The multi-agent linear bandit setting is a well-known setting for which designing efficient collaboration between agents remains challenging. This paper studies the impact of data sharing among agents on regret minimization. Unlike most existing approaches, our contribution does not rely on any assumptions on the bandit parameters structure. Our main result formalizes the trade-off between the bias and uncertainty of the bandit parameter estimation for efficient collaboration. This result is the cornerstone of the Bandit Adaptive Sample Sharing (BASS) algorithm, whose efficiency over the current state-of-the-art is validated through both theoretical analysis and empirical evaluations on both synthetic and real-world datasets. Furthermore, we demonstrate that, when agents' parameters display a cluster structure, our algorithm accurately recovers them.

Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals by constraining the ℓ1-norm of the first order derivative of the estimated signal. The resulting optimization problem is usually solved using iterative algorithms such as proximal gradient descent, primal-dual algorithms or ADMM. However, such methods can require a very large number of iterations to converge to a suitable solution. In this paper, we accelerate such iterative algorithms by unfolding proximal gradient descent solvers in order to learn their parameters for 1D TV regularized problems. While this could be done using the synthesis formulation, we demonstrate that this leads to slower performances. The main difficulty in applying such methods in the analysis formulation lies in proposing a way to compute the derivatives through the proximal operator. As our main contribution, we develop and characterize two approaches to do so, describe their benefits and limitations, and discuss the regime where they can actually improve over iterative procedures. We validate those findings with experiments on synthetic and real data.

The estimation of the hemodynamic response function (HRF) in functional magnetic resonance imaging (fMRI) is critical to deconvolve a time-resolved neural activity and get insights on the underlying cognitive processes. Existing methods propose to estimate the HRF using the experimental paradigm (EP) in task fMRI as a surrogate of neural activity. These approaches induce a bias as they do not account for latencies in the cognitive responses compared to EP and cannot be applied to resting-state data as no EP is available. In this work, we formulate the joint estimation of the HRF and neural activation signal as a semi blind deconvolution problem. Its solution can be approximated using an efficient alternate minimization algorithm. The proposed approach is applied to task fMRI data for validation purpose and compared to a state-of-the-art HRF estimation technique. Numerical experiments suggest that our approach is competitive with others while not requiring EP information.