Policy Gradients for General Contextual Bandits

Contextual bandits algorithms have been successfully deployed to various industrial applications for the trade-off between exploration and exploitation and the state-of-art performance on minimizing online costs. However, the applicability is limited by the over-simplified assumptions on the problem, such as assuming the rewards linearly depend on the contexts, or assuming a static environment where the states are not affected by previous actions. In this work, we put forward an alternative method for general contextual bandits using actor-critic neural networks to directly optimize in the policy space, coined policy gradient for contextual bandits (PGCB). It optimizes over a class of policies in which the marginal probability of choosing an arm (in expectation of other arms) has a simple closed form so that the objective is differentiable. In particular, the gradient of this class of policies is in a succinct form. Moreover, we propose two useful heuristic techniques called Time-Dependent Greed and Actor-Dropout. The former ensures PGCB to be empirically greedy in the limit, while the later balances a trade-off between exploration and exploitation by using the actor-network with dropout as a Bayesian approximation. PGCB can solve contextual bandits in the standard case as well as the Markov Decision Process generalization where there is a state that decides the distribution of contexts of arms and affects the immediate reward when choosing an arm, therefore can be applied to a wide range of realistic settings such as personalized recommender systems and natural language generations. We evaluate PGCB on toy datasets as well as a music recommender dataset. Experiments show that PGCB has fast convergence and low regret and outperforms both classic contextual-bandits methods and vanilla policy gradient methods.