Gambler Bandits and the Regret of Being Ruined

Filipo Perotto; Sattar Vakili; Pratik Gajane; Yaser Faghan; Mathieu Bourgais

Gambler Bandits and the Regret of Being Ruined

Filipo Perotto, Sattar Vakili, Pratik Gajane, Yaser Faghan, Mathieu Bourgais

Chair of Information Technology (150)

Research output: Contribution to conference › Paper › peer-review

Abstract

In this paper we consider a particular class of problems called
multiarmed gambler bandits (MAGB) which constitutes a modified
version of the Bernoulli MAB problem where two new elements
must be taken into account: the budget and the risk of ruin. The agent has an initial budget that evolves in time following the received rewards, which can be either +1 after a success or −1 after a failure. The problem can also be seen as a MAB version of the classic gambler’s ruin game. The contribution of this paper is a preliminary analysis on the probability of being ruined given the current budget and observations, and the proposition of an alternative regret formulation, combining the classic regret notion with the expected loss due to the probability of being ruined. Finally, standard state-of-the-art methods are experimentally compared using the proposed metric.

Original language	English
Publication status	Submitted - 17 Mar 2021
Event	20th International Conference on Autonomous Agents and Multiagent Systems : International Foundation for Autonomous Agents and MultiagentSystems (IFAAMAS) - fully virtual event, London Duration: 3 May 2021 → 7 May 2021 Conference number: hal-03120813 http://www.ifaamas.org

Conference

Conference	20th International Conference on Autonomous Agents and Multiagent Systems
Abbreviated title	AAMAS 2021
City	London
Period	3/05/21 → 7/05/21
Internet address	http://www.ifaamas.org

Keywords

Peer-reviewed

Access to Document

https://hal.archives-ouvertes.fr/hal-03120813

Cite this

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title = "Gambler Bandits and the Regret of Being Ruined",

abstract = "In this paper we consider a particular class of problems calledmultiarmed gambler bandits (MAGB) which constitutes a modifiedversion of the Bernoulli MAB problem where two new elementsmust be taken into account: the budget and the risk of ruin. The agent has an initial budget that evolves in time following the received rewards, which can be either +1 after a success or −1 after a failure. The problem can also be seen as a MAB version of the classic gambler{\textquoteright}s ruin game. The contribution of this paper is a preliminary analysis on the probability of being ruined given the current budget and observations, and the proposition of an alternative regret formulation, combining the classic regret notion with the expected loss due to the probability of being ruined. Finally, standard state-of-the-art methods are experimentally compared using the proposed metric.",

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TY - CONF

T1 - Gambler Bandits and the Regret of Being Ruined

AU - Perotto, Filipo

AU - Vakili, Sattar

AU - Gajane, Pratik

AU - Faghan, Yaser

AU - Bourgais, Mathieu

N1 - Conference code: hal-03120813

PY - 2021/3/17

Y1 - 2021/3/17

N2 - In this paper we consider a particular class of problems calledmultiarmed gambler bandits (MAGB) which constitutes a modifiedversion of the Bernoulli MAB problem where two new elementsmust be taken into account: the budget and the risk of ruin. The agent has an initial budget that evolves in time following the received rewards, which can be either +1 after a success or −1 after a failure. The problem can also be seen as a MAB version of the classic gambler’s ruin game. The contribution of this paper is a preliminary analysis on the probability of being ruined given the current budget and observations, and the proposition of an alternative regret formulation, combining the classic regret notion with the expected loss due to the probability of being ruined. Finally, standard state-of-the-art methods are experimentally compared using the proposed metric.

AB - In this paper we consider a particular class of problems calledmultiarmed gambler bandits (MAGB) which constitutes a modifiedversion of the Bernoulli MAB problem where two new elementsmust be taken into account: the budget and the risk of ruin. The agent has an initial budget that evolves in time following the received rewards, which can be either +1 after a success or −1 after a failure. The problem can also be seen as a MAB version of the classic gambler’s ruin game. The contribution of this paper is a preliminary analysis on the probability of being ruined given the current budget and observations, and the proposition of an alternative regret formulation, combining the classic regret notion with the expected loss due to the probability of being ruined. Finally, standard state-of-the-art methods are experimentally compared using the proposed metric.

KW - Peer-reviewed

M3 - Paper

T2 - 20th International Conference on Autonomous Agents and Multiagent Systems

Y2 - 3 May 2021 through 7 May 2021

ER -