  As an autonomous system performs a task, it should maintain a calibrated
estimate of the probability that it will achieve the user's goal. If that
probability falls below some desired level, it should alert the user so that
appropriate interventions can be made. This paper considers settings where the
user's goal is specified as a target interval for a real-valued performance
summary, such as the cumulative reward, measured at a fixed horizon $H$. At
each time $t \in \{0, \ldots, H-1\}$, our method produces a calibrated estimate
of the probability that the final cumulative reward will fall within a
user-specified target interval $[y^-,y^+].$ Using this estimate, the autonomous
system can raise an alarm if the probability drops below a specified threshold.
We compute the probability estimates by inverting conformal prediction. Our
starting point is the Conformalized Quantile Regression (CQR) method of Romano
et al., which applies split-conformal prediction to the results of quantile
regression. CQR is not invertible, but by using the conditional cumulative
distribution function (CDF) as the non-conformity measure, we show how to
obtain an invertible modification that we call Probability-space Conformalized
Quantile Regression (PCQR). Like CQR, PCQR produces well-calibrated conditional
prediction intervals with finite-sample marginal guarantees. By inverting PCQR,
we obtain guarantees for the probability that the cumulative reward of an
autonomous system will fall below a threshold sampled from the marginal
distribution of the response variable (i.e., a calibrated CDF estimate) that we
employ to predict coverage probabilities for user-specified target intervals.
Experiments on two domains confirm that these probabilities are
well-calibrated.
