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What is optimization? What is the relationship between a computational optimization process — say, a computer program solving an optimization problem — and a physical optimization process — say, a team of humans building a house?

We propose the concept of an optimizing system as a physically closed system containing both that which is being optimized and that which is doing the optimizing, and defined by a tendency to evolve from a broad basin of attraction towards a small set of target configurations despite perturbations to the system. We compare our definition to that proposed by Yudkowsky, and place our work in the context of work by Demski and Garrabrant’s Embedded Agency, and Drexler’s Comprehensive AI Services. We show that our definition resolves difficult cases proposed by Daniel Filan. We work through numerous examples of biological, computational, and simple physical systems showing how our definition relates to each.

Introduction

In the field of computer science, an optimization algorithm is a computer program that outputs the solution, or an approximation thereof, to an optimization problem. An optimization problem consists of an objective function to be maximized or minimized, and a feasible region within which to search for a solution. For example we might take the objective function $(x^{2} - 2)^{2}$ as a minimization problem and the whole real number line as the feasible region. The solution then would be $x = \sqrt{2}$ and a working optimization algorithm for this problem is one that outputs a close approximation to this value.

In the field of operations research and engineering more broadly, optimization involves improving some process or physical artifact so that it is fit for a certain purpose or fulfills some set of requirements. For example, we might choose to measure a nail factory by the rate at which it outputs nails, relative to the cost of production inputs. We can view this as a kind of objective function, with the factory as the object of optimization just as the variable x was the ob...

Dynamical systems