Contextual linear dueling bandits have recently garnered significant attention due to their widespread applications in important domains such as recommender systems and large language models. Classical dueling bandit algorithms are typically only applicable to a single agent. However, many applications of dueling bandits involve multiple agents who wish to collaborate for improved performance yet are unwilling to share their data. This motivates us to draw inspirations from federated learning, which involves multiple agents aiming to collaboratively train their neural networks via gradient descent (GD) without sharing their raw data. Previous works have developed federated linear bandit algorithms which rely on closed-form updates of the bandit parameters (e.g., the linear function parameters) to achieve collaboration. However, in linear dueling bandits, the linear function parameters lack a closed-form expression and their estimation requires minimizing a loss function. This renders these previous methods inapplicable. In this work, we overcome this challenge through an innovative and principled combination of online gradient descent (OGD, for minimizing the loss function to estimate the linear function parameters) and federated learning, hence introducing our federated linear dueling bandit with OGD (FLDB-OGD) algorithm. Through rigorous theoretical analysis, we prove that FLDB-OGD enjoys a sub-linear upper bound on its cumulative regret and demonstrate a theoretical trade-off between regret and communication complexity. We conduct empirical experiments to demonstrate the effectiveness of FLDB-OGD and reveal valuable insights, such as the benefit of a larger number of agents, the regret-communication trade-off, among others.

To realize orthogonal frequency division multiplexing (OFDM)-based grant-free access for wideband systems under frequency-selective fading, existing device activity detection and channel estimation methods need substantial accuracy improvement or computation time reduction. In this paper, we aim to resolve this issue. First, we present an exact time-domain signal model for OFDM-based grant-free access under frequency-selective fading. Then, we present a maximum a posteriori (MAP)-based device activity detection problem and two minimum mean square error (MMSE)-based channel estimation problems. The MAP-based device activity detection problem and one of the MMSE-based channel estimation problems are formulated for the first time. Next, we build a new factor graph that captures the exact statistics of time-domain channels and device activities. Based on it, we propose two approximate message passing (AMP)-based algorithms,AMP-A-ECandAMP-A-AC, to approximately solve the MAP-based device activity detection problem and two MMSE-based channel estimation problems. Both proposed algorithms alleviate the AMP’s inherent convergence problem when the pilot length is smaller or comparable to the number of active devices. Then, we analyzeAMP-A-EC’s error probability of activity detection and mean square error (MSE) of channel estimation via state evolution and show thatAMP-A-AChas the lower computational complexity (in dominant term). Finally, numerical results show the two proposed AMP-based algorithms’ superior performance and respective preferable regions, revealing their significant values for OFDM-based grant-free access.