WIRED was the first magazine to cover Theranos and its enticing billionaire founder. There were warning signs even then. Elizabeth Holmes, the disgraced founder of the fraud-ridden blood-test company Theranos, made her national press debut in The Wall Street Journal in 2013. It ran in the Opinion section, by a writer on the Journal's editorial board named Joseph Rago, winner of a Pulitzer Prize for critiques of the Affordable Care Act. He wrote that he was impressed by the prospect of individuals having more direct control of their health care; no less an eminence than former secretary of state George Shultz, a Theranos board member, had told Rago that Holmes was the next Steve Jobs or Bill Gates. By 2014, Holmes was the youngest woman billionaire ever, and the mid-2010s were electric with tech-industry success stories--the iPhone, Tesla, Airbnb, Twitter.

We show that the answer to this question depends on the properties of underlying preference distributions.

We show that the answer to this question depends on the properties of underlying preference distributions.

We study nonparametric contextual bandits where Lipschitz mean reward functions may change over time. We first establish the minimax dynamic regret rate in this less understood setting in terms of number of changes $L$ and total-variation $V$, both capturing all changes in distribution over context space, and argue that state-of-the-art procedures are suboptimal in this setting. Next, we tend to the question of an adaptivity for this setting, i.e. achieving the minimax rate without knowledge of $L$ or $V$. Quite importantly, we posit that the bandit problem, viewed locally at a given context $X_t$, should not be affected by reward changes in other parts of context space $\cal X$. We therefore propose a notion of change, which we term experienced significant shifts, that better accounts for locality, and thus counts considerably less changes than $L$ and $V$. Furthermore, similar to recent work on non-stationary MAB (Suk & Kpotufe, 2022), experienced significant shifts only count the most significant changes in mean rewards, e.g., severe best-arm changes relevant to observed contexts. Our main result is to show that this more tolerant notion of change can in fact be adapted to.