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Summary of Optimal Control Of Agent-based Dynamics Under Deep Galerkin Feedback Laws, by Frederik Kelbel


Optimal Control of Agent-Based Dynamics under Deep Galerkin Feedback Laws

by Frederik Kelbel

First submitted to arxiv on: 13 Jun 2024

Categories

  • Main: Machine Learning (cs.LG)
  • Secondary: None

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GrooveSquid.com Paper Summaries

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Summary difficulty Written by Summary
High Paper authors High Difficulty Summary
Read the original abstract here
Medium GrooveSquid.com (original content) Medium Difficulty Summary
This paper tackles the challenge of high-dimensional control problems, which have long been an obstacle in dynamic programming. The authors propose a novel solution using Deep Neural Networks (DNNs) to address this issue. Specifically, they investigate the sampling issues affecting the Deep Galerkin Method and introduce a drift relaxation-based sampling approach to mitigate high-variance policy approximations. This approach is validated on mean-field control problems, including variations of the Sznajd and Hegselmann-Krause opinion dynamics models. The resulting policies show significant cost reductions compared to manually optimised control functions and outperform the Deep FBSDE approach in Linear-Quadratic Regulator problems.
Low GrooveSquid.com (original content) Low Difficulty Summary
This research paper solves a long-standing problem in computer science called “high-dimensional control”. It’s like trying to solve a really hard puzzle that gets harder and harder as you go along. The authors use special kinds of math models called Deep Neural Networks to make it easier. They tested their idea on some complex problems, including ones about how people agree or disagree with each other. Their solution worked better than other methods at solving these problems and could be used in real-life applications.

Keywords

» Artificial intelligence