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Restless multi-armed bandits (RMAB) has been widely used to model constrained sequential decision making problems, where the state of each restless arm evolves according to a Markov chain and each state transition generates a scalar reward. However, the success of RMAB crucially relies on the availability and quality of reward signals. Unfortunately, specifying an exact reward function in practice can be challenging and even infeasible. In this paper, we introduce Pref-RMAB, a new RMAB model in the presence of preference signals, where the decision maker only observes pairwise preference feedback rather than scalar reward from the activated arms at each decision epoch. Preference feedback, however, arguably contains less information than the scalar reward, which makes Pref-RMAB seemingly more difficult. To address this challenge, we present a direct online preference learning (DOPL) algorithm for Pref-RMAB to efficiently explore the unknown environments, adaptively collect preference data in an online manner, and directly leverage the preference feedback for decision-makings. We prove that DOPL yields a sublinear regret. To our best knowledge, this is the first algorithm to ensure $$\tilde{\mathcal{O}}(\sqrt{T\ln T})$$ regret for RMAB with preference feedback. Experimental results further demonstrate the effectiveness of DOPL.
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Online Restless Multi-Armed Bandits with Long-Term Fairness Constraints
Restless multi-armed bandits (RMAB) have been widely used to model sequential decision making problems with constraints. The decision maker (DM) aims to maximize the expected total reward over an infinite horizon under an “instantaneous activation constraint” that at most B arms can be activated at any decision epoch, where the state of each arm evolves stochastically according to a Markov decision process (MDP). However, this basic model fails to provide any fairness guarantee among arms. In this paper, we introduce RMAB-F, a new RMAB model with “long-term fairness constraints”, where the objective now is to maximize the longterm reward while a minimum long-term activation fraction for each arm must be satisfied. For the online RMAB-F setting (i.e., the underlying MDPs associated with each arm are unknown to the DM), we develop a novel reinforcement learning (RL) algorithm named Fair-UCRL. We prove that Fair-UCRL ensures probabilistic sublinear bounds on both the reward regret and the fairness violation regret. Compared with off-the-shelf RL methods, our Fair-UCRL is much more computationally efficient since it contains a novel exploitation that leverages a low-complexity index policy for making decisions. Experimental results further demonstrate the effectiveness of our Fair-UCRL.
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- Award ID(s):
- 2148309
- PAR ID:
- 10501336
- Publisher / Repository:
- Proceedings of the AAAI Conference on Artificial Intelligence
- Date Published:
- Journal Name:
- Proceedings of the AAAI Conference on Artificial Intelligence
- Volume:
- 38
- Issue:
- 14
- ISSN:
- 2159-5399
- Page Range / eLocation ID:
- 15616 to 15624
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1609/aaai.v38i14.29489
