Neural Contextual Bandits without Regret
This work provides theoretical guarantees for neural networks in contextual bandits, addressing an open problem with applications in areas like recommender systems.
The authors tackled the problem of proving sublinear regret bounds for neural contextual bandits with general context sequences, achieving a convergence rate of $ ilde{\mathcal{O}}(T^{-1/2d})$ to the optimal policy under non-parametric assumptions.
Contextual bandits are a rich model for sequential decision making given side information, with important applications, e.g., in recommender systems. We propose novel algorithms for contextual bandits harnessing neural networks to approximate the unknown reward function. We resolve the open problem of proving sublinear regret bounds in this setting for general context sequences, considering both fully-connected and convolutional networks. To this end, we first analyze NTK-UCB, a kernelized bandit optimization algorithm employing the Neural Tangent Kernel (NTK), and bound its regret in terms of the NTK maximum information gain $γ_T$, a complexity parameter capturing the difficulty of learning. Our bounds on $γ_T$ for the NTK may be of independent interest. We then introduce our neural network based algorithm NN-UCB, and show that its regret closely tracks that of NTK-UCB. Under broad non-parametric assumptions about the reward function, our approach converges to the optimal policy at a $\tilde{\mathcal{O}}(T^{-1/2d})$ rate, where $d$ is the dimension of the context.