Logarithmic Regret for Learning Linear Quadratic Regulators Efficiently

• URL: http://arxiv.org/abs/2002.08095v2
• Date: Wed, 1 Jul 2020 20:37:42 GMT
• Title: Logarithmic Regret for Learning Linear Quadratic Regulators Efficiently
• Authors: Asaf Cassel (1), Alon Cohen (2), Tomer Koren (1) ((1) School of Computer Science, Tel Aviv University, (2) Google Research, Tel Aviv)
• Abstract summary: Recent results have demonstrated efficient learning algorithms with regret growing with the square root of the number of decision steps. We present new efficient algorithms that achieve, perhaps surprisingly, regret that scales only (poly)logarithmically with the number of steps.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the problem of learning in Linear Quadratic Control systems whose transition parameters are initially unknown. Recent results in this setting have demonstrated efficient learning algorithms with regret growing with the square root of the number of decision steps. We present new efficient algorithms that achieve, perhaps surprisingly, regret that scales only (poly)logarithmically with the number of steps in two scenarios: when only the state transition matrix $A$ is unknown, and when only the state-action transition matrix $B$ is unknown and the optimal policy satisfies a certain non-degeneracy condition. On the other hand, we give a lower bound that shows that when the latter condition is violated, square root regret is unavoidable.

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