{"ID":2832703,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.06109","arxiv_id":"2512.06109","title":"Unifying Entropy Regularization in Optimal Control: From and Back to Classical Objectives via Iterated Soft Policies and Path Integral Solutions","abstract":"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 RSOC, which yield tractable surrogates. Beyond being regularized variants, these soft-policy formulations majorize the original SOC and RSOC, thus, 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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2512.06109","url_pdf":"https://arxiv.org/pdf/2512.06109v3","authors":"[\"Ajinkya Bhole\",\"Mohammad Mahmoudi Filabadi\",\"Guillaume Crevecoeur\",\"Tom Lefebvre\"]","published":"2025-12-05T19:31:39Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.LG\",\"cs.RO\",\"eess.SY\"]","methods":"[\"Large Language Model\"]","has_code":false}