A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Paper introduces privacy-preserving inventory policy learning for feature-based newsvendor with unknown demand.
problem Privacy-preserving inventory policy learning for feature-based newsvendor with unknown demand distribution and nonsmooth loss function.
method Developed a clipped noisy gradient descent algorithm based on convolution smoothing for optimal inventory estimation within f-differential privacy framework.
result Achieved privacy-preserving optimal inventory policy with provable privacy guarantees and desirable statistical precision.
In retailer management, the Newsvendor problem has widely attracted attention as one of basic inventory models. In the traditional approach to solving this problem, it relies on the probability distribution of the demand. In theory, if the probability distribution is known, the problem can be considered as fully solved…
Inventory control with unknown demand distribution is considered, with emphasis placed on the case involving discrete nonperishable items. We focus on an adaptive policy which in every period uses, as much as possible, the optimal newsvendor ordering quantity for the empirical distribution learned up to that period. Th…
In this paper we study convex stochastic search problems where a noisy objective function value is observed after a decision is made. There are many stochastic search problems whose behavior depends on an exogenous state variable which affects the shape of the objective function. Currently, there is no general purpose …
Price of anarchy, the performance ratio, which could characterize the loss of efficiency of the distributed supply chain management compared with the integrated supply chain management is discussed by utilizing newsvendor problem in single period which is well-known. In particular, some of remarkable distributed polici…
We consider a repeated newsvendor problem where the inventory manager has no prior information about the demand, and can access only censored/sales data. In analogy to multi-armed bandit problems, the manager needs to simultaneously "explore" and "exploit" with her inventory decisions, in order to minimize the cumulati…
Wasserstein distributionally robust optimization (DRO) has recently achieved empirical success for various applications in operations research and machine learning, owing partly to its regularization effect. Although connection between Wasserstein DRO and regularization has been established in several settings, existin…
We present a model of credit card profitability, assuming that the card-holder always pays the full outstanding balance. The motivation for the model is to calculate an optimal credit limit, which requires an expression for the expected outstanding balance. We derive its Laplace transform, assuming that purchases are m…
We address the problem of prescribing an optimal decision in a framework where the cost function depends on uncertain problem parameters that need to be learned from data. Earlier work proposed prescriptive formulations based on supervised machine learning methods. These prescriptive methods can factor in contextual in…
Inspired from recent insights into the common ground of machine learning, optimization and decision-making, this paper proposes an easy-to-implement, but effective procedure to enhance both the quality of renewable energy forecasts and the competitive edge of renewable energy producers in electricity markets with a dua…
In this paper we study a continuous time stochastic inventory model for a commodity traded in the spot market and whose supply purchase is affected by price and demand uncertainty. A firm aims at meeting a random demand of the commodity at a random time by maximizing total expected profits. We model the firm's optimal …
This study analyzes decision-making in diverse environments where past data may not predict future outcomes.
problem How to make decisions when past data is not indicative of future outcomes due to unobserved confounders.
method Developed a framework to analyze and bound the performance of data-driven policies in heterogeneous environments.
result Established a method to upper bound the asymptotic worst-case regret of policies and analyzed the performance of Sample Average Approximation (SAA).
We construct low regularity solutions of the vacuum Einstein constraint equations. In particular, on 3-manifolds we obtain solutions with metrics in $H^s\loc$ with s>23. The theory of maximal asymptotically Euclidean solutions of the constraint equations descends completely the low regularity setting. Moreove…
Let n≥3 and m=n+2n−2. We construct 5-parameters, 4-parameters, 3-parameters ancient solutions of the equation vt=(vm)xx+v−vm, v>0, in R×(−∞,T) for some T∈R. This equation arises in the study of Yamabe flow. We obtain various properties of the ancient so…
We construct new ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as t→−∞, to two self-similar complete non-compact solutions to the Yamabe flow moving in opposite directions. They are type I ancient solutions.
Minimax solutions are weak solutions to Cauchy problems involving Hamilton--Jacobi equations, constructed from generating families quadratic at infinity of their geometric solutions. We give a complete description of minimax solutions and we classify their generic singularities of codimension not greater than 2.
We construct new ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as t→−∞, to two self-similar complete non-compact solutions to the Yamabe flow moving in opposite directions. They are type I ancient solutions.
The paper concerns singular solutions of nonlinear elliptic equations, which include removable singularities for viscosity solutions, a strengthening of the Hopf Lemma including parabolic equations, Strong maximum principle and Hopf Lemma for viscosity solutions including also parabolic equations.