{"paper":{"title":"Target Updates May Stabilize Linear Q-Learning: Periodic and Soft Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG"],"primary_cat":"stat.ML","authors_text":"Donghwan Lee","submitted_at":"2026-05-31T15:46:20Z","abstract_excerpt":"Periodic target updates in Q-learning and soft target updates in actor-critic methods are empirically well established stabilization mechanisms, but their precise theoretical explanation is still incomplete. This paper gives a rigorous and exact analysis of these mechanisms for Q-learning with linear function approximation (linear Q-learning) using the exact switched linear system (SLS) dynamics induced by the Bellman maximum and the joint spectral radius (JSR) of the resulting switching matrix families. Although linear Q-learning can fail to converge in general, we prove that, under explicit "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02645","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/2606.02645/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"}