An Efficient Algorithm for Deep Stochastic Contextual Bandits
This work addresses convergence guarantees for deep learning methods in stochastic contextual bandits, which is an incremental improvement for researchers in reinforcement learning and bandit algorithms.
The paper tackled the lack of convergence analysis in deep stochastic contextual bandits by formulating it as a non-convex stochastic optimization problem and designing a stage-wise stochastic gradient descent algorithm, proving high-probability convergence to a locally optimal policy and demonstrating effectiveness on real-world datasets.
In stochastic contextual bandit (SCB) problems, an agent selects an action based on certain observed context to maximize the cumulative reward over iterations. Recently there have been a few studies using a deep neural network (DNN) to predict the expected reward for an action, and the DNN is trained by a stochastic gradient based method. However, convergence analysis has been greatly ignored to examine whether and where these methods converge. In this work, we formulate the SCB that uses a DNN reward function as a non-convex stochastic optimization problem, and design a stage-wise stochastic gradient descent algorithm to optimize the problem and determine the action policy. We prove that with high probability, the action sequence chosen by this algorithm converges to a greedy action policy respecting a local optimal reward function. Extensive experiments have been performed to demonstrate the effectiveness and efficiency of the proposed algorithm on multiple real-world datasets.