Neural Contextual Bandits with Upper Confidence Bound-Based Exploration

We study the stochastic contextual bandit problem, where the reward is generated from an unknown bounded function with additive noise. We propose the NeuralUCB algorithm, which leverages the representation power of deep neural networks and uses a neural network-based random feature mapping to construct an upper confidence bound (UCB) of reward for efficient exploration. We prove that, under mild assumptions, NeuralUCB achieves $\tilde O(\sqrt{T})$ regret, where $T$ is the number of rounds. To the best of our knowledge, our algorithm is the first neural network-based contextual bandit algorithm with near-optimal regret guarantee. Preliminary experiment results on synthetic data corroborate our theory, and shed light on potential applications of our algorithm to real-world problems.