Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio.
This is: The ground of optimization, published...
Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio.
This is: The ground of optimization, published by Alex Flint on the AI Alignment Forum.
This work was supported by OAK, a monastic community in the Berkeley hills. This document could not have been written without the daily love of living in this beautiful community. The work involved in writing this cannot be separated from the sitting, chanting, cooking, cleaning, crying, correcting, fundraising, listening, laughing, and teaching of the whole community.
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
√
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 object of optimization in the previous example.
There is clearly a connection between optimizing the factory and optimizing for x, but what exactly is this connection? What is it that identifies an algorithm as an optimization algorithm? What is it that identifies a process as an optimization process?
The answer proposed in this essay is: an optimizing system is a physical process in which the configuration of some part of the universe moves predictably towards a small set of target configurations from any point in a broad basin of optimization, despite perturbations during the optimization process.
We do not imagine that there is some engine or agent or mind performing optimization, separately from that which is being optimized. We consider the whole system jointly — engine and object of optimization — and ask whether it exhibits a tendency to evolve towards a predictable target configuration. If so, then we call it an optimizing system. If the basin of attraction is deep and wide then we say that this is a robust optimizing system.
An optimizing system as defined in this essay is known in dynamical systems theory as a dynamical system with one or more attractors. In this essay we show how this framework can help to understand optimization as manifested in physically closed systems containing both engine and object of optimization.
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