Differentiable Bandit Exploration

TL;DR

This paper introduces a meta-learning approach for Bayesian bandit exploration policies, optimizing them via differentiable parameterizations and policy gradients, with theoretical guarantees and versatile experimental results.

Contribution

It proposes a differentiable, gradient-based method for learning exploration policies in Bayesian bandits, including novel variance reduction and a softmax policy with regret guarantees.

Findings

Neural network policies can learn implicit biases from instances.

The softmax policy has theoretical regret guarantees.

The approach is versatile and effective across different policy classes.

Abstract

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.