  Reward-biased maximum likelihood estimation (RBMLE) is a classic principle in
the adaptive control literature for tackling explore-exploit trade-offs. This
paper studies the stochastic contextual bandit problem with general bounded
reward functions and proposes NeuralRBMLE, which adapts the RBMLE principle by
adding a bias term to the log-likelihood to enforce exploration. NeuralRBMLE
leverages the representation power of neural networks and directly encodes
exploratory behavior in the parameter space, without constructing confidence
intervals of the estimated rewards. We propose two variants of NeuralRBMLE
algorithms: The first variant directly obtains the RBMLE estimator by gradient
ascent, and the second variant simplifies RBMLE to a simple index policy
through an approximation. We show that both algorithms achieve
$\widetilde{\mathcal{O}}(\sqrt{T})$ regret. Through extensive experiments, we
demonstrate that the NeuralRBMLE algorithms achieve comparable or better
empirical regrets than the state-of-the-art methods on real-world datasets with
non-linear reward functions.
