Lazy Lagrangians for Optimistic Learning With Budget Constraints

Daron Anderson, George Iosifidis, Douglas J. Leith

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)


We consider the general problem of online convex optimization with time-varying budget constraints in the presence of predictions for the next cost and constraint functions, that arises in a plethora of network resource management problems. A novel saddle-point algorithm is designed by combining a Follow-The-Regularized-Leader iteration with prediction-adaptive dynamic steps. The algorithm achieves <inline-formula> <tex-math notation="LaTeX">$\c O(T^{(3-\beta)/4})$</tex-math> </inline-formula> regret and <inline-formula> <tex-math notation="LaTeX">$\c O(T^{(1+\beta)/2})$</tex-math> </inline-formula> constraint violation bounds that are tunable via parameter <inline-formula> <tex-math notation="LaTeX">$\beta\!\in\![1/2,1)$</tex-math> </inline-formula> and have constant factors that shrink with the predictions quality, achieving eventually <inline-formula> <tex-math notation="LaTeX">$\c O(1)$</tex-math> </inline-formula> regret for perfect predictions. Our work extends the seminal FTRL framework for this new OCO setting and outperforms the respective state-of-the-art greedy-based solutions which naturally cannot benefit from predictions, without imposing conditions on the (unknown) quality of predictions, the cost functions or the geometry of constraints, beyond convexity.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalIEEE/ACM Transactions on Networking
Publication statusE-pub ahead of print - 2023


  • Network control
  • network management
  • online convex optimization (OCO)
  • online learning
  • resource allocation


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