduces the sharing path in a pinned, unmodified TVCache stack using 256 scripted rollouts. These results do not measure language-model training performance or refute TVCache's deterministic-output contract. They establish that marginal output validity alone cannot certify a stochastic cache as training-equivalent.
Comments: 8 pages, 1 figure, 2 tables. Code and reproducibility materials: this https URL
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2609.26866 [cs.LG]
(or arXiv:2609.26866v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.26866
arXiv-issued DOI via DataCite
Submission history
From: Shivam Gupta [view email] [v1] Tue, 22 Sep 2026 16:15:47 UTC (35 KB)
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