{"id":826702,"date":"2022-03-15T06:49:05","date_gmt":"2022-03-15T13:49:05","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=826702"},"modified":"2022-03-15T06:49:05","modified_gmt":"2022-03-15T13:49:05","slug":"batched-bandits-with-crowd-externalities","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/batched-bandits-with-crowd-externalities\/","title":{"rendered":"Batched Bandits with Crowd Externalities"},"content":{"rendered":"

In Batched Multi-Armed Bandits (BMAB), the policy is not allowed to be updated at each time step. Usually, the setting asserts a maximum number of allowed policy updates and the algorithm schedules them so that to minimize the expected regret. In this paper, we describe a novel setting for BMAB, with the following twist: the timing of the policy update is not controlled by the BMAB algorithm, but instead the amount of data received during each batch, called crowd<\/em>, is influenced by the past selection of arms. We first design a near-optimal policy with approximate knowledge of the parameters that we prove to have a regret in O<\/span><\/span><\/span>(sqrt{<\/span>ln <\/span><\/span>x \/ x}<\/span><\/span><\/span><\/span><\/span>+<\/span>\u03f5<\/span>)<\/span><\/span><\/span><\/span>\u00a0where\u00a0x<\/span><\/span><\/span><\/span>\u00a0is the size of the crowd and\u00a0\u03f5<\/span><\/span><\/span><\/span>\u00a0is the parameter error. Next, we implement a UCB-inspired algorithm that guarantees an additional regret in\u00a0O<\/span><\/span><\/span>(<\/span>max<\/span>(<\/span>K <\/span>ln <\/span><\/span>T)<\/span>, sqrt{<\/span>T <\/span>ln <\/span><\/span>T}<\/span><\/span><\/span>)<\/span>)<\/span><\/span><\/span><\/span><\/span>, where\u00a0K<\/span><\/span><\/span><\/span>\u00a0is the number of arms and\u00a0T<\/span><\/span><\/span><\/span>\u00a0is the horizon.<\/p>\n","protected":false},"excerpt":{"rendered":"

In Batched Multi-Armed Bandits (BMAB), the policy is not allowed to be updated at each time step. Usually, the setting asserts a maximum number of allowed policy updates and the algorithm schedules them so that to minimize the expected regret. In this paper, we describe a novel setting for BMAB, with the following twist: the 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