
Online Discrepancy Minimization for Stochastic Arrivals
In the stochastic online vector balancing problem, vectors v_1,v_2,…,v_T...
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Prefix Discrepancy, Smoothed Analysis, and Combinatorial Vector Balancing
A wellknown result of Banaszczyk in discrepancy theory concerns the pre...
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Discrepancy Minimization via a SelfBalancing Walk
We study discrepancy minimization for vectors in ℝ^n under various setti...
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Online Geometric Discrepancy for Stochastic Arrivals with Applications to Envy Minimization
Consider a unit interval [0,1] in which n points arrive onebyone indep...
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Online Discrepancy with Recourse for Vectors and Graphs
The vectorbalancing problem is a fundamental problem in discrepancy the...
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Balancing Gaussian vectors in high dimension
Motivated by problems in controlled experiments, we study the discrepanc...
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OnLine Balancing of Random Inputs
We consider an online vector balancing game where vectors v_t, chosen un...
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Online Discrepancy Minimization via Persistent SelfBalancing Walks
We study the online discrepancy minimization problem for vectors in ℝ^d in the oblivious setting where an adversary is allowed fix the vectors x_1, x_2, …, x_n in arbitrary order ahead of time. We give an algorithm that maintains O(√(log(nd/δ))) discrepancy with probability 1δ, matching the lower bound given in [Bansal et al. 2020] up to an O(√(loglog n)) factor in the highprobability regime. We also provide results for the weighted and multicolor versions of the problem.
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