Contextual Bandits with Smooth Regret: Efficient Learning in Continuous Action Spaces
This work addresses a key problem for applications like recommendation systems and continuous control by providing a more efficient learning framework, though it builds incrementally on existing regret notions.
The paper tackles the challenge of designing efficient contextual bandit algorithms for large or continuous action spaces, such as in information retrieval and recommendation systems, by proposing a smooth regret notion and algorithms that achieve statistical and computational efficiency with general function approximation, including empirical demonstrations of efficacy.
Designing efficient general-purpose contextual bandit algorithms that work with large -- or even continuous -- action spaces would facilitate application to important scenarios such as information retrieval, recommendation systems, and continuous control. While obtaining standard regret guarantees can be hopeless, alternative regret notions have been proposed to tackle the large action setting. We propose a smooth regret notion for contextual bandits, which dominates previously proposed alternatives. We design a statistically and computationally efficient algorithm -- for the proposed smooth regret -- that works with general function approximation under standard supervised oracles. We also present an adaptive algorithm that automatically adapts to any smoothness level. Our algorithms can be used to recover the previous minimax/Pareto optimal guarantees under the standard regret, e.g., in bandit problems with multiple best arms and Lipschitz/H{ö}lder bandits. We conduct large-scale empirical evaluations demonstrating the efficacy of our proposed algorithms.