Adaptive Regret for Control of Time-Varying Dynamics

Paula Gradu, Elad Hazan, Edgar Minasyan

Research output: Contribution to journalConference articlepeer-review


We consider the problem of online control of systems with time-varying linear dynamics. To state meaningful guarantees over changing environments, we introduce the metric of adaptive regret to the field of control. This metric, originally studied in online learning, measures performance in terms of regret against the best policy in hindsight on any interval in time, and thus captures the adaptation of the controller to changing dynamics. Our main contribution is a novel efficient meta-algorithm: it converts a controller with sublinear regret bounds into one with sublinear adaptive regret bounds in the setting of time-varying linear dynamical systems. The underlying technical innovation is the first adaptive regret bound for the more general framework of online convex optimization with memory. Furthermore, we give a lower bound showing that our attained adaptive regret bound is nearly tight for this general framework.

Original languageEnglish (US)
Pages (from-to)560-572
Number of pages13
JournalProceedings of Machine Learning Research
StatePublished - 2023
Event5th Annual Conference on Learning for Dynamics and Control, L4DC 2023 - Philadelphia, United States
Duration: Jun 15 2023Jun 16 2023

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


  • adaptive regret
  • online control
  • online learning
  • time-varying dynamics


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