Online Stochastic Optimization with Wasserstein Based Non-stationarity

Understand

We consider a general online stochastic optimization problem with multiple budget constraints over a horizon of finite time periods.

• In each time period, a reward function and multiple cost functions are revealed, and the decision maker needs to specify an action from a convex and compact action set to collect the reward and consume the budget.
• Each cost function corresponds to the consumption of one budget.
• In each period, the reward and cost functions are drawn from an unknown distribution, which is non-stationary across time.