  Estimation of the complete distribution of a random variable is a useful
primitive for both manual and automated decision making. This problem has
received extensive attention in the i.i.d. setting, but the arbitrary data
dependent setting remains largely unaddressed. Consistent with known
impossibility results, we present computationally felicitous time-uniform and
value-uniform bounds on the CDF of the running averaged conditional
distribution of a real-valued random variable which are always valid and
sometimes trivial, along with an instance-dependent convergence guarantee. The
importance-weighted extension is appropriate for estimating complete
counterfactual distributions of rewards given controlled experimentation data
exhaust, e.g., from an A/B test or a contextual bandit.
