From 961151b4011f866fdb0ae3dea9126a16a9c6380e Mon Sep 17 00:00:00 2001 From: Miles Olson Date: Mon, 24 Feb 2025 11:52:17 -0800 Subject: [PATCH] Intro to Adaptive Experimentation Summary: Basic doc motivating adaptive experiment design over traditional doe Differential Revision: D69267231 --- docs/assets/discrepancy_dims.png | Bin 0 -> 45406 bytes docs/assets/doe.png | Bin 0 -> 116617 bytes docs/assets/line_square_cube.png | Bin 0 -> 21292 bytes docs/assets/traditional_vs_adaptive.svg | 2 + docs/intro-to-ae.md | 119 ++++++++++++++++++++++++ website/sidebars.js | 2 +- 6 files changed, 122 insertions(+), 1 deletion(-) create mode 100644 docs/assets/discrepancy_dims.png create mode 100644 docs/assets/doe.png create mode 100644 docs/assets/line_square_cube.png create mode 100644 docs/assets/traditional_vs_adaptive.svg create mode 100644 docs/intro-to-ae.md diff --git a/docs/assets/discrepancy_dims.png b/docs/assets/discrepancy_dims.png new file mode 100644 index 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100644 index 00000000000..e1ece5243a9 --- /dev/null +++ b/docs/intro-to-ae.md @@ -0,0 +1,119 @@ +--- +id: intro-to-ae +title: Introduction to Adaptive Experimentation +--- + +# Introduction to Adaptive Experimentation + +In engineering tasks we often encounter so-called "black box" optimization +problems, situations where the relationship between inputs and outputs of a +system don’t have a closed-form solution and cannot be easily modeled. In these +scenarious practitioners must tune parameters using many time- and/or +resource-consuming trials. For example: + +- Machine learning engineers may seek optimal hyperparameters such as learning + rate or number of training steps to maximize accuracy or minimize size/runtime + for a model. +- Roboticists may seek to jointly find optimal gait parameters such as stride + length or foot angle to maximize walking speed for a legged robot. +- Materials scientists may seek to find the composition and heat treatment + parameters that maximize strength for an aerospace alloy. +- Chemists may seek to find the synthesis path for a molecule that is likely to + be a good drug candidate for an infectious disease. + +Adaptive experimentation is an approach to solving these problems efficiently by +leveraging data from prior iterations to inform future decisions on which trials +to run next. + +![Traditional vs. Adaptive design](assets/traditional_vs_adaptive.svg) + +## Traditional methods are inefficient, especially in high dimensions + +To solve black-box problems, there are two common approaches to suggest what +points or “trials” to evaluate (i.e., measurements of objective(s) for a given +set of input parameters). One is to use manual trial-and-error based on +intuition. The second is a more systematic method called “design of experiments” +(DoE). These methods can provide a strong understanding of the relationship +between the inputs and outputs of a system by providing broad coverage of the +entire input space. Examples of traditional DoE methods include: + +- Grid search: testing points on an equally spaced grid, +- Random search: randomly picking parameter combinations. Although somewhat + counterintuitive, random search is often more effective than grid search + because it avoids systematic gaps. + +An alternative class of methods referred to as quasi-random search offer the +"best of both worlds" between grid and random search by strategically selecting +points that are more uniformly dispersed. Examples include: + +- Sobol sampling, +- Latin Hypercube Sampling. Both rely on some form of subdividing a search space + and assigning points in relation to these subdivisions. + +![DoE sampling methods](assets/doe.png) + +Unfortunately getting broad coverage of the domain requires many samples, which +can be expensive. Worse, as more dimensions are added more points are required +to achieve the same coverage. To illustrate, imagine points distributed on a +line (1D), a square (2D), and a cube (3D). + +![Sampling from a line, a square, and a cube](assets/line_square_cube.png) + +Notice how even though there are 9x more points in the cube than on the line, +the +[discrepancy](https://en.wikipedia.org/wiki/Equidistributed_sequence#Discrepancy) +is 3x higher than for the line (0.100 vs. 0.028). This is often referred to as +the +["curse of dimensionality"](https://en.wikipedia.org/wiki/Curse_of_dimensionality). + +| | Line | Square | Cube | Hypercube | +| ----------- | :-------: | :-------: | :-------: | :---------: | +| Num. Points | $$3^1$$ | $$3^2$$ | $$3^3$$ | $$n^d$$ | +| Discrepancy | $$0.028$$ | $$0.061$$ | $$0.100$$ | $$f(3, d)$$ | + +Real-world black box optimization tasks often have many dimensions and can only +afford to conduct very few trials. For example, imagine you have a budget of 100 +trials and are optimizing over a parameter space with 20 dimensions. The +differences in discrepancy between algorithms can become drastic, as shown +below. In the case of grid search, to have even just two subdivisions in each of +20 dimensions would require $$20^2 = 400$$ points, well over our 100 point +budget! + +![Discrepancy vs. input dimensionality](assets/discrepancy_dims.png) + +## Adaptive experimentation outperforms traditional methods + +Although simple to implement, traditional DoE methods such as grid search, +random search, and quasi-random search are uninformed, meaning they do not +incorporate information about the objective function to be optimized. Likewise, +manual trial-and-error can be slow, expensive, and too complicated to +effectively reason about; domain experts often restrict their search space to +just a few parameters to help it feel like it’s something they can handle. + +Adaptive experimentation is a more efficient version of DoE that iteratively +incorporates information from prior results to suggest the next parameter set to +run. A typical adaptive experiment involves the following series of steps: + +1. **Configure** your optimization experiment, defining the search space, + objective(s), constraints, etc. +2. **Suggest** new trials, either one at a time or in a batch +3. **Evaluate** the suggested trials by executing the black box function and + reporting the results back to the optimization algorithm +4. **Repeat** steps 2 and 3 until a stopping condition is met or the evaluation + budget is exhausted + +Bayesian optimization, one of the most effective forms of adaptive +experimentation, uses acquisition functions to intelligently balance the +tradeoffs between exploration (learning how new parameterizations perform) and +exploitation (refining parameterizations previously observed to be good). To +achieve this, one must also create a surrogate model that predicts the average +behavior and the uncertainty of the objective(s) as a function of the input +parameters Typically this surrogate model is much less expensive to evaluate +than the true, underlying black box function. + +Black box optimization problems are everywhere, whether in machine learning, +robotics, materials science, or chemistry. Moving from manual trial-and-error +and uninformed strategies such as grid, random, and quasi-random search to an +adaptive experimentation setup can dramatically improve optimization +performance, whether it’s a state-of-the-art machine learning model, a faster +robot, a stronger alloy, or a better medicine. diff --git a/website/sidebars.js b/website/sidebars.js index 6f194df6169..ff93a53b95e 100644 --- a/website/sidebars.js +++ b/website/sidebars.js @@ -45,7 +45,7 @@ const tutorials = () => { export default { docs: { - Introduction: ['why-ax'], + Introduction: ['why-ax', 'intro-to-ae'], }, tutorials: tutorials(), };