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[2509.19800] Analysis of approximate linear programming solution to Markov decision problem with log barrier function
Summary
This paper explores a novel approach to solving Markov decision problems (MDPs) using approximate linear programming with a log barrier function, aiming to enhance the effectiveness of LP-based methods in reinforcement learning.
Why It Matters
The study addresses the underutilization of linear programming in solving MDPs, particularly in reinforcement learning contexts. By providing a theoretical foundation for using log barrier functions, it opens new avenues for more efficient optimization methods, which could significantly impact AI applications.
Key Takeaways
- Introduces a method to reformulate MDPs using log barrier functions.
- Aims to simplify the solving of inequality-constrained optimization problems.
- Provides a theoretical basis for the effectiveness of LP-based approaches in reinforcement learning.
- Highlights the potential for gradient descent to yield approximate solutions.
- Addresses a gap in existing literature regarding LP-based MDP solutions.
Computer Science > Artificial Intelligence arXiv:2509.19800 (cs) [Submitted on 24 Sep 2025 (v1), last revised 23 Feb 2026 (this version, v3)] Title:Analysis of approximate linear programming solution to Markov decision problem with log barrier function Authors:Donghwan Lee, Hyukjun Yang, Bum Geun Park View a PDF of the paper titled Analysis of approximate linear programming solution to Markov decision problem with log barrier function, by Donghwan Lee and 2 other authors View PDF Abstract:There are two primary approaches to solving Markov decision problems (MDPs): dynamic programming based on the Bellman equation and linear programming (LP). Dynamic programming methods are the most widely used and form the foundation of both classical and modern reinforcement learning (RL). By contrast, LP-based methods have been less commonly employed, although they have recently gained attention in contexts such as offline RL. The relative underuse of the LP-based methods stems from the fact that it leads to an inequality-constrained optimization problem, which is generally more challenging to solve effectively compared with Bellman-equation-based methods. The purpose of this paper is to establish a theoretical foundation for solving LP-based MDPs in a more effective and practical manner. Our key idea is to leverage the log-barrier function, widely used in inequality-constrained optimization, to transform the LP formulation of the MDP into an unconstrained optimization problem. This refo...
