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The Basics of Optimization in Eating Disorder Recovery

Part 1: Introducing cost functions and their limitations.

Key points

  • Recovery from an eating disorder can be framed as an optimization problem, in which we aim to maximize utility and minimize costs.
  • Optimization is a powerful framework for making decisions, but it has its limitations, which can leave people in semi-recovery.
  • Two limitations are that one's model of recovery may not be a good fit for reality and that partial recovery may seem better than the costs linked to full recovery.

“Optimizing for” something has a simple colloquial meaning of setting things up to get as much as you can of something—anything from health to happiness to salary payments in the bank at the end of the month. It also has a more specific meaning in the mathematics of optimization: selecting the best option (with regard to an agreed-upon scoring metric) from a set of alternatives.

In the last two parts of my recent series on cognitive dissonance, I used optimization in the first sense: as a simple concept to structure questions we can usefully ask ourselves about what we’re doing in life and why. In this new series of posts, I’d like to explore how the more technical aspects of optimization theory can also provide tools to help in recovery from an eating disorder. This series has been written in collaboration with my partner James Anderson, an engineer/mathematician who specializes in optimization amongst other topics (and who also made this excellent contribution to the blog a few years ago), so you needn’t take my word for it! Our aim is to convince you that a little maths goes a long way when it comes to any big life decisions you may be making, recovery included.

Recovery from an eating disorder is readily framed as an optimization problem. Here our goal is to either maximize some utility (e.g. health or happiness), or minimize costs (e.g. time off work/studies), or discomfort, or weight gain (more on this later), or probably to do both simultaneously. An algorithm is at play, with some degree of explicitness, constantly trying to find the optimal solution to the choice between getting more of the utility and incurring more of the costs. Optimization algorithms are iterative, i.e. they begin at some initial point with a candidate decision variable, and then proceed by incrementally adjusting the decision variable until it is not possible to make the objective function cost any smaller (or larger if you’re maximizing).

The Limitations of Optimization

Optimization is a powerful framework for generating decisions in response to complex sets of aims and constraints, but like everything, it has its limitations. The main two inherent limitations of optimization algorithms are:

  1. The optimization algorithm is based on a model of the process, and the model is the only reality that exists for the purposes of this algorithm.
  2. Optimization algorithms are myopic, in the sense that at each iteration, the algorithm will always choose to update its choice of decision variable so as to reduce its cost.

Thinking through the implications of these limitations, using analogies of a skier lost on a mountain and an investment banker trying to keep her clients happy, gives us a new lens through which to understand recovery. We focus on the question of why it’s so easy to end up in semi-recovery, with reference to the two intrinsic limitations of optimization: 1) your model of recovery or health may or may not be a good fit for reality, and 2) your local optimum (partial recovery) may seem better than incurring the costs required to get to the global optimum (full recovery).

Our full exploration of how optimization helps us understand recovery better is on my website here.

Or read on for Part 2, on the case where we have multiple objectives in tension with each other.

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