Neural Combinatorial Clustered Bandits for Recommendation Systems

We consider the contextual combinatorial bandit setting where in each round, the learning agent, e.g., a recommender system, selects a subset of "arms," e.g., products, and observes rewards for both the individual base arms, which are a function of known features (called "context"), and the super arm (the subset of arms), which is a function of the base arm rewards. The agent's goal is to simultaneously learn the unknown reward functions and choose the highest-reward arms. For example, the "reward" may represent a user's probability of clicking on one of the recommended products. Conventional bandit models, however, employ restrictive reward function models in order to obtain performance guarantees. We make use of deep neural networks to estimate and learn the unknown reward functions and propose Neural UCB Clustering (NeUClust), which adopts a clustering approach to select the super arm in every round by exploiting underlying structure in the context space. Unlike prior neural bandit works, NeUClust uses a neural network to estimate the super arm reward and select the super arm, thus eliminating the need for a known optimization oracle. We non-trivially extend prior neural combinatorial bandit works to prove that NeUClust achieves $\widetilde{O}\left(\widetilde{d}\sqrt{T}\right)$ regret, where $\widetilde{d}$ is the effective dimension of a neural tangent kernel matrix, $T$ the number of rounds. Experiments on real world recommendation datasets show that NeUClust achieves better regret and reward than other contextual combinatorial and neural bandit algorithms.

Contextual Combinatorial Volatile Bandits with Satisfying via Gaussian Processes

In many real-world applications of combinatorial bandits such as content caching, rewards must be maximized while satisfying minimum service requirements. In addition, base arm availabilities vary over time, and actions need to be adapted to the situation to maximize the rewards. We propose a new bandit model called Contextual Combinatorial Volatile Bandits with Group Thresholds to address these challenges. Our model subsumes combinatorial bandits by considering super arms to be subsets of groups of base arms. We seek to maximize super arm rewards while satisfying thresholds of all base arm groups that constitute a super arm. To this end, we define a new notion of regret that merges super arm reward maximization with group reward satisfaction. To facilitate learning, we assume that the mean outcomes of base arms are samples from a Gaussian Process indexed by the context set ${\cal X}$, and the expected reward is Lipschitz continuous in expected base arm outcomes. We propose an algorithm, called Thresholded Combinatorial Gaussian Process Upper Confidence Bounds (TCGP-UCB), that balances between maximizing cumulative reward and satisfying group reward thresholds and prove that it incurs $\tilde{O}(K\sqrt{T\overline{\gamma}_{T}} )$ regret with high probability, where $\overline{\gamma}_{T}$ is the maximum information gain associated with the set of base arm contexts that appeared in the first $T$ rounds and $K$ is the maximum super arm cardinality of any feasible action over all rounds. We show in experiments that our algorithm accumulates a reward comparable with that of the state-of-the-art combinatorial bandit algorithm while picking actions whose groups satisfy their thresholds.