{"paper":{"title":"Unifying Entropy Regularization in Optimal Control: From and Back to Classical Objectives via Iterated Soft Policies and Path Integral Solutions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A KL-regularized umbrella problem unifies optimal control formulations and recovers the classical objectives through iteration of soft-policy solutions.","cross_cats":["cs.LG","cs.RO","cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Ajinkya Bhole, Guillaume Crevecoeur, Mohammad Mahmoudi Filabadi, Tom Lefebvre","submitted_at":"2025-12-05T19:31:39Z","abstract_excerpt":"This paper develops a unified perspective on several optimal control formulations through the lens of Kullback-Leibler (KL) regularization. We propose a central problem that separates the KL penalties on policies and transitions with independent weights, thus generalizing the standard trajectory-level KL-regularization used in probabilistic optimal control. This umbrella formulation recovers various control problems: the classical Stochastic Optimal Control (SOC), Risk-Sensitive Stochastic Optimal Control (RSOC), and their policy-based KL-regularized counterparts, termed soft-policy SOC and RS"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"iterating their solutions recovers the original objectives. We further identify a synchronized case of soft-policy RSOC where the policy and transition KL weights coincide, yielding a linear Bellman operator, path-integral solution, and compositionality -- extending these computationally favourable properties to a broad class of control problems.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"the soft-policy formulations majorize the original SOC and RSOC, thus, iterating their solutions recovers the original objectives.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A KL-regularized optimal control umbrella recovers classical SOC and RSOC via iterated soft policies and yields linear Bellman operators with path-integral solutions when policy and transition weights coincide.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A KL-regularized umbrella problem unifies optimal control formulations and recovers the classical objectives through iteration of soft-policy solutions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"e51d1e72361ffddee84c8bc1b10f0312be5f456ab5d61885eea28b19b8fe0dde"},"source":{"id":"2512.06109","kind":"arxiv","version":3},"verdict":{"id":"d946f5c7-c4c7-47ec-9456-05045272207e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-17T00:12:22.323581Z","strongest_claim":"iterating their solutions recovers the original objectives. We further identify a synchronized case of soft-policy RSOC where the policy and transition KL weights coincide, yielding a linear Bellman operator, path-integral solution, and compositionality -- extending these computationally favourable properties to a broad class of control problems.","one_line_summary":"A KL-regularized optimal control umbrella recovers classical SOC and RSOC via iterated soft policies and yields linear Bellman operators with path-integral solutions when policy and transition weights coincide.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"the soft-policy formulations majorize the original SOC and RSOC, thus, iterating their solutions recovers the original objectives.","pith_extraction_headline":"A KL-regularized umbrella problem unifies optimal control formulations and recovers the classical objectives through iteration of soft-policy solutions."},"references":{"count":5,"sample":[{"doi":"","year":2012,"title":"Dvijotham, K. and Todorov, E. (2012). Linearly solvable optimal control.Reinforcement learning and approxi- mate dynamic programming for feedback control, 119–","work_id":"c5484cd7-4191-429d-8658-57b7b4a06896","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2002,"title":"F¨ ollmer, H. and Schied, A. (2002). Convex measures of risk and trading constraints.Finance and stochastics, 6(4), 429–447. Ito, K. and Kashima, K. (2024). Risk-sensitive control as inference with r´","work_id":"eb194833-26a6-4636-ac2a-65d044a8bf85","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review","work_id":"e29031ac-37fe-4702-86de-bb869d1f5c9a","ref_index":3,"cited_arxiv_id":"1805.00909","is_internal_anchor":true},{"doi":"","year":2011,"title":"Neumann, G. (2011). Variational inference for policy search in changing situations. InInternational confer- ence on machine learning, 817–824. Nishimura, H., Mehr, N., Gaidon, A., and Schwager, M. (20","work_id":"3a495531-8540-40d4-a3e0-5295cac2d83b","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"Toussaint, M. (2009). Robot trajectory optimization via approximate inference. InInternational conference on machine learning, 1049–1056. Toussaint, M. and Storkey, A. (2006). Probabilistic infer- enc","work_id":"8e5894b3-7799-4db8-bb2e-ea3cff869256","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":5,"snapshot_sha256":"38e86502367ed562337676526006ad3aefa916f5f5597a15a692b744f580f399","internal_anchors":1},"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"}