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Stabilizing Dynamical Systems via Policy Gradient Methods Juan C. Perdomo University of California, Berkeley Jack Umenberger MIT Max Simchowitz MIT
Stabilizing an unknown control system is one of the most fundamental problems in control systems engineering. In this paper, we provide a simple, model-free algorithm for stabilizing fully observed dynamical systems. While model-free methods have become increasingly popular in practice due to their simplicity and flexibility, stabilization via direct policy search has received surprisingly little attention. Our algorithm proceeds by solving a series of discounted LQR problems, where the discount factor is gradually increased. We prove that this method efficiently recovers a stabilizing controller for linear systems, and for smooth, nonlinear systems within a neighborhood of their equilibria. Our approach overcomes a significant limitation of prior work, namely the need for a pre-given stabilizing control policy. We empirically evaluate the effectiveness of our approach on common control benchmarks.
Stronger NAS with Weaker Predictors Appendix A Implementation details of baselines methods
We show the runtime comparison of WeakNAS and its BO variant in Table 1. Improvement (EI) acquisition function [2] being extremely costly.Method Predictors Config Train proxy model (s/arch) Derive new samples (s/arch) WeakNAS MLP 4 layers @1000 hidden 8. 59 10 We compare the effect of using different architecture encodings in in Table 2. As shown in Table 3. We conduct a controlled experiment on NAS-Bench-201 by varying number of samples. Evolution [1] in all three subsets, with better stability indicated by confidence intervals.
A Appendix
A.1 Pseudocode for our search algorithm Our framework follows a standard search pipeline: 1. Candidate proposal: the search algorithm samples an optimizer from the search space. Search: The optimizer score is used to guide the search algorithm to propose new optimizers. Our set of operators is a subset of the full operator set presented in Section 4.1 of the NOS-RL paper. We refer the readers to "Further discussions on NOS-RL baseline" in Appendix D.3 for more For inspiration on what to add, the user might look into 1). With an augmented operator set, other components in our algorithm can largely remain the same.