Robust trajectory guarantees under adaptive Markov sampling

Determine whether clipping or robust aggregation can improve the tradeoff between shrinking accuracy tolerances and confidence under adaptive Markov sampling, while controlling the bias introduced by robust updates and establishing matching lower bounds under a common sampling budget.

Background

The paper proves that, under finite second moments, the polynomial exponent in its all-future shrinking-tube exit-probability bound is unimprovable in general. The sharpness construction uses rare heavy-tailed observations, motivating the study of robust stochastic-approximation procedures.

The unresolved question is whether robustification mechanisms such as clipping or robust aggregation can improve the confidence–accuracy tradeoff when sampling is adaptive and Markovian. A satisfactory resolution must account for the bias caused by robust updates and compare the resulting guarantees with matching lower bounds under a shared sampling-budget constraint.