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This paper surveys recent work by the author on the theoretical and algorithmic aspects of restless bandit indexation as well as on its application to a variety of problems involving the dynamic allocation of priority to multiple stochastic…

Optimization and Control · Mathematics 2023-04-14 José Niño-Mora

We study the stochastic multi-armed bandit (MAB) problem in the presence of side-observations across actions that occur as a result of an underlying network structure. In our model, a bipartite graph captures the relationship between…

Machine Learning · Computer Science 2017-07-14 Swapna Buccapatnam , Fang Liu , Atilla Eryilmaz , Ness B. Shroff

We study a novel multi-armed bandit problem that models the challenge faced by a company wishing to explore new strategies to maximize revenue whilst simultaneously maintaining their revenue above a fixed baseline, uniformly over time.…

Machine Learning · Statistics 2016-02-16 Yifan Wu , Roshan Shariff , Tor Lattimore , Csaba Szepesvári

We consider the restless multi-armed bandit (RMAB) problem with unknown dynamics in which a player chooses M out of N arms to play at each time. The reward state of each arm transits according to an unknown Markovian rule when it is played…

Optimization and Control · Mathematics 2011-12-30 Haoyang Liu , Keqin Liu , Qing Zhao

In the classic Bayesian restless multi-armed bandit (RMAB) problem, there are $N$ arms, with rewards on all arms evolving at each time as Markov chains with known parameters. A player seeks to activate $K \geq 1$ arms at each time in order…

Optimization and Control · Mathematics 2010-11-23 Wenhan Dai , Yi Gai , Bhaskar Krishnamachari , Qing Zhao

We consider a resource-aware variant of the classical multi-armed bandit problem: In each round, the learner selects an arm and determines a resource limit. It then observes a corresponding (random) reward, provided the (random) amount of…

Machine Learning · Computer Science 2022-10-18 Viktor Bengs , Eyke Hüllermeier

We consider a multi-armed bandit problem in a setting where each arm produces a noisy reward realization which depends on an observable random covariate. As opposed to the traditional static multi-armed bandit problem, this setting allows…

Statistics Theory · Mathematics 2013-05-27 Vianney Perchet , Philippe Rigollet

Restless Multi-Armed Bandits (RMABs) are powerful models for decision-making under uncertainty, yet classical formulations typically assume fixed dynamics, an assumption often violated in nonstationary environments. We introduce MARBLE…

Machine Learning · Computer Science 2026-04-13 Mohsen Amiri , Konstantin Avrachenkov , Ibtihal El Mimouni , Sindri Magnússon

We study the Lagrangian Index Policy (LIP) for restless multi-armed bandits with long-run average reward. In particular, we compare the performance of LIP with the performance of the Whittle Index Policy (WIP), both heuristic policies known…

Machine Learning · Computer Science 2026-01-01 Konstantin Avrachenkov , Vivek S. Borkar , Pratik Shah

We consider a bandit problem which involves sequential sampling from two populations (arms). Each arm produces a noisy reward realization which depends on an observable random covariate. The goal is to maximize cumulative expected reward.…

Statistics Theory · Mathematics 2010-03-09 Philippe Rigollet , Assaf Zeevi

We consider finite state restless multi-armed bandit problem. The decision maker can act on M bandits out of N bandits in each time step. The play of arm (active arm) yields state dependent rewards based on action and when the arm is not…

Machine Learning · Computer Science 2023-05-02 Vishesh Mittal , Rahul Meshram , Deepak Dev , Surya Prakash

High-content screening microscopy generates large amounts of live-cell imaging data, yet its potential remains constrained by the inability to determine when and where to image most effectively. Optimally balancing acquisition time,…

Applications · Statistics 2025-12-18 Jaume Anguera Peris , Songtao Cheng , Hanzhao Zhang , Wei Ouyang , Joakim Jaldén

Entropy maximization and free energy minimization are general physical principles for modeling the dynamics of various physical systems. Notable examples include modeling decision-making within the brain using the free-energy principle,…

We consider a novel stochastic multi-armed bandit setting, where playing an arm makes it unavailable for a fixed number of time slots thereafter. This models situations where reusing an arm too often is undesirable (e.g. making the same…

Machine Learning · Computer Science 2024-07-31 Soumya Basu , Rajat Sen , Sujay Sanghavi , Sanjay Shakkottai

We consider a large number of agents collaborating on a multi-armed bandit problem with a large number of arms. The goal is to minimise the regret of each agent in a communication-constrained setting. We present a decentralised algorithm…

Machine Learning · Computer Science 2021-09-21 Conor Newton , Ayalvadi Ganesh , Henry W. J. Reeve

This paper proposes a new formulation for the dynamic resource allocation problem, which converts the traditional MDP model with known parameters and no capacity constraints to a new model with uncertain parameters and a resource capacity…

Optimization and Control · Mathematics 2020-11-10 Onur Demiray , Evrim Didem Güneş , Lerzan Örmeci

We consider the combinatorial bandits problem with semi-bandit feedback under finite sampling budget constraints, in which the learner can carry out its action only for a limited number of times specified by an overall budget. The action is…

Machine Learning · Computer Science 2022-10-17 Jasmin Brandt , Viktor Bengs , Björn Haddenhorst , Eyke Hüllermeier

Restless multi-arm bandits (RMABs) is a popular decision-theoretic framework that has been used to model real-world sequential decision making problems in public health, wildlife conservation, communication systems, and beyond. Deployed…

Artificial Intelligence · Computer Science 2023-01-20 Paritosh Verma , Shresth Verma , Aditya Mate , Aparna Taneja , Milind Tambe

In the contextual linear bandit setting, algorithms built on the optimism principle fail to exploit the structure of the problem and have been shown to be asymptotically suboptimal. In this paper, we follow recent approaches of deriving…

Machine Learning · Computer Science 2020-11-23 Andrea Tirinzoni , Matteo Pirotta , Marcello Restelli , Alessandro Lazaric

We consider a general online resource allocation model with bandit feedback and time-varying demands. While online resource allocation has been well studied in the literature, most existing works make the strong assumption that the demand…

Machine Learning · Computer Science 2023-06-13 Lixing Lyu , Wang Chi Cheung