{"paper":{"title":"PhiBE-Q-Learning: Bridging Off-Policy Reinforcement Learning and Continuous-Time Control","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Yuhua Zhu, Yutong Ren","submitted_at":"2026-06-20T07:47:41Z","abstract_excerpt":"In this paper, we develop an off-policy method for continuous-time reinforcement learning (CTRL), where the system dynamics are governed by an unknown stochastic differential equation (SDE) and only discrete-time trajectory data are available. A central challenge is that the classical state-action value function $Q(s,a)$, which enables off-policy learning in discrete-time RL, does not exist in CTRL (Baird, 1994; Jia and Zhou, 2023; Tallec et al., 2019). On the other hand, continuous-time control provides local notions such as the instantaneous advantage function $q(s,a)$, but these typically r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21925","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.21925/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}