# Approximation algorithms for restless bandit problems

@inproceedings{Guha2010ApproximationAF, title={Approximation algorithms for restless bandit problems}, author={Sudipto Guha and Kamesh Munagala and Peng Shi}, booktitle={JACM}, year={2010} }

The restless bandit problem is one of the most well-studied generalizations of the celebrated stochastic multi-armed bandit (MAB) problem in decision theory. In its ultimate generality, the restless bandit problem is known to be PSPACE-Hard to approximate to any nontrivial factor, and little progress has been made on this problem despite its significance in modeling activity allocation under uncertainty.
In this article, we consider the Feedback MAB problem, where the reward obtained by…

## 126 Citations

### Learning of Uncontrolled Restless Bandits with Logarithmic Strong Regret

- Computer Science
- 2013

This paper proposes a learning algorithm with near-logarithmic regret uniformly over time with respect to the optimal (dynamic) finite horizon policy, referred to as strong regret, to contrast with commonly studied notion of weak regret.

### Approximations of the Restless Bandit Problem

- Computer ScienceJ. Mach. Learn. Res.
- 2019

It is shown that under some conditions on the $\varphi$-mixing coefficients, a modified version of UCB can prove effective, and a sub-class of the multi-armed restless bandit problem is characterized where approximate solutions can be found using tractable approaches.

### Non-Stationary Bandits under Recharging Payoffs: Improved Planning with Sublinear Regret

- Computer ScienceArXiv
- 2022

This work improves the best-known guarantees for the planning problem by developing a polynomial-time (1 − 1 /e ) -approximation algorithm (asymptotically and in expectation), based on a novel combination of randomized LP rounding and a time-correlated (interleaved) scheduling method.

### Approximations of the Restless Bandit Problem

- Computer Science
- 2016

A special setting is characterised where good approximate solutions can indeed be found via simple UCB-type algorithms, and it is shown that under some conditions on the φ-mixing coefficients, a modified version of UCB recovers the best achievable regret of the i.i.d. setting.

### Optimality of Myopic Policy for Restless Multiarmed Bandit with Imperfect Observation

- Mathematics2016 IEEE Global Communications Conference (GLOBECOM)
- 2016

This paper performs an analytical study on the considered RMAB problem, and establishes a set of closed-form conditions to guarantee the optimality of the myopic policy.

### Multi-policy posterior sampling for restless Markov bandits

- Computer Science2014 IEEE Global Conference on Signal and Information Processing (GlobalSIP)
- 2014

A polynomial time algorithm is proposed that learns transitional parameters for each arm and selects the perceived optimal policy from a set of predefined policies using a beliefs or probability distributions using randomized probability matching or better known as Thompson Sampling.

### Near-optimality for infinite-horizon restless bandits with many arms

- Computer Science, EconomicsArXiv
- 2022

By replacing a global Lagrange multiplier used by the Whittle index with a sequence of Lagrangian multipliers, one per time period up to a finite truncation point, a class of policies are derived that have a O(√N) optimality gap and are demonstrated to provide state-of-the-art performance on specific problems.

### The non-Bayesian restless multi-armed bandit: A case of near-logarithmic regret

- Computer Science2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- 2011

This work develops an original approach to the RMAB problem that is applicable when the corresponding Bayesian problem has the structure that the optimal solution is one of a prescribed finite set of policies, and develops a novel sensing policy for opportunistic spectrum access over unknown dynamic channels.

### The Non-Bayesian Restless Multi-Armed Bandit: A Case of Near-Logarithmic Strict Regret

- Computer Science, MathematicsArXiv
- 2011

It is proved that the original approach to the non-Bayesian RMAB problem, in which the parameters of the Markov chain are assumed to be unknown, achieves near-logarithmic regret, which leads to the same average reward that can be achieved by the optimal policy under a known model.

### Optimal Adaptive Learning in Uncontrolled Restless Bandit Problems

- Computer Science
- 2012

This paper proposes a learning algorithm with logarithmic regret uniformly over time with respect to the optimal finite horizon policy for uncontrolled restless bandit problems, and extends the optimal adaptive learning of MDPs to POMDPs.

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