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Compactly Restrictable Metric Policy Optimization Problems

arXiv 2207.05850 ↗First posted 12 Jul 2022math.OC cs.LG cs.SYcited by 0

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Abstract (arXiv)

We study policy optimization problems for deterministic Markov decision processes (MDPs) with metric state and action spaces, which we refer to as Metric Policy Optimization Problems (MPOPs). Our goal is to establish theoretical results on the well-posedness of MPOPs that can characterize practically relevant continuous control systems. To do so, we define a special class of MPOPs called Compactly Restrictable MPOPs (CR-MPOPs), which are flexible enough to capture the complex behavior of robotic systems but specific enough to admit solutions using dynamic programming methods such as value iteration. We show how to arrive at CR-MPOPs using forward-invariance. We further show that our theoretical results on CR-MPOPs can be used to characterize feedback linearizable control affine systems.

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References · 11

  1. 2015Continuous control with deep reinforcement learningcited by 3,279
  2. 2015End-to-End Training of Deep Visuomotor Policiescited by 847
  3. 2017Safe Model-based Reinforcement Learning with Stability Guaranteescited by 347
  4. 2016Control Barrier Function Based Quadratic Programs for Safety Critical Systemscited by 261
  5. 2019End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Taskscited by 256
  6. 2020Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functionscited by 61
  7. 2016Learning Model Predictive Control for iterative tasks. A Data-Driven Control Frameworkcited by 38
  8. 2020MDPs with Setwise Continuous Transition Probabilitiescited by 3
  9. 2013A Mixed Value and Policy Iteration Method for Stochastic Control with Universally Measurable Policiescited by 2
  10. 2022Safety of Sampled-Data Systems with Control Barrier Functions via Approximate Discrete Time Modelscited by 2
  11. 2021Sampled-Data Stabilization with Control Lyapunov Functions via Quadratically Constrained Quadratic Programscited by 1

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