{"paper":{"title":"Approximate Dynamic Programming based on Projection onto the (min,+) subsemimodule","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.SY","authors_text":"Chandrashekar Lakshminarayanan, Shalabh Bhatnagar","submitted_at":"2014-03-17T17:15:07Z","abstract_excerpt":"We develop a new Approximate Dynamic Programming (ADP) method for infinite horizon discounted reward Markov Decision Processes (MDP) based on projection onto a subsemimodule. We approximate the value function in terms of a $(\\min,+)$ linear combination of a set of basis functions whose $(\\min,+)$ linear span constitutes a subsemimodule. The projection operator is closely related to the Fenchel transform. Our approximate solution obeys the $(\\min,+)$ Projected Bellman Equation (MPPBE) which is different from the conventional Projected Bellman Equation (PBE). We show that the approximation error"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4175","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":""},"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"}