Mario Meets Pareto

We've had a bit of fun here, but don't you see the pattern? We're often faced with similar trade-offs. You want a meal that's both cheap and delicious? A job that's both well-paid, easy, and fulfilling? A portfolio with low risks and high returns? A flexible and strong material that's also easy to produce? A fair taxation that remains efficient ? A high quality LLM that is also fast and cost-efficient. In all these cases, you're facing a multi-objective optimization problem, and you have to make trade-offs.

Of course, if you already know the exact weights you want to assign to each dimension (i.e., you know your utility function), you reduce the problem to a single objective optimization. This is because you can combine the dimensions with the weights into a single quantity to optimize (often called utility, cost, or fitness). In that case, you don't need Pareto at all.

But you're often faced with situations where your utility function is unknown or uncertain. In those situations, the Pareto front helps you eliminate objectively all the sub-optimal options. It won't reveal the one best option right from the outset, but you may now experiment with these efficient options and select the one that fits you the best.