  We develop confidence bounds that hold uniformly over time for off-policy
evaluation in the contextual bandit setting. These confidence sequences are
based on recent ideas from martingale analysis and are non-asymptotic,
non-parametric, and valid at arbitrary stopping times. We provide algorithms
for computing these confidence sequences that strike a good balance between
computational and statistical efficiency. We empirically demonstrate the
tightness of our approach in terms of failure probability and width and apply
it to the "gated deployment" problem of safely upgrading a production
contextual bandit system.
