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Learning Linear-Quadratic Regulators Efficiently with only √(T) Regret
We present the first computationally-efficient algorithm with O(√(T)) r...
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Incremental Truncated LSTD
Balancing between computational efficiency and sample efficiency is an i...
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Low-Rank Generalized Linear Bandit Problems
In a low-rank linear bandit problem, the reward of an action (represente...
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Primal-Dual Block Frank-Wolfe
We propose a variant of the Frank-Wolfe algorithm for solving a class of...
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Fast and Sample Efficient Inductive Matrix Completion via Multi-Phase Procrustes Flow
We revisit the inductive matrix completion problem that aims to recover ...
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RES-PCA: A Scalable Approach to Recovering Low-rank Matrices
Robust principal component analysis (RPCA) has drawn significant attenti...
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More Practical and Adaptive Algorithms for Online Quantum State Learning
Online quantum state learning is a recently proposed problem by Aaronson...
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Episodic Linear Quadratic Regulators with Low-rank Transitions
Linear Quadratic Regulators (LQR) achieve enormous successful real-world applications. Very recently, people have been focusing on efficient learning algorithms for LQRs when their dynamics are unknown. Existing results effectively learn to control the unknown system using number of episodes depending polynomially on the system parameters, including the ambient dimension of the states. These traditional approaches, however, become inefficient in common scenarios, e.g., when the states are high-resolution images. In this paper, we propose an algorithm that utilizes the intrinsic system low-rank structure for efficient learning. For problems of rank-m, our algorithm achieves a K-episode regret bound of order O(m^3/2 K^1/2). Consequently, the sample complexity of our algorithm only depends on the rank, m, rather than the ambient dimension, d, which can be orders-of-magnitude larger.
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