Online Local False Discovery Rate Control: A Resource Allocation Approach
SSRN Electronic Journal(2024)
摘要
We consider the problem of online local false discovery rate (FDR) control
where multiple tests are conducted sequentially, with the goal of maximizing
the total expected number of discoveries. We formulate the problem as an online
resource allocation problem with accept/reject decisions, which from a high
level can be viewed as an online knapsack problem, with the additional
uncertainty of random budget replenishment. We start with general arrival
distributions and propose a simple policy that achieves a O(√(T)) regret.
We complement the result by showing that such regret rate is in general not
improvable. We then shift our focus to discrete arrival distributions. We find
that many existing re-solving heuristics in the online resource allocation
literature, albeit achieve bounded loss in canonical settings, may incur a
Ω(√(T)) or even a Ω(T) regret. With the observation that
canonical policies tend to be too optimistic and over accept arrivals, we
propose a novel policy that incorporates budget buffers. We show that small
additional logarithmic buffers suffice to reduce the regret from
Ω(√(T)) or even Ω(T) to O(ln^2 T). Numerical experiments
are conducted to validate our theoretical findings. Our formulation may have
wider applications beyond the problem considered in this paper, and our results
emphasize how effective policies should be designed to reach a balance between
circumventing wrong accept and reducing wrong reject in online resource
allocation problems with uncertain budgets.
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