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arXiv · 2601.19499

Progress-Certified Reversible Simplex Supervision of Goal-Reaching Reinforcement Learning

Mehdi Heydari Shahna·Jouni Mattila
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Abstract

Task completion is difficult to certify when state aggregation, model mismatch, and disturbances invalidate nominal RL transitions. We present a reversible Simplex framework combining a frozen finite-state policy with goal-level robust-adaptive recovery and explicit accounting for post-action progress debt. Outward-rounded reachability verifies disturbed transitions, bounds debt from rejected learned actions, and constructs robust recovery and re-entry sets. If an independent checker accepts both certificates and the recovery decrement exceeds the verified debt, every completed switching cycle decreases storage, yielding finite switching and finite-sample goal entry. In a restricted end-to-end instance, the checker resolves all retained obligations, certifies $\kappa_L=0.482$, and establishes $\varepsilon_{\mathrm{sw}}\ge 0.060$. Matched numerical episodes yield 20/20 goal entries and 0/320 debt-test violations with debt gating, versus 18/20 and 742/796 without it. Twenty-four hardware trials evaluate 50 ms supervision above a 1 kHz actuator stack; formal certification remains limited to the checked model.

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Mehdi Heydari Shahna, Jouni Mattila. 2026-01-27. Progress-Certified Reversible Simplex Supervision of Goal-Reaching Reinforcement Learning. https://arxiv.org/abs/2601.19499

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