We analyze the problem of private learning in generalized linear contextual bandits. Our approach is based on a novel method of re-weighted regression, yielding an efficient algorithm with regret of order $\sqrt{T}+\frac{1}{\alpha}$ and $\sqrt{T}/\alpha$ in the joint and local model of $\alpha$-privacy, respectively. Further, we provide near-optimal private procedures that achieve dimension-independent rates in private linear models and linear contextual bandits. In particular, our results imply that joint privacy is almost "for free" in all the settings we consider, partially addressing the open problem posed by Azize and Basu (2024).

We conduct a systematic study of solving the learning parity with noise problem (LPN) using neural networks. Our main contribution is designing families of two-layer neural networks that practically outperform classical algorithms in high-noise, low-dimension regimes. We consider three settings where the numbers of LPN samples are abundant, very limited, and in between. In each setting we provide neural network models that solve LPN as fast as possible. For some settings we are also able to provide theories that explain the rationale of the design of our models. Comparing with the previous experiments of Esser, Kubler, and May (CRYPTO 2017), for dimension $n = 26$, noise rate $\tau = 0.498$, the ''Guess-then-Gaussian-elimination'' algorithm takes 3.12 days on 64 CPU cores, whereas our neural network algorithm takes 66 minutes on 8 GPUs. Our algorithm can also be plugged into the hybrid algorithms for solving middle or large dimension LPN instances.