  Consider learning a decision support assistant to serve as an intermediary
between (oracle) expert behavior and (imperfect) human behavior: At each time,
the algorithm observes an action chosen by a fallible agent, and decides
whether to *accept* that agent's decision, *intervene* with an alternative, or
*request* the expert's opinion. For instance, in clinical diagnosis,
fully-autonomous machine behavior is often beyond ethical affordances, thus
real-world decision support is often limited to monitoring and forecasting.
Instead, such an intermediary would strike a prudent balance between the former
(purely prescriptive) and latter (purely descriptive) approaches, while
providing an efficient interface between human mistakes and expert feedback. In
this work, we first formalize the sequential problem of *online decision
mediation* -- that is, of simultaneously learning and evaluating mediator
policies from scratch with *abstentive feedback*: In each round, deferring to
the oracle obviates the risk of error, but incurs an upfront penalty, and
reveals the otherwise hidden expert action as a new training data point.
Second, we motivate and propose a solution that seeks to trade off (immediate)
loss terms against (future) improvements in generalization error; in doing so,
we identify why conventional bandit algorithms may fail. Finally, through
experiments and sensitivities on a variety of datasets, we illustrate
consistent gains over applicable benchmarks on performance measures with
respect to the mediator policy, the learned model, and the decision-making
system as a whole.
