Add MOO recipe (#3528)

Summary:

as titled - any edits are greatly appreciated!

Differential Revision: D71397358

Author: paschai

docs/recipes/multi-objective-optimization.md

@@ -0,0 +1,50 @@
+# Multi-Objective Optimization with Ax
+
+Multi-objective optimization (MOO) allows you to optimize multiple objectives simultaneously, which is particularly useful when you have competing objectives. In this recipe, we will explore how to perform multi-objective optimization using the Ax Client.
+
+Note that while MOO can handle multiple objectives, it's generally recommended to keep the number of objectives relatively small. Having too many objectives can lead decreased optimization performance and difficulties in interpreting the results.
+
+## Prerequisites
+
+We will assume you are already familiar with [using Ax for ask-tell optimization](#)
+
+## Setup
+
+Before we begin you must instantiate the `Client` and configure it with your
+experiment and metrics.
+
+```python
+client = Client()
+
+client.configure_experiment(...)
+client.configure_metrics(...)
+```
+
+## Steps
+
+1. Configure an optimization with multiple objectives
+2. Continue with iterating over trials and evaluating them
+
+### 1. Configure an optimization with multiple objectives
+We can leverage the Client's `configure_optimization` method to configure a multi-objective optimization. This method takes in an objective goal as a string, and can be used to specify single-objective, scalarized-objective, and multi-objective goals. For this recipe, we will use a multi-objective goal:
+
+```
+client.configure_optimization(objectives="-min_objective, max_objective")
+```
+
+By default, objectives are assumed to be maximized. If you want to minimize an objective, you can prepend the objective with a `-`.
+
+### 2. Continue with iterating over trials and evaluating them
+Now that your experiment has been configured for a multi-objective optimization, you can simply continue with iterating over trials and evaluating them as you typically would.
+
+```python
+trial_idx, parameters = client.get_next_trials().popitem()
+client.complete_trial(...)
+```
+
+## Learn more
+
+Take a look at these other resources to continue your learning:
+
+- [Set scalarized-objective optimizations](#)
+- [Set outcome constraints](#)

website/sidebars.js

@@ -56,6 +56,7 @@ export default {
       'recipes/tracking-metrics',
       'recipes/experiment-to-json',
       'recipes/experiment-to-sqlite',
+      'recipes/multi-objective-optimization',
     ],
   },
 };