Add line breaks to MOBO documentation (#2436)

Summary:
## Motivation

I want to update this documentation, but the changes would be hard to review due to very long line length.

This PR:
* Adds line breaks that have no effect on how the website renders.

Pull Request resolved: #2436

Test Plan:
Built the website locally. Screenshot:

<img width="854" alt="Screenshot 2024-07-21 at 10 40 27 AM" src="https://github.com/user-attachments/assets/98f2c927-0093-4ff6-94f9-d5280e7c858f">

Reviewed By: saitcakmak

Differential Revision: D60019275

Pulled By: esantorella

fbshipit-source-id: 82f3b245dc5a08608e2f390f2532631b3fd744c2

Author: esantorella

docs/multi_objective.md

@@ -3,27 +3,83 @@ id: multi_objective
 title: Multi-Objective Bayesian Optimization
 ---
 
-BoTorch provides first-class support for Multi-Objective (MO) Bayesian Optimization (BO) including implementations of [`qNoisyExpectedHypervolumeImprovement`](../api/acquisition.html#botorch.acquisition.multi_objective.monte_carlo.qNoisyExpectedHypervolumeImprovement)  (qNEHVI)[^qNEHVI], [`qExpectedHypervolumeImprovement`](../api/acquisition.html#botorch.acquisition.multi_objective.monte_carlo.qExpectedHypervolumeImprovement) (qEHVI), qParEGO[^qEHVI], qNParEGO[^qNEHVI], and analytic [`ExpectedHypervolumeImprovement`](../api/acquisition.html#botorch.acquisition.multi_objective.analytic.ExpectedHypervolumeImprovement) (EHVI) with gradients via auto-differentiation acquisition functions[^qEHVI].
+BoTorch provides first-class support for Multi-Objective (MO) Bayesian
+Optimization (BO) including implementations of
+[`qNoisyExpectedHypervolumeImprovement`](../api/acquisition.html#botorch.acquisition.multi_objective.monte_carlo.qNoisyExpectedHypervolumeImprovement)
+(qNEHVI)[^qNEHVI],
+[`qExpectedHypervolumeImprovement`](../api/acquisition.html#botorch.acquisition.multi_objective.monte_carlo.qExpectedHypervolumeImprovement)
+(qEHVI), qParEGO[^qEHVI], qNParEGO[^qNEHVI], and analytic
+[`ExpectedHypervolumeImprovement`](../api/acquisition.html#botorch.acquisition.multi_objective.analytic.ExpectedHypervolumeImprovement)
+(EHVI) with gradients via auto-differentiation acquisition functions[^qEHVI].
 
-The goal in MOBO is learn the *Pareto front*: the set of optimal trade-offs, where an improvement in one objective means deteriorating another objective. Botorch provides implementations for a number of acquisition functions specifically for the multi-objective scenario, as well as generic interfaces for implemented new multi-objective acquisition functions.
+The goal in MOBO is learn the *Pareto front*: the set of optimal trade-offs,
+where an improvement in one objective means deteriorating another objective.
+Botorch provides implementations for a number of acquisition functions
+specifically for the multi-objective scenario, as well as generic interfaces for
+implemented new multi-objective acquisition functions.
 
 ## Multi-Objective Acquisition Functions
-MOBO leverages many advantages of BoTorch to make provide practical algorithms for computationally intensive and analytically intractable problems. For example, analytic EHVI has no known analytical gradient for when there are more than two objectives, but BoTorch computes analytic gradients for free via auto-differentiation, regardless of the number of objectives [^qEHVI].
+MOBO leverages many advantages of BoTorch to make provide practical algorithms
+for computationally intensive and analytically intractable problems. For
+example, analytic EHVI has no known analytical gradient for when there are more
+than two objectives, but BoTorch computes analytic gradients for free via
+auto-differentiation, regardless of the number of objectives [^qEHVI].
 
-For analytic and MC-based MOBO acquisition functions like qNEHVI, qEHVI, and qParEGO, BoTorch leverages GPU acceleration and quasi-second order methods for acquisition optimization for efficient computation and optimization in many practical scenarios [^qNEHVI][^qEHVI]. The MC-based acquisition functions support using the sample average approximation for rapid convergence [^BoTorch].
+For analytic and MC-based MOBO acquisition functions like qNEHVI, qEHVI, and
+qParEGO, BoTorch leverages GPU acceleration and quasi-second order methods for
+acquisition optimization for efficient computation and optimization in many
+practical scenarios [^qNEHVI][^qEHVI]. The MC-based acquisition functions
+support using the sample average approximation for rapid convergence [^BoTorch].
 
-All analytic MO acquisition functions derive from [`MultiObjectiveAnalyticAcquisitionFunction`](../api/acquisition.html#botorch.acquisition.multi_objective.analytic.MultiObjectiveAnalyticAcquisitionFunction) and all MC-based acquisition functions derive from [`MultiObjectiveMCAcquisitionFunction`](../api/acquisition.html#botorch.acquisition.multi_objective.monte_carlo.MultiObjectiveMCAcquisitionFunction). These abstract classes easily integrate with BoTorch's standard optimization machinery.
+All analytic MO acquisition functions derive from
+[`MultiObjectiveAnalyticAcquisitionFunction`](../api/acquisition.html#botorch.acquisition.multi_objective.analytic.MultiObjectiveAnalyticAcquisitionFunction)
+and all MC-based acquisition functions derive from
+[`MultiObjectiveMCAcquisitionFunction`](../api/acquisition.html#botorch.acquisition.multi_objective.monte_carlo.MultiObjectiveMCAcquisitionFunction).
+These abstract classes easily integrate with BoTorch's standard optimization
+machinery.
 
-Additionally, qParEGO and qNParEGO are trivially implemented using an augmented Chebyshev scalarization as the objective with the [`qExpectedImprovement`](../api/acquisition.html#qexpectedimprovement) acquisition function or the [`qNoisyExpectedImprovement`](../api/acquisition.html#qnoisyexpectedimprovement) acquisition function, respectively. Botorch provides a [`get_chebyshev_scalarization`](../api/utils.html#botorch.utils.multi_objective.scalarization.get_chebyshev_scalarizationconvenience) convenience function for generating these scalarizations. In the batch setting, qParEGO and qNParEGO both use a new random scalarization for each candidate [^qEHVI]. Candidates are selected in a sequential greedy fashion, each with a different scalarization, via the [`optimize_acqf_list`](../api/optim.html#botorch.optim.optimize.optimize_acqf_list) function.
+Additionally, qParEGO and qNParEGO are trivially implemented using an augmented
+Chebyshev scalarization as the objective with the
+[`qExpectedImprovement`](../api/acquisition.html#qexpectedimprovement)
+acquisition function or the
+[`qNoisyExpectedImprovement`](../api/acquisition.html#qnoisyexpectedimprovement)
+acquisition function, respectively. Botorch provides a
+[`get_chebyshev_scalarization`](../api/utils.html#botorch.utils.multi_objective.scalarization.get_chebyshev_scalarizationconvenience)
+convenience function for generating these scalarizations. In the batch setting,
+qParEGO and qNParEGO both use a new random scalarization for each candidate
+[^qEHVI]. Candidates are selected in a sequential greedy fashion, each with a
+different scalarization, via the
+[`optimize_acqf_list`](../api/optim.html#botorch.optim.optimize.optimize_acqf_list)
+function.
 
-For a more in-depth example using these acquisition functions, check out the [Multi-Objective Bayesian Optimization tutorial notebook](../tutorials/multi_objective_bo).
+For a more in-depth example using these acquisition functions, check out the
+[Multi-Objective Bayesian Optimization tutorial
+notebook](../tutorials/multi_objective_bo).
 
 ## Multi-Objective Utilities
 
-BoTorch provides several utility functions for evaluating performance in MOBO including a method for computing the Pareto front [`is_non_dominated`](../api/utils.html#botorch.utils.multi_objective.pareto.is_non_dominated) and efficient box decomposition algorithms for efficiently partitioning the the space dominated [`DominatedPartitioning`](../api/utils.html#botorch.utils.multi_objective.box_decompositions.dominated.DominatedPartitioning) or non-dominated [`NonDominatedPartitioning`](../api/utils.html#botorch.utils.multi_objective.box_decompositions.non_dominated.NonDominatedPartitioning) by the Pareto frontier into axis-aligned hyperrectangular boxes. For exact box decompositions, BoTorch uses a two-step approach similar to that in [^Yang2019], where (1) Algorithm 1 from [Lacour17]_ is used to find the local lower bounds for the maximization problem and (2) the local lower bounds are used as the Pareto frontier for the minimization problem, and [Lacour17]_ is applied again to partition the space dominated by that Pareto frontier. Approximate box decompositions are also supported using the algorithm from [^Couckuyt2012]. See Appendix F.4 in [^qEHVI] for an analysis of approximate vs exact box decompositions with EHVI. These box decompositions  (approximate or exact) can also be used to efficiently compute hypervolumes.
+BoTorch provides several utility functions for evaluating performance in MOBO
+including a method for computing the Pareto front
+[`is_non_dominated`](../api/utils.html#botorch.utils.multi_objective.pareto.is_non_dominated)
+and efficient box decomposition algorithms for efficiently partitioning the the
+space dominated
+[`DominatedPartitioning`](../api/utils.html#botorch.utils.multi_objective.box_decompositions.dominated.DominatedPartitioning)
+or non-dominated
+[`NonDominatedPartitioning`](../api/utils.html#botorch.utils.multi_objective.box_decompositions.non_dominated.NonDominatedPartitioning)
+by the Pareto frontier into axis-aligned hyperrectangular boxes. For exact box
+decompositions, BoTorch uses a two-step approach similar to that in [^Yang2019],
+where (1) Algorithm 1 from [Lacour17]_ is used to find the local lower bounds
+for the maximization problem and (2) the local lower bounds are used as the
+Pareto frontier for the minimization problem, and [Lacour17]_ is applied again
+to partition the space dominated by that Pareto frontier. Approximate box
+decompositions are also supported using the algorithm from [^Couckuyt2012]. See
+Appendix F.4 in [^qEHVI] for an analysis of approximate vs exact box
+decompositions with EHVI. These box decompositions  (approximate or exact) can
+also be used to efficiently compute hypervolumes.
 
-[^qNEHVI]: S. Daulton, M. Balandat, and E. Bakshy. Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement. Advances in Neural
-Information Processing Systems 34, 2021.
+[^qNEHVI]: S. Daulton, M. Balandat, and E. Bakshy. Parallel Bayesian
+Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement.
+Advances in Neural Information Processing Systems 34, 2021.
 [paper](https://arxiv.org/abs/2105.08195)
 
 [^qEHVI]: S. Daulton, M. Balandat, and E. Bakshy. Differentiable Expected Hypervolume