The optimal value V^n for online vector balancing with Gaussian vectors converges to the value of a mean-field stochastic control problem that finds the narrowest terminal interval for a Brownian motion under uniform L2 drift constraint.
Algorithmic threshold for high-dimensional projection pursuit I: general theory
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The Mean-Field Limit of Online Stochastic Vector Balancing
The optimal value V^n for online vector balancing with Gaussian vectors converges to the value of a mean-field stochastic control problem that finds the narrowest terminal interval for a Brownian motion under uniform L2 drift constraint.