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This mixed retraining thus focuses on enforcing the desired behaviors in the collected areas. We develop the theory for both policy and value-based methods, showing that: (i) in policy-based settings, our method retains monotonic improvement bounds; and (ii) in value-based settings,\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\varepsilon $$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    \u00a0preserves convergence properties without additional assumptions. The approach is simple to integrate into existing RL algorithms and improves sample efficiency and behavioral adherence in the locomotion, power systems, and navigation tasks tested. These results establish\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\varepsilon $$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    \u00a0as a lightweight, theoretically grounded mechanism for incorporating behavioral preferences into RL.\n                  <\/jats:p>","DOI":"10.1007\/s10458-026-09748-6","type":"journal-article","created":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T15:05:52Z","timestamp":1777907152000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["$$\\varepsilon $$-retraining reinforcement learning algorithms"],"prefix":"10.1007","volume":"40","author":[{"given":"Luca","family":"Marzari","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changliu","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Priya L.","family":"Donti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Enrico","family":"Marchesini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,5,4]]},"reference":[{"key":"9748_CR1","unstructured":"Amodei, D., Olah, C., Steinhardt, J., Christiano, P. 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