aiqbench analysis
This article introduces LOCU, a novel optimization method for constrained Markov decision processes that uses Lowdin orthogonalization to resolve numerical instabilities caused by interacting constraint gradients. By reducing the problem space and ensuring symmetric handling of constraints, the approach improves stability in scenarios involving high coupling or narrow feasible regions without relying on external hardware or quantum mechanics.
LOCU: Lowdin-Orthogonalized Constraint Updates for Multi-Constraint Policy Optimization
arXiv:2610.26256v1 Announce Type: new Abstract: We investigate multi-constraint policy optimization in constrained Markov decision processes (CMDPs), where interactions among constraint gradients often yield ill-conditioned update directions, causing numerically fragile steps and unintended cancellation or redundant overlap in constraint corrections. To address this, we propose LOCU, which mitigates numerical instability arising from constraint interactions by applying symmetric Lowdin orthogonalization to the natural gradients of the reward and constraints under the Fisher-Rao metric. Combined with Fisher-geometric screening and near-collinear compression, LOCU yields a compact reduced space in which the trust region becomes a Euclidean ball and constraints are handled symmetrically through a low-dimensional active-set solve. For infeasible iterates, LOCU constructs a Pareto-descent direction which preserves the local feasibility of satisfied constraints within the same reduced formulation. Experiments show that LOCU remains stable under high constraint coupling, narrow feasible regions, and infeasible starts, and generalizes across different cost critic architectures.
Abstract:We investigate multi-constraint policy optimization in constrained Markov decision processes (CMDPs), where interactions among constraint gradients often yield ill-conditioned update directions, causing numerically fragile steps and unintended cancellation or redundant overlap in constraint corrections. To address this, we propose LOCU, which mitigates numerical instability arising from constraint interactions by applying symmetric Lowdin orthogonalization to the natural gradients of the reward and constraints under the Fisher-Rao metric. Combined with Fisher-geometric screening and near-collinear compression, LOCU yields a compact reduced space in which the trust region becomes a Euclidean ball and constraints are handled symmetrically through a low-dimensional active-set solve. For infeasible iterates, LOCU constructs a Pareto-descent direction which preserves the local feasibility of satisfied constraints within the same reduced formulation. Experiments show that LOCU remains stable under high constraint coupling, narrow feasible regions, and infeasible starts, and generalizes across different cost critic architectures.
Artificial Intelligence (cs.AI)
arXiv:2610.26256 [cs.AI]
(or arXiv:2610.26256v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2610.26256 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 234 words