Online learning with Erdős-Rényi side-observation graphs

• URL: http://arxiv.org/abs/2604.25271v1
• Date: Tue, 28 Apr 2026 06:29:13 GMT
• Title: Online learning with Erdős-Rényi side-observation graphs
• Abstract summary: We consider adversarial multi-armed bandit problems where the learner is allowed to observe losses of a number of arms beside the arm that it actually chose.<n>We study the case where all non-chosen arms reveal their loss with a fixed but unknown probability $r$, independently of each other and the action of the learner.<n>We show that after $T$ rounds in a bandit problem with $N$ arms, the expected regret of our first algorithm is $O(sqrt(T /r) log N )$ whenever $rge(log T)/(2
• Score: 23.85024184793822
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider adversarial multi-armed bandit problems where the learner is allowed to observe losses of a number of arms beside the arm that it actually chose. We study the case where all non-chosen arms reveal their loss with a fixed but unknown probability $r$, independently of each other and the action of the learner. We propose two algorithms that work for different ranges of $r$. We show that after $T$ rounds in a bandit problem with $N$ arms, the expected regret of our first algorithm is $O(\sqrt{(T /r) \log N })$ whenever $r\ge(\log T)/(2N)$, while our second algorithm achieves a regret of $O(\sqrt{(T/r) \log (N+T)})$ for smaller values of $r$. We also give a quick estimation procedure that decides the range of~$r$. All our bounds are within logarithmic factors of the best achievable performance of any algorithm that is even allowed to know~$r$.

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