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Quantifying Distributional Model Risk Via Optimal Transport
The approach consists in computing bounds for the expectation of interest regardless of the probability measure used, as long as the measure lies within a prescribed tolerance measured within a flexible class of distances from a suitable baseline model.
A markov chain approximation to choice modeling
Assortment planning is an important problem that arises in many industries such as retailing and airlines. One of the key challenges in an assortment planning problem is to identify the "right model"
Robust Wasserstein profile inference and applications to machine learning
Wasserstein Profile Inference is introduced, a novel inference methodology which extends the use of methods inspired by Empirical Likelihood to the setting of optimal transport costs (of which Wasserstein distances are a particular case).
Efficient simulation of tail probabilities of sums of correlated lognormals
This work considers the problem of efficient estimation of tail probabilities of sums of correlated lognormals via simulation and proposes two estimators that can be rigorously shown to be efficient as the tail probability of interest decreases to zero.
Convergence Rate Analysis of a Stochastic Trust-Region Method via Supermartingales
It is shown that the stochastic process defined by the algorithm satisfies the assumptions of the proposed general framework, with the stopping time defined as reaching accuracy, and the resulting bound for this stopping time is the first global complexity bound for a Stochastic trust-region method.
A Markov Chain Approximation to Choice Modeling
A Markov chain based choice model is considered and it is shown that it provides a simultaneous approximation for all random utility based discrete choice models including the multinomial logit (MNL), the probit, the nested logit and mixtures of multin coefficients logit models.
Efficient rare-event simulation for the maximum of heavy-tailed random walks
An importance sampling algorithm to estimate the tail of M=\max \{S_n:n\geq 0\}$ that is strongly efficient for both light and heavy-tailed increment distributions and under additional technical assumptions, which can be shown to have asymptotically vanishing relative variance.
Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances
We revisit Markowitz’s mean-variance portfolio selection model by considering a distributionally robust version, in which the region of distributional uncertainty is around the empirical measure and
Unbiased Monte Carlo for optimization and functions of expectations via multi-level randomization
We present general principles for the design and analysis of unbiased Monte Carlo estimators for quantities such as α = g(E (X)), where E (X) denotes the expectation of a (possibly multidimensional)
Online EXP3 Learning in Adversarial Bandits with Delayed Feedback
A two player zero-sum game where players experience asynchronous delays is considered and it is shown that even when the delays are large enough such that players no longer enjoy the “no-regret property”, the ergodic average of the strategy profile still converges to the set of Nash equilibria of the game.