The Survival Bandit Problem

7 Jun 2022  ·  Charles Riou, Junya Honda, Masashi Sugiyama ·

We study the survival bandit problem, a variant of the multi-armed bandit problem introduced in an open problem by Perotto et al. (2019), with a constraint on the cumulative reward; at each time step, the agent receives a (possibly negative) reward and if the cumulative reward becomes lower than a prespecified threshold, the procedure stops, and this phenomenon is called ruin. This is the first paper studying a framework where the ruin might occur but not always. We first discuss that a sublinear regret is unachievable under a naive definition of the regret. Next, we provide tight lower bounds on the probability of ruin (as well as matching policies). Based on this lower bound, we define the survival regret as an objective to minimize and provide a policy achieving a sublinear survival regret (at least in the case of integral rewards) when the time horizon $T$ is known.

PDF Abstract
No code implementations yet. Submit your code now

Tasks


Datasets


  Add Datasets introduced or used in this paper

Results from the Paper


  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

Methods


No methods listed for this paper. Add relevant methods here