The Mathematics of Optimization in Recovery

In Part 1 of this series on optimization and recovery, we considered two limitations of optimization processes and the light they shed on pseudo-recovery. Let’s now think more about what the implications of optimization are for getting full recovery to happen.

In Part 1, we only considered problems where there was just a single objective, i.e. just one thing to be minimized or maximized. Of course, this is not necessarily realistic. In this post, we build on those simpler principles to explore the more lifelike situation of optimization with multiple objectives.

Often when we have multiple objectives they’re in conflict: You can’t get all you want of one thing without compromising on another (often on multiple others). Whenever you’re trying to optimize for more than one objective, there is always a family of solutions. Any choice you make will result in an optimization problem for which there exists an optimal solution, and you cannot say one solution is “better” than another. Technically they are all optimal.

Let’s say your two cost functions are ill health and bodyweight. (We choose ill health rather than good health for simplicity, so we’re minimizing both the “bad” things. And we choose bodyweight because fear of weight gain tends to be the greatest sticking point for the majority of people who struggle to get fully better from restrictive eating disorders.) This means there are multiple different combinations of ill health and bodyweight that will satisfy the optimality requirement because where you get more of one, you typically get less of the other.

How do you choose from amongst the range of technically optimal solutions that your (explicit or inexplicit) recovery optimization algorithm generates? Some choices should be ruled out by including appropriate constraints and ruling out extreme points on the curve. Not doing either or both of these things can be understood as responsible for why many recovery efforts end in failure. These kinds of mistakes may often occur because “textbook” versions of an optimization process, inherited from clinical or cultural models that may or may not bear a close resemblance to what you need, are treated as self-evidently sufficient.

Algorithms of often fiendish complexity are at work in our lives all the time, whether or not we realize it, and if we don’t realize it, the default parameters will tend to dominate. Given how low-quality much eating disorder treatment is, and how well it aligns with the most common anorexic fears, the defaults are unlikely to do you as much good as your tailored versions could: They’re likely to push you into errors such as fruitless psychologizing or adhering to nonsensically low BMI limits (Troscianko and Leon, 2020). Your personal definition of health combined with your body’s physiology, for example, mean that not all points on the theoretically optimal curve are equally optimal for you. In the optimization processes constantly running to dictate our behaviours (anything from whether to walk or run over to the window right now, to whether to up my energy intake by 500 calories from tomorrow), choices are being made, with priors shaped by a lifetime’s worth of learning, and decisions reached via rapid and complex simulations of predicted outcomes. Turning a critical gaze on some of these often near-automatic choices, and injecting a bit more individually oriented intuition (or common sense, whatever you want to call it), is often crucial to helping algorithmically optimal translate into actually good.

In a more directly positive sense, too, the existence of a curve of optimal solutions is a useful thing to bear in mind because it counters the paralysis it’s easy to feel during recovery at the idea that there is only one endpoint. This is in stark contrast to the reality, which is that fully recovered is by definition flexible, nonsingular, comfortably inhabiting a range of options—in your bodyweight and everything else.

You can find our full exploration of these ideas, complete with examples and graphical illustrations, here.

Or read on for the third and final part here.