Neural Information Processing Systems http://nips.cc/

We study multi-task representation learning for the problem of pure exploration in bilinear bandits. In bilinear bandits, an action takes the form of a pair of arms from two different entity types and the reward is a bilinear function of the known feature vectors of the arms. In the multi-task bilinear bandit problem, we aim to find optimal actions for multiple tasks that share a common low-dimensional linear representation. The objective is to leverage this characteristic to expedite the process of identifying the best pair of arms for all tasks. We propose the algorithm GOBLIN that uses an experimental design approach to optimize sample allocations for learning the global representation as well as minimize the number of samples needed to identify the optimal pair of arms in individual tasks. To the best of our knowledge, this is the first study to give sample complexity analysis for pure exploration in bilinear bandits with shared representation. Our results demonstrate that by learning the shared representation across tasks, we achieve significantly improved sample complexity compared to the traditional approach of solving tasks independently.

We introduce a "learning-based" algorithm for the low-rank decomposition problem: given an n d matrix A, and a parameter k, compute a rank-k matrix A

This paper studies the properties of solutions to multi-task shallow ReLU neural network learning problems, wherein the network is trained to fit a dataset with minimal sum of squared weights. Remarkably, the solutions learned for each individual task resemble those obtained by solving a kernel regression problem, revealing a novel connection between neural networks and kernel methods. It is known that single-task neural network learning problems are equivalent to a minimum norm interpolation problem in a non-Hilbertian Banach space, and that the solutions of such problems are generally non-unique. In contrast, we prove that the solutions to univariate-input, multi-task neural network interpolation problems are almost always unique, and coincide with the solution to a minimum-norm interpolation problem in a Sobolev (Reproducing Kernel) Hilbert Space.

Spectral methods are widely used to estimate eigenvectors of a low-rank signal matrix subject to noise. These methods use the leading eigenspace of an observed matrix to estimate this low-rank signal. Typically, the entrywise estimation error of these methods depends on the coherence of the low-rank signal matrix with respect to the standard basis. In this work, we present a novel method for eigenvector estimation that avoids this dependence on coherence. Assuming a rank-one signal matrix, under mild technical conditions, the entrywise estimation error of our method provably has no dependence on the coherence under Gaussian noise (i.e., in the spiked Wigner model), and achieves the optimal estimation rate up to logarithmic factors. Simulations demonstrate that our method performs well under non-Gaussian noise and that an extension of our method to the case of a rank-r signal matrix has little to no dependence on the coherence.

Many reinforcement learning (RL) algorithms are too costly to use in practice due to the large sizes S, A of the problem's state and action space. To resolve this issue, we study transfer RL with latent low rank structure. We consider the problem of transferring a latent low rank representation when the source and target MDPs have transition kernels with Tucker rank (S, d, A), (S, S, d), (d, S, A), or (d, d, d). In each setting, we introduce the transfer-ability coefficient α that measures the difficulty of representational transfer. Our algorithm learns latent representations in each source MDP and then exploits the linear structure to remove the dependence on S, A, or SA in the target MDP regret bound. We complement our positive results with information theoretic lower bounds that show our algorithms (excluding the (d, d, d) setting) are minimax-optimal with respect to α.

Precision livestock farming (PLF) has been transformed by machine learning (ML), enabling more precise and timely interventions that enhance overall farm productivity, animal welfare, and environmental sustainability. However, despite the availability of various sensing technologies, few datasets leverage multiple modalities, which are crucial for developing more accurate and efficient monitoring devices and ML models.

Most neural networks assume that input images have a fixed number of channels (three for RGB images). However, there are many settings where the number of channels may vary, such as microscopy images where the number of channels changes depending on instruments and experimental goals. Yet, there has not been a systemic attempt to create and evaluate neural networks that are invariant to the number and type of channels. As a result, trained models remain specific to individual studies and are hardly reusable for other microscopy settings. In this paper, we present a benchmark for investigating channel-adaptive models in microscopy imaging, which consists of 1) a dataset of varied-channel single-cell images, and 2) a biologically relevant evaluation framework. In addition, we adapted several existing techniques to create channel-adaptive models and compared their performance on this benchmark to fixed-channel, baseline models. We find that channel-adaptive models can generalize better to out-of-domain tasks and can be computationally efficient.