{"paper":{"title":"Distributionally Robust Regret Optimal LQR with Common Stage-Law Ambiguity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Multistage distributionally robust regret-optimal LQR under common stage-law ambiguity admits an exact SDP reformulation over linear disturbance-feedback policies.","cross_cats":["cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Jose Blanchet, Lukas-Benedikt Fiechtner","submitted_at":"2026-04-07T17:55:56Z","abstract_excerpt":"We study, to our knowledge, the first tractable multistage ex-ante distributionally robust regret optimization (DRRO) formulation for stochastic control. We consider finite-horizon LQR under common stage-law ambiguity: disturbances are independent across time but share an unknown stage law whose mean and covariance lie in a Gelbrich ball around nominal parameters. Unlike the single-stage quadratic case, the nominal certainty-equivalent (CE) controller is generally not regret-optimal, because reuse of the stage law makes past disturbances informative for future decisions. Despite the general NP"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that over linear disturbance-feedback policies the resulting multistage DRRO-LQR problem admits an exact semidefinite programming reformulation. The optimal controller is the nominal certainty-equivalent LQR law plus a strictly causal empirical-mean correction.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The restriction to linear disturbance-feedback policies is sufficient to achieve both tractability and optimality, together with the common stage-law ambiguity model using a Gelbrich ball.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The multistage DRRO-LQR problem over linear disturbance-feedback policies admits an exact SDP reformulation whose solution is the nominal certainty-equivalent LQR law plus a strictly causal empirical-mean correction.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Multistage distributionally robust regret-optimal LQR under common stage-law ambiguity admits an exact SDP reformulation over linear disturbance-feedback policies.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"03dd003a19b958b81dee44188120ecc6101f19c60d0579f20f96d4902540e1d5"},"source":{"id":"2604.06158","kind":"arxiv","version":2},"verdict":{"id":"b63e8081-1961-4114-843e-5e08d24a9e3c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T18:44:45.215300Z","strongest_claim":"We show that over linear disturbance-feedback policies the resulting multistage DRRO-LQR problem admits an exact semidefinite programming reformulation. The optimal controller is the nominal certainty-equivalent LQR law plus a strictly causal empirical-mean correction.","one_line_summary":"The multistage DRRO-LQR problem over linear disturbance-feedback policies admits an exact SDP reformulation whose solution is the nominal certainty-equivalent LQR law plus a strictly causal empirical-mean correction.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The restriction to linear disturbance-feedback policies is sufficient to achieve both tractability and optimality, together with the common stage-law ambiguity model using a Gelbrich ball.","pith_extraction_headline":"Multistage distributionally robust regret-optimal LQR under common stage-law ambiguity admits an exact SDP reformulation over linear disturbance-feedback policies."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.06158/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"}