Mostly Exploration-Free Algorithms for Contextual Bandits
研究发现，在上下文（协变量）足够随机时，简单的贪婪算法无需探索即可达到渐近最优的遗憾值，并据此提出Greedy-First算法，在无需额外假设下实现率最优，减少不必要的探索。
The contextual bandit literature has traditionally focused on algorithms that address the exploration–exploitation tradeoff. In particular, greedy algorithms that exploit current estimates without any exploration may be suboptimal in general. However, exploration-free greedy algorithms are desirable in practical settings where exploration may be costly or unethical (e.g., clinical trials). Surprisingly, we find that a simple greedy algorithm can be rate optimal (achieves asymptotically optimal regret) if there is sufficient randomness in the observed contexts (covariates). We prove that this is always the case for a two-armed bandit under a general class of context distributions that satisfy a condition we term covariate diversity. Furthermore, even absent this condition, we show that a greedy algorithm can be rate optimal with positive probability. Thus, standard bandit algorithms may unnecessarily explore. Motivated by these results, we introduce Greedy-First, a new algorithm that uses only observed contexts and rewards to determine whether to follow a greedy algorithm or to explore. We prove that this algorithm is rate optimal without any additional assumptions on the context distribution or the number of arms. Extensive simulations demonstrate that Greedy-First successfully reduces exploration and outperforms existing (exploration-based) contextual bandit algorithms such as Thompson sampling or upper confidence bound. This paper was accepted by J. George Shanthikumar, big data analytics.