{"paper":{"title":"Revisit Policy Optimization in Matrix Form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Doina Precup, Sitao Luan, Xiao-Wen Chang","submitted_at":"2019-09-19T18:43:56Z","abstract_excerpt":"In tabular case, when the reward and environment dynamics are known, policy evaluation can be written as $\\bm{V}_{\\bm{\\pi}} = (I - \\gamma P_{\\bm{\\pi}})^{-1} \\bm{r}_{\\bm{\\pi}}$, where $P_{\\bm{\\pi}}$ is the state transition matrix given policy ${\\bm{\\pi}}$ and $\\bm{r}_{\\bm{\\pi}}$ is the reward signal given ${\\bm{\\pi}}$. What annoys us is that $P_{\\bm{\\pi}}$ and $\\bm{r}_{\\bm{\\pi}}$ are both mixed with ${\\bm{\\pi}}$, which means every time when we update ${\\bm{\\pi}}$, they will change together. In this paper, we leverage the notation from \\cite{wang2007dual} to disentangle ${\\bm{\\pi}}$ and environm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.09186","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/1909.09186/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"}