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Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
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A Novel Approach for Sampling in Approximate Dynamic Programming Based on $F$ -Discrepancy.

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    Approximate dynamic programming (ADP) effectively solves Markovian decision problems by improving state-space sampling. This study introduces a novel hybrid approach for infinite-horizon problems, balancing system-driven and uniform sampling for better value function approximation.

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    Area of Science:

    • Operations Research
    • Artificial Intelligence
    • Control Theory

    Background:

    • Approximate dynamic programming (ADP) is crucial for solving Markovian decision problems.
    • The curse of dimensionality necessitates efficient state-space sampling for value function approximation.
    • Existing sampling methods include uniform covering and system trajectory-driven approaches.

    Purpose of the Study:

    • To extend the F-discrepancy framework for efficient ADP sampling to infinite-horizon discounted problems.
    • To develop a constructive algorithm for generating system-behavior-driven sampling points.
    • To refine the algorithm into a hybrid approach balancing system-driven and uniform sampling.

    Main Methods:

    • Extension of the F-discrepancy concept to infinite-horizon discounted Markovian decision problems.
    • Development of a constructive algorithm for generating sampling points based on system behavior.
    • Refinement of the algorithm to create a hybrid sampling strategy.
    • Theoretical analysis using a novel F-discrepancy notion and simulation tests.

    Main Results:

    • A constructive algorithm for generating efficient sampling points for infinite-horizon ADP.
    • A refined hybrid sampling method that balances system-driven and uniform designs.
    • Theoretical validation of the proposed F-discrepancy and sampling properties.
    • Demonstration of the sampling method's effectiveness through simulations.

    Conclusions:

    • The proposed hybrid sampling method enhances ADP efficiency for infinite-horizon problems.
    • The novel F-discrepancy framework provides theoretical underpinnings for improved sampling.
    • This approach offers a more balanced and effective state-space exploration for ADP.