  This paper develops a model-free sequential test for conditional
independence. The proposed test allows researchers to analyze an incoming
i.i.d. data stream with any arbitrary dependency structure, and safely conclude
whether a feature is conditionally associated with the response under study. We
allow the processing of data points online, as soon as they arrive, and stop
data acquisition once significant results are detected, rigorously controlling
the type-I error rate. Our test can work with any sophisticated machine
learning algorithm to enhance data efficiency to the extent possible. The
developed method is inspired by two statistical frameworks. The first is the
model-X conditional randomization test, a test for conditional independence
that is valid in offline settings where the sample size is fixed in advance.
The second is testing by betting, a ``game-theoretic'' approach for sequential
hypothesis testing. We conduct synthetic experiments to demonstrate the
advantage of our test over out-of-the-box sequential tests that account for the
multiplicity of tests in the time horizon, and demonstrate the practicality of
our proposal by applying it to real-world tasks.
