  Online allocation is a broad class of problems where items arriving online
have to be allocated to agents who have a fixed utility/cost for each assigned
item so to maximize/minimize some objective. This framework captures a broad
range of fundamental problems such as the Santa Claus problem (maximizing
minimum utility), Nash welfare maximization (maximizing geometric mean of
utilities), makespan minimization (minimizing maximum cost), minimization of
$\ell_p$-norms, and so on. We focus on divisible items (i.e., fractional
allocations) in this paper. Even for divisible items, these problems are
characterized by strong super-constant lower bounds in the classical worst-case
online model.
  In this paper, we study online allocations in the {\em learning-augmented}
setting, i.e., where the algorithm has access to some additional
(machine-learned) information about the problem instance. We introduce a {\em
general} algorithmic framework for learning-augmented online allocation that
produces nearly optimal solutions for this broad range of maximization and
minimization objectives using only a single learned parameter for every agent.
As corollaries of our general framework, we improve prior results of Lattanzi
et al. (SODA 2020) and Li and Xian (ICML 2021) for learning-augmented makespan
minimization, and obtain the first learning-augmented nearly-optimal algorithms
for the other objectives such as Santa Claus, Nash welfare,
$\ell_p$-minimization, etc. We also give tight bounds on the resilience of our
algorithms to errors in the learned parameters, and study the learnability of
these parameters.
