MARBLE: Multi-Armed Restless Bandits in Latent Markovian Environment
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918437310169088 |
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| author | Amiri, Mohsen Avrachenkov, Konstantin Mimouni, Ibtihal El Magnússon, Sindri |
| author_facet | Amiri, Mohsen Avrachenkov, Konstantin Mimouni, Ibtihal El Magnússon, Sindri |
| contents | 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 (Multi-Armed Restless Bandits in a Latent Markovian Environment), which augments RMABs with a latent Markov state that induces nonstationary behavior. In MARBLE, each arm evolves according to a latent environment state that switches over time, making policy learning substantially more challenging. We further introduce the Markov-Averaged Indexability (MAI) criterion as a relaxed indexability assumption and prove that, despite unobserved regime switches, under the MAI criterion, synchronous Q-learning with Whittle Indices (QWI) converges almost surely to the optimal Q-function and the corresponding Whittle indices. We validate MARBLE on a calibrated simulator-embedded (digital twin) recommender system, where QWI consistently adapts to a shifting latent state and converges to an optimal policy, empirically corroborating our theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09324 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | MARBLE: Multi-Armed Restless Bandits in Latent Markovian Environment Amiri, Mohsen Avrachenkov, Konstantin Mimouni, Ibtihal El Magnússon, Sindri Machine Learning 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 (Multi-Armed Restless Bandits in a Latent Markovian Environment), which augments RMABs with a latent Markov state that induces nonstationary behavior. In MARBLE, each arm evolves according to a latent environment state that switches over time, making policy learning substantially more challenging. We further introduce the Markov-Averaged Indexability (MAI) criterion as a relaxed indexability assumption and prove that, despite unobserved regime switches, under the MAI criterion, synchronous Q-learning with Whittle Indices (QWI) converges almost surely to the optimal Q-function and the corresponding Whittle indices. We validate MARBLE on a calibrated simulator-embedded (digital twin) recommender system, where QWI consistently adapts to a shifting latent state and converges to an optimal policy, empirically corroborating our theoretical findings. |
| title | MARBLE: Multi-Armed Restless Bandits in Latent Markovian Environment |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2511.09324 |