Multiple-stopping problems with random horizon

Krasnosielska-Kobos, Anna

doi:10.1080/02331934.2013.869808

Cited by 8 publications

(9 citation statements)

References 17 publications

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“…It is straightforward to check that the conditions in (16) in Theorem 4 satisfy the conditions in (C.12).…”

Section: C7 Proof Of Theoremmentioning

confidence: 99%

“…In the classic L-secretary problem [13], independent and identically (i.i.d) observations are presented sequentially to the decision maker and the objective is to select L observations so as to maximize the sum of reward (a function of observation). The classical setting with i.i.d observations have been extended to consider variety of scenarios such as the observation times arising out of Poisson process [14], observations with a joint distribution and possibly depending on the stopping times in [15] and for random horizon in [16]. However, very few works consider optimal multiple stopping over a partially observed Markov chain.…”

Section: Context and Related Literaturementioning

confidence: 99%

“…A strong motivation to consider the problem of interactive ad scheduling in live online videos stems from the fact that ads are currently scheduled using passive techniques: periodic [37], and manual methods; and yet advertisement revenues are significant for social media companies 16 . The technique of interactive scheduling, where viewer engagement is utilized to schedule ads, has not been addressed in the literature.…”

Section: Real Dataset: Interactive Ad Scheduling On Periscope Using V...mentioning

confidence: 99%

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Multiple stopping time POMDPs: Structural results & application in interactive advertising on social media

2018

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This paper considers a multiple stopping time problem for a Markov chain observed in noise, where a decision maker chooses at most L stopping times to maximize a cumulative objective. We formulate the problem as a Partially Observed Markov Decision Process (POMDP) and derive structural results for the optimal multiple stopping policy. The main results are as follows: i) The optimal multiple stopping policy is shown to be characterized by threshold curves Γ l , for l = 1, · · · , L, in the unit simplex of Bayesian Posteriors. ii) The stopping sets S l (defined by the threshold curves Γ l ) are shown to exhibit the following nested structure S l−1 ⊂ S l . iii) The optimal cumulative reward is shown to be monotone with respect to the copositive ordering of the transition matrix. iv) A stochastic gradient algorithm is provided for estimating linear threshold policies by exploiting the structural results. These linear threshold policies approximate the threshold curves Γ l , and share the monotone structure of the optimal multiple stopping policy. As an illustrative example, we apply the multiple stopping framework to interactively schedule advertisements in live online social media. It is shown that advertisement scheduling using multiple stopping performs significantly better than currently used methods.

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“…It is straightforward to check that the conditions in (16) in Theorem 4 satisfy the conditions in (C.12).…”

Section: C7 Proof Of Theoremmentioning

confidence: 99%

Section: Context and Related Literaturementioning

confidence: 99%

Section: Real Dataset: Interactive Ad Scheduling On Periscope Using V...mentioning

confidence: 99%

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Multiple stopping time POMDPs: Structural results & application in interactive advertising on social media

2018

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“…Structural Results: The problem of optimal multiple stopping has been well studied in the literature see [10], [11], [12], [13] and the references therein. The optimal multiple stopping problem generalizes the classical (single) stopping problem, where the objective is to stop once to obtain maximum reward.…”

Section: )mentioning

confidence: 99%

“…Nakai [10] considers optimal L-stopping over a finite horizon of length N in a partially observed Markov chain. More recently, [13] considers L-stopping over a random horizon. The state of the finite horizon partially observed Markov chain in [10] above can be summarized by the "belief state" 7 .…”

Section: )mentioning

confidence: 99%

Opportunistic Advertisement Scheduling in Live Social Media: A Multiple Stopping Time POMDP Approach

Krishnamurthy¹,

Aprem²,

Bhatt³

2016

Preprint

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Popularity of online video streaming has seen a sharp growth due to improved bandwidth for streaming and the ease of sharing User-Generated-Content (UGC) on the internet platforms. One of the primary motivations for users to generate content is that platforms like YouTube, Twitch etc., allow users to generate revenue through advertising and royalties. The revenue of Twitch which deals with live video gaming, play through of video games, and e-sport competitions, is around 3.8 billion for the year 2015, out of which 77% of the revenue was generated from advertisements 1 . Some of the common ways advertisements (ads) are scheduled on pre-recorded video contents on social media like YouTube are pre-roll, mid-roll and post-roll; where the names indicate the time at which the ads are displayed. In a recent research on viewer engagement, Adobe Research 2 concluded that mid-roll video ads constitute the most engaging ad type for pre-recorded video contents, outperforming pre-roll and post-rolls when it comes to completion rate (the probability that the ad will not be skipped). Viewers are more likely to engage with an ad if they are interested in the content of the video that the ad is been inserted into. Most content sharing platforms hosted pre-recorded videos, until recently, owing to higher 1

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Construction of Nash equilibrium based on multiple stopping problem in multi-person game

Krasnosielska-Kobos

2015

Math Meth Oper Res

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We consider a multi-person stopping game with players' priorities and multiple stopping. Players observe sequential offers at random or fixed times. Each accepted offer results in a reward. Each player can obtain fixed number of rewards. If more than one player wants to accept an offer, then the player with the highest priority among them obtains it. The aim of each player is to maximize the expected total reward. For the game defined this way, we construct a Nash equilibrium. The construction is based on the solution of an optimal multiple stopping problem. We show the connections between expected rewards and stopping times of the players in Nash equilibrium in the game and the optimal expected rewards and optimal stopping times in the multiple stopping problem. A Pareto optimum of the game is given. It is also proved that the presented Nash equilibrium is a sub-game perfect Nash equilibrium. Moreover, the Nash equilibrium payoffs are unique. We also present new results related to multiple stopping problem.

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Multiple-stopping problems with random horizon

Cited by 8 publications

References 17 publications

Multiple stopping time POMDPs: Structural results & application in interactive advertising on social media

Multiple stopping time POMDPs: Structural results & application in interactive advertising on social media

Opportunistic Advertisement Scheduling in Live Social Media: A Multiple Stopping Time POMDP Approach

Construction of Nash equilibrium based on multiple stopping problem in multi-person game

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