Bandits with Delayed, Aggregated Anonymous Feedback
This addresses a practical challenge in online learning systems like ad placement or recommendation engines where feedback is aggregated and delayed, offering incremental improvements over prior work on non-anonymous delays.
The paper tackles the problem of multi-armed bandits with delayed, aggregated anonymous feedback, where rewards are observed only as sums after stochastic delays, losing arm-specific information. It shows that an additive regret increase, similar to non-anonymous delays, can be maintained in this harder setting, with algorithms matching worst-case regret exactly for bounded delays or up to logarithmic factors for unbounded ones.
We study a variant of the stochastic $K$-armed bandit problem, which we call "bandits with delayed, aggregated anonymous feedback". In this problem, when the player pulls an arm, a reward is generated, however it is not immediately observed. Instead, at the end of each round the player observes only the sum of a number of previously generated rewards which happen to arrive in the given round. The rewards are stochastically delayed and due to the aggregated nature of the observations, the information of which arm led to a particular reward is lost. The question is what is the cost of the information loss due to this delayed, aggregated anonymous feedback? Previous works have studied bandits with stochastic, non-anonymous delays and found that the regret increases only by an additive factor relating to the expected delay. In this paper, we show that this additive regret increase can be maintained in the harder delayed, aggregated anonymous feedback setting when the expected delay (or a bound on it) is known. We provide an algorithm that matches the worst case regret of the non-anonymous problem exactly when the delays are bounded, and up to logarithmic factors or an additive variance term for unbounded delays.