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Updated: Jul 15, 2025

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A Gradient-Aware Search Algorithm for Constrained Markov Decision Processes.

Sami Khairy, Prasanna Balaprakash, Lin X Cai

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    |September 29, 2023
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    This summary is machine-generated.

    A new gradient-aware search (GAS) algorithm efficiently solves constrained Markov decision processes (CMDPs) by exploiting a piecewise linear convex (PWLC) objective function. This method offers rapid convergence to optimal solutions without hyperparameter tuning.

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    Area of Science:

    • Operations Research
    • Artificial Intelligence
    • Control Theory

    Background:

    • Constrained Markov Decision Processes (CMDPs) are typically solved using convex linear programming (LP).
    • Existing methods may require hyperparameter tuning and can be sensitive to initial conditions.

    Purpose of the Study:

    • To develop a novel, efficient algorithm for solving finite CMDPs.
    • To analyze the properties of the dual linear program in CMDPs.
    • To compare the proposed algorithm against existing benchmark methods.

    Main Methods:

    • Proving the piecewise linear convex (PWLC) structure of the dual linear program's objective function in finite CMDPs.
    • Developing a two-level gradient-aware search (GAS) algorithm leveraging the PWLC property.
    • Applying the GAS algorithm to two constrained stochastic control problems.

    Main Results:

    • The dual objective function of a finite CMDP is proven to be PWLC with respect to Lagrange multipliers.
    • The proposed GAS algorithm converges quickly to the optimal solution for CMDPs.
    • GAS demonstrates robustness, being insensitive to the initialization of Lagrange multipliers and requiring no hyperparameter tuning.

    Conclusions:

    • The GAS algorithm provides a provably optimal and efficient method for solving finite CMDPs.
    • The PWLC structure of the dual problem is key to the algorithm's performance.
    • GAS offers a significant improvement over traditional methods like binary search and LP-based approaches.