Neural Logistic Bandits

We study the problem of neural logistic bandits, where the main task is to learn an unknown reward function within a logistic link function using a neural network. Existing approaches either exhibit unfavorable dependencies on $\kappa$, where $1/\kappa$ represents the minimum variance of reward distributions, or suffer from direct dependence on the feature dimension $d$, which can be huge in neural network–based settings. In this work, we introduce a novel Bernstein-type inequality for self-normalized vector-valued martingales that is designed to bypass a direct dependence on the ambient dimension. This lets us deduce a regret upper bound that grows with the effective dimension $\widetilde{d}$, not the feature dimension, while keeping a minimal dependence on $\kappa$. Based on the concentration inequality, we propose two algorithms, NeuralLog-UCB-1 and NeuralLog-UCB-2, that guarantee regret upper bounds of order $\widetilde{O}(\widetilde{d}\sqrt{\kappa T})$ and $\widetilde{O}(\widetilde{d}\sqrt{T/\kappa})$, respectively, improving on the existing results. Lastly, we report numerical results on both synthetic and real datasets to validate our theoretical findings.

Many online services need to learn from repeated user feedback while making decisions in real time. For example, a system may repeatedly choose which item, recommendation, or action to show, observe whether the user responds positively or negatively, and then improve its future choices. A major challenge is that modern systems often use neural networks, which can represent very complex patterns but also create extremely large internal feature spaces. This paper studies how to make such learning more efficient when feedback is binary, such as click/no-click or success/failure. Existing methods can become inefficient either when the feedback is highly uncertain or when the neural network representation is very large. We develop a new mathematical tool that allows the learning algorithm to focus on the amount of useful information actually present in the data, rather than on the full size of the neural network representation. Using this tool, we design two new algorithms that make better decisions over time with stronger theoretical guarantees than previous methods. Experiments on synthetic and real datasets support the theory and show that the proposed methods can be effective in practice.