Differentiable Bandit Exploration
This work addresses the challenge of efficient exploration in bandit problems for scenarios where the distribution of instances is unknown, offering a general and implementable method that is incremental in its application of existing techniques to this specific bottleneck.
The paper tackles the problem of learning exploration policies for Bayesian bandits from an unknown distribution of problem instances, using a differentiable meta-learning approach optimized via policy gradients, and demonstrates its versatility across various policy classes including neural networks and a novel softmax policy with regret guarantees.
Exploration policies in Bayesian bandits maximize the average reward over problem instances drawn from some distribution $\mathcal{P}$. In this work, we learn such policies for an unknown distribution $\mathcal{P}$ using samples from $\mathcal{P}$. Our approach is a form of meta-learning and exploits properties of $\mathcal{P}$ without making strong assumptions about its form. To do this, we parameterize our policies in a differentiable way and optimize them by policy gradients, an approach that is general and easy to implement. We derive effective gradient estimators and introduce novel variance reduction techniques. We also analyze and experiment with various bandit policy classes, including neural networks and a novel softmax policy. The latter has regret guarantees and is a natural starting point for our optimization. Our experiments show the versatility of our approach. We also observe that neural network policies can learn implicit biases expressed only through the sampled instances.