Qin, Junjie and Rajagopal, Ram and Vardi, Shai and Wierman, Adam
(2018)
*Convex Prophet Inequalities.*
Performance Evaluation Review, 46
(2).
pp. 39-41.
ISSN 0163-5999.
http://resolver.caltech.edu/CaltechAUTHORS:20190128-080449154

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## Abstract

We introduce a new class of prophet inequalities-convex prophet inequalities-where a gambler observes a sequence of convex cost functions c_i(x_i) and is required to assign some fraction 0 ≤ x_i ≤ 1 to each, such that the sum of assigned values is exactly 1. The goal of the gambler is to minimize the sum of the costs. We provide an optimal algorithm for this problem, a dynamic program, and show that it can be implemented in polynomial time when the cost functions are polynomial. We also precisely characterize the competitive ratio of the optimal algorithm in the case where the gambler has an outside option and there are polynomial costs, showing that it grows as Θ(n^(p-1)/l), where n is the number of stages, p is the degree of the polynomial costs and the coefficients of the cost functions are bounded by [l, u].

Item Type: | Article | ||||||
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Additional Information: | © 2018 is held by author/owner(s). | ||||||

Subject Keywords: | Prophet inequality, online algorithms, resource allocation, stochastic control | ||||||

Record Number: | CaltechAUTHORS:20190128-080449154 | ||||||

Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20190128-080449154 | ||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||

ID Code: | 92487 | ||||||

Collection: | CaltechAUTHORS | ||||||

Deposited By: | Tony Diaz | ||||||

Deposited On: | 29 Jan 2019 20:08 | ||||||

Last Modified: | 29 Jan 2019 20:08 |

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