  This paper studies algorithmic decision-making in the presence of strategic
individual behaviors, where an ML model is used to make decisions about human
agents and the latter can adapt their behavior strategically to improve their
future data. Existing results on strategic learning have largely focused on the
linear setting where agents with linear labeling functions best respond to a
(noisy) linear decision policy. Instead, this work focuses on general
non-linear settings where agents respond to the decision policy with only
"local information" of the policy. Moreover, we simultaneously consider the
objectives of maximizing decision-maker welfare (model prediction accuracy),
social welfare (agent improvement caused by strategic behaviors), and agent
welfare (the extent that ML underestimates the agents). We first generalize the
agent best response model in previous works to the non-linear setting, then
reveal the compatibility of welfare objectives. We show the three welfare can
attain the optimum simultaneously only under restrictive conditions which are
challenging to achieve in non-linear settings. The theoretical results imply
that existing works solely maximizing the welfare of a subset of parties
inevitably diminish the welfare of the others. We thus claim the necessity of
balancing the welfare of each party in non-linear settings and propose an
irreducible optimization algorithm suitable for general strategic learning.
Experiments on synthetic and real data validate the proposed algorithm.
