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Online Learning of the Kalman Filter with Logarithmic Regret
In this paper, we consider the problem of predicting observations genera...
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Improper Learning for Non-Stochastic Control
We consider the problem of controlling a possibly unknown linear dynamic...
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SLIP: Learning to Predict in Unknown Dynamical Systems with Long-Term Memory
We present an efficient and practical (polynomial time) algorithm for on...
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Parameter-free Online Convex Optimization with Sub-Exponential Noise
We consider the problem of unconstrained online convex optimization (OCO...
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Regret-Optimal Filtering
We consider the problem of filtering in linear state-space models (e.g.,...
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Provably Efficient Online Agnostic Learning in Markov Games
We study online agnostic learning, a problem that arises in episodic mul...
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Alice's Adventures in the Markovian World
This paper proposes an algorithm Alice having no access to the physics l...
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No-Regret Prediction in Marginally Stable Systems
We consider the problem of online prediction in a marginally stable linear dynamical system subject to bounded adversarial or (non-isotropic) stochastic perturbations. This poses two challenges. Firstly, the system is in general unidentifiable, so recent and classical results on parameter recovery do not apply. Secondly, because we allow the system to be marginally stable, the state can grow polynomially with time; this causes standard regret bounds in online convex optimization to be vacuous. In spite of these challenges, we show that the online least-squares algorithm achieves sublinear regret (improvable to polylogarithmic in the stochastic setting), with polynomial dependence on the system's parameters. This requires a refined regret analysis, including a structural lemma showing the current state of the system to be a small linear combination of past states, even if the state grows polynomially. By applying our techniques to learning an autoregressive filter, we also achieve logarithmic regret in the partially observed setting under Gaussian noise, with polynomial dependence on the memory of the associated Kalman filter.
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