  Beam parameter optimization in accelerators involves multiple, sometimes
competing objectives. Condensing these individual objectives into a single
figure of merit unavoidably results in a bias towards particular outcomes, in
absence of prior knowledge often in a non-desired way. Finding an optimal
objective definition then requires operators to iterate over many possible
objective weights and definitions, a process that can take many times longer
than the optimization itself. A more versatile approach is multi-objective
optimization, which establishes the trade-off curve or Pareto front between
objectives. Here we present the first results on multi-objective Bayesian
optimization of a simulated laser-plasma accelerator. We find that
multi-objective optimization reaches comparable performance to its
single-objective counterparts while allowing for instant evaluation of entirely
new objectives. This dramatically reduces the time required to find appropriate
objective definitions for new problems. Additionally, our multi-objective,
multi-fidelity method reduces the time required for an optimization run by an
order of magnitude. It does so by dynamically choosing simulation resolution
and box size, requiring fewer slow and expensive simulations as it learns about
the Pareto-optimal solutions from fast low-resolution runs. The techniques
demonstrated in this paper can easily be translated into many different
computational and experimental use cases beyond accelerator optimization.
