Marginally Correct Tool Caches Can Reverse Group-Normalized Policy Updates

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.

8 pages, 1 figure, 2 tables. Code and reproducibility materials: this https URL

Machine Learning (cs.LG)

arXiv:2609.26866 [cs.LG]

(or arXiv:2609.26866v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.26866 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.