Optimization is usually drawn as a climb.
There is a landscape. Each candidate has a height. Better candidates sit above worse ones. But many real systems have no single height. An industrial process may need output, safety, energy use, maintenance burden, and environmental impact to move together. These objectives do not collapse cleanly into one direction.
Dominance
If one candidate gives higher return with lower risk, it is better. It dominates the other. No preference model is needed. The inferior candidate can be discarded because it offers no compensating advantage. A candidate dominates another when it is at least as good on every objective and strictly better on at least one. It removes what is wasteful.
One strategy returns more and draws down more. Another trades less but adapts more slowly. A third sacrifices upside for stability under regime change. When no solution clearly dominates the others, the optimizer has reached the shape of the problem.
The frontier
The non-dominated candidates form the Pareto set. Their objective values form the Pareto frontier. These days we encounter the frontier in various AI model benchmarks that places model performance on a two-dimensional plot (e.g. cost vs task performance). In two objectives, the frontier can be drawn as a curve. In three, as a surface, and so on. We are searching for the set of choices that remain after removing candidates that are unambiguously worse, i.e. the effective trade-offs between objectives. Candidates can be anything from model parameters to portfolio weights to programs; to belong to the same surface they must just be comparable in the objective space, and assigned eval scores. What can we do with this interesting object? We can choose a point based on our preferences: a utility function can reduce the frontier to a single point. So can a constraint. So can an allocator, a policy, a risk limit, a budget, and so on. Selection may be a dynamic process: at any given time, the best point may be different depending on the current state of the environment or regime.
Measures such as hypervolume are evaluate a set by asking how much objective space it dominates relative to a reference point. In some multi-objective search algorithms, the hypervolume is the objective to maximize.
Optimization as an interface
That’s a nice concept, but surely it is too expensive for training large models? Yes and no. It turns out that large models often harbor many experts that are adjacent. In other words, it is not necessary to train separate models for each point on the frontier. Recent studies show that even slight pertubations of a single model can reveal such latent behaviors. We may also keep the model weights fixed and evolve prompts (see GEPA), do RL and so on.
That turns optimization into an interface between search and commitment. An interface for who or what? For human judgement, but it just happens to be a good interface for AI agents too (e.g. autoresearch agents).
The optimizer exposes the geometry of the decision. The agent supplies preference under context. This is especially valuable in adaptive systems. Conditions shift. Evidence arrives unevenly. Different histories matter. A behavior that was inferior under one evaluation window may become relevant under another. A point that looks unattractive in isolation may occupy an important niche in the population. Premature scalarization erases that structure.
Better is not always a point. Sometimes it is the boundary of what has been learned so far. Sometimes it is the population that remains alive under pressure.