  We address the online combinatorial choice of weight multipliers for
multi-objective optimization of many loss terms parameterized by neural works
via a probabilistic graphical model (PGM) for the joint model parameter and
multiplier evolution process, with a hypervolume based likelihood promoting
multi-objective descent. The corresponding parameter and multiplier estimation
as a sequential decision process is then cast into an optimal control problem,
where the multi-objective descent goal is dispatched hierarchically into a
series of constraint optimization sub-problems. The subproblem constraint
automatically adapts itself according to Pareto dominance and serves as the
setpoint for the low level multiplier controller to schedule loss landscapes
via output feedback of each loss term. Our method is multiplier-free and
operates at the timescale of epochs, thus saves tremendous computational
resources compared to full training cycle multiplier tuning. It also
circumvents the excessive memory requirements and heavy computational burden of
existing multi-objective deep learning methods. We applied it to domain
invariant variational auto-encoding with 6 loss terms on the PACS domain
generalization task, and observed robust performance across a range of
controller hyperparameters, as well as different multiplier initial conditions,
outperforming other multiplier scheduling methods. We offered modular
implementation of our method, admitting extension to custom definition of many
loss terms.
