Entropy-Guided Multiplicative Updates: KL Projections for Multi-Factor Target Exposures
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908619665047552 |
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| author | Qiu, Yimeng |
| author_facet | Qiu, Yimeng |
| contents | We introduce Entropy-Guided Multiplicative Updates (EGMU), a convex optimization framework for constructing multi-factor target-exposure portfolios by minimizing Kullback-Leibler divergence from a benchmark under linear factor constraints. We establish feasibility and uniqueness of strictly positive solutions when the benchmark and targets satisfy convex-hull conditions. We derive the dual concave formulation with explicit gradient, Hessian, and sensitivity expressions, and provide two provably convergent solvers: a damped dual Newton method with global convergence and local quadratic rate, and a KL-projection scheme based on iterative proportional fitting and Bregman-Dykstra projections. We further generalize EGMU to handle elastic targets and robust target sets, and introduce a path-following ordinary differential equation for tracing solution trajectories. Stable and scalable implementations are provided using LogSumExp stabilization, covariance regularization, and half-space KL projections. Our focus is on theory and reproducible algorithms; empirical benchmarking is optional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24607 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entropy-Guided Multiplicative Updates: KL Projections for Multi-Factor Target Exposures Qiu, Yimeng Portfolio Management Optimization and Control 90C25, 90C90, 62F10, 94A17 We introduce Entropy-Guided Multiplicative Updates (EGMU), a convex optimization framework for constructing multi-factor target-exposure portfolios by minimizing Kullback-Leibler divergence from a benchmark under linear factor constraints. We establish feasibility and uniqueness of strictly positive solutions when the benchmark and targets satisfy convex-hull conditions. We derive the dual concave formulation with explicit gradient, Hessian, and sensitivity expressions, and provide two provably convergent solvers: a damped dual Newton method with global convergence and local quadratic rate, and a KL-projection scheme based on iterative proportional fitting and Bregman-Dykstra projections. We further generalize EGMU to handle elastic targets and robust target sets, and introduce a path-following ordinary differential equation for tracing solution trajectories. Stable and scalable implementations are provided using LogSumExp stabilization, covariance regularization, and half-space KL projections. Our focus is on theory and reproducible algorithms; empirical benchmarking is optional. |
| title | Entropy-Guided Multiplicative Updates: KL Projections for Multi-Factor Target Exposures |
| topic | Portfolio Management Optimization and Control 90C25, 90C90, 62F10, 94A17 |
| url | https://arxiv.org/abs/2510.24607 |