TL;DR
A new, combined forecasting and optimization algorithm called the Residual Tree method is proposed, which generalizes the classical Scenario Tree method by using covariates to link historical data on similar products to construct demand forecasts for the new product.
Controlling tail risk is an important objective in online optimization, and recently it has been studied in the context of competitive analysis. Continuing this line of research, we investigate pure tail constraints, which capture the tradeoff between expected and worst-case competitiveness. For two fundamental search...
For the Gaussian two-armed bandit, which occurs during the analysis of batch data processing, the case of variable batch size is considered. This optimal control problem has a classical interpretation as a game with nature. The player’s payment function is the mathematical expectation of the regrets of full income caus...
Online decision-makers often obtain predictions on future variables, such as arrivals, demands, inventories, and so on. These predictions can be generated from simple forecasting algorithms for univariate time-series, all the way to state-of-the-art machine learning models that leverage multiple time-series and additio...
This work proposes an efficient algorithm to achieve regret bound O(K sqrt(T) log T) under concave revenue conditions and O(K^(2/3) T^(2/3) (log T)^(1/2) for the general case, with matching lower bounds confirming optimality.
This paper forms the resulting $\ell_0$-constrained empirical newsvendor problem with $\ell_2$-regularization, establishes its computational hardness, and develops a mixed-integer second-order cone programming reformulation that strengthens the standard Big-$M$ formulation.
The contribution is a proof that there exist measurable versions of intermediate value functions, which reveals regularity in addition, and a verification theorems allow stating traditional problem specifications in the novel setting with mathematical rigor.
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