9 papers
Learning and Control Beyond Linearity: Towards a Non-asymptotic Theory for Bilinear Systems
Yahya Sattar, Yassir Jedra, Robin Strässer +3
This tutorial provides a unified view of the emerging area of bilinear learning and control. Using linear systems as a benchmark, it explains what fundamentally changes in the bili…
Extracting Algorithms in Pre-trained LLMs: A Case on Hidden Markov Models
Yijia Dai, Zhaolin Gao, Yahya Sattar +2
Large language models (LLMs) display a striking ability to predict next observations from Hidden Markov Models (HMMs) via in-context learning (ICL), but the algorithm underlying th…
Two-Layer Linear Auto-Regressive Models Estimate Latent States
Yahya Sattar, Sunmook Choi, Leo Maynard-Zhang +3
Auto-regressive models have emerged as powerful tools for sequential data, from language to video. Understanding how and why these models learn latent representations remains an op…
Dual Control of Linear Systems from Bilinear Observations with Belief Space Model Predictive Control
Daniel Cao, Beixi Du, Andrew Lowitt +3
We study finite-horizon quadratic control of linear systems with bilinear observations, in which the control input affects not only the state dynamics but also the partial observat…
Explore-then-Commit for Nonstationary Linear Bandits with Latent Dynamics
Sunmook Choi, Yahya Sattar, Yassir Jedra +2
We study a nonstationary bandit problem where rewards depend on both actions and latent states, the latter governed by unknown linear dynamics. Crucially, the state dynamics also d…
Sub-optimality of the Separation Principle for Quadratic Control from Bilinear Observations
Yahya Sattar, Sunmook Choi, Yassir Jedra +2
We consider the problem of controlling a linear dynamical system from bilinear observations with minimal quadratic cost. Despite the similarity of this problem to standard linear q…
Finite Sample Identification of Partially Observed Bilinear Dynamical Systems
Yahya Sattar, Yassir Jedra, Maryam Fazel +1
We consider the problem of learning a realization of a partially observed bilinear dynamical system (BLDS) from noisy input-output data. Given a single trajectory of input-output s…
Learning Linear Dynamics from Bilinear Observations
Yahya Sattar, Yassir Jedra, Sarah Dean
We consider the problem of learning a realization of a partially observed dynamical system with linear state transitions and bilinear observations. Under very mild assumptions on t…
Random Features Approximation for Control-Affine Systems
Kimia Kazemian, Yahya Sattar, Sarah Dean
Modern data-driven control applications call for flexible nonlinear models that are amenable to principled controller synthesis and realtime feedback. Many nonlinear dynamical syst…