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作者：Zheng, Zeyu; Honnappa, Harsha; Glynn, Peter W.
作者单位：University of California System; University of California Berkeley; Purdue University System; Purdue University; Stanford University
摘要：This paper introduces a new asymptotic regime for simplifying stochastic models having nonstationary effects, such as those that arise in the presence of time-of-day effects. This regime describes an operating environment within which the arrival process to a service system has an arrival intensity that is fluctuating rapidly. We show that such a service system is well approximated by the corresponding model in which the arrival process is Poisson with a constant arrival rate. In addition to t...
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作者：Tsitsiklis, John N.; Xu, Kuang; Xu, Zhi
作者单位：Massachusetts Institute of Technology (MIT); Stanford University
摘要：We formulate a private learning model to study an intrinsic tradeoff between privacy and query complexity in sequential learning. Our model involves a learner who aims to determine a scalar value v* by sequentially querying an external database and receiving binary responses. In the meantime, an adversary observes the learner's queries, although not the responses, and tries to infer from them the value of v*. The objective of the learner is to obtain an accurate estimate of v* using only a sma...
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作者：Ma, Qingyin; Stachurski, John
作者单位：Capital University of Economics & Business; Australian National University
摘要：Some approaches to solving challenging dynamic programming problems, such as Q-learning, begin by transforming the Bellman equation into an alternative functional equation to open up a new line of attack. Our paper studies this idea systematically with a focus on boosting computational efficiency. We provide a characterization of the set of valid transformations of the Bellman equation, for which validity means that the transformed Bellman equation maintains the link to optimality held by the ...
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作者：Terca, Goncalo; Wozabal, David
作者单位：Technical University of Munich
摘要：We propose a method to compute derivatives of multistage linear stochastic optimization problems with respect to parameters that influence the problem's data. Our results are based on classical envelope theorems and can be used in problems directly solved via their deterministic equivalents as well as in stochastic dual dynamic programming for which the derivatives of the optimal value are sampled. We derive smoothness properties for optimal values of linear optimization problems, which we use...
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作者：Gotoh, Jun-ya; Kim, Michael Jong; Lim, Andrew E. B.
作者单位：Chuo University; University of British Columbia; National University of Singapore; National University of Singapore; National University of Singapore
摘要：We study the out-of-sample properties of robust empirical optimization problems with smooth phi-divergence penalties and smooth concave objective functions, and we develop a theory for data-driven calibration of the nonnegative robustness parameter delta that controls the size of the deviations from the nominal model. Building on the intuition that robust optimization reduces the sensitivity of the expected reward to errors in the model by controlling the spread of the reward distribution, we ...
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作者：Chen, Xin; Li, Menglong
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：Ma-convexity, one of the main concepts in discrete convex analysis, possesses many salient structural properties and allows for the design of efficient algorithms. In this paper, we establish several new fundamental properties of Ma-convexity and its variant SSQMa-convexity (semistrictly quasi Ma-convexity). We show that in a parametric maximization model, the optimal solution is nonincreasing in the parameters when the objective function is SSQMa-concave and the constraint is a box and illust...
