Distributionally Robust Optimization with Correlated Data from Vector Autoregressive Processes
This addresses optimization under correlated data for applications like finance or time series, but is incremental as it extends existing distributionally robust methods to a specific non-i.i.d. setting.
The authors tackled the problem of stochastic optimization with non-i.i.d. vector autoregressive data by proposing a distributionally robust formulation using Wasserstein distance, showing it reduces to a finite convex-concave saddle point problem via duality theory, and demonstrated performance on synthetic and real data.
We present a distributionally robust formulation of a stochastic optimization problem for non-i.i.d vector autoregressive data. We use the Wasserstein distance to define robustness in the space of distributions and we show, using duality theory, that the problem is equivalent to a finite convex-concave saddle point problem. The performance of the method is demonstrated on both synthetic and real data.