Can Direct Latent Model Learning Solve Linear Quadratic Gaussian Control?

• URL: http://arxiv.org/abs/2212.14511v2
• Date: Wed, 13 Mar 2024 17:44:52 GMT
• Title: Can Direct Latent Model Learning Solve Linear Quadratic Gaussian Control?
• Authors: Yi Tian, Kaiqing Zhang, Russ Tedrake, Suvrit Sra
• Abstract summary: We study the task of learning state representations from potentially high-dimensional observations. We pursue a direct latent model learning approach, where a dynamic model in some latent state space is learned by predicting quantities directly related to planning.
• Score: 75.14973944905216
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the task of learning state representations from potentially high-dimensional observations, with the goal of controlling an unknown partially observable system. We pursue a direct latent model learning approach, where a dynamic model in some latent state space is learned by predicting quantities directly related to planning (e.g., costs) without reconstructing the observations. In particular, we focus on an intuitive cost-driven state representation learning method for solving Linear Quadratic Gaussian (LQG) control, one of the most fundamental partially observable control problems. As our main results, we establish finite-sample guarantees of finding a near-optimal state representation function and a near-optimal controller using the directly learned latent model. To the best of our knowledge, despite various empirical successes, prior to this work it was unclear if such a cost-driven latent model learner enjoys finite-sample guarantees. Our work underscores the value of predicting multi-step costs, an idea that is key to our theory, and notably also an idea that is known to be empirically valuable for learning state representations.

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