By Edward Rothberg, PhD
August 4, 2021

“What’s the difference between mathematical optimization and machine learning?”

This is a question that â€” as the CEO of a mathematical optimization software company â€” I get asked all the time. Although it seems like a simple question, it’s actually quite difficult to come up with a concise, coherent answer. There are two main reasons why this is the case:

1. Mathematical optimization and machine learning are two highly sophisticated advanced analytics software technologies that are used in a vast array of applications, making it hard to swiftly and succinctly define them and draw distinctions between them.

2. Mathematical optimization and machine learning actually have many significant similarities, such as:

• They are both popular and powerful AI problem-solving tools that scores of organizationsÂ across many different industries use today to manage complexity and achieve better business outcomes.
• Both run on data and require extensive computing resources, and both have benefited greatly from advancements over the past few decades in computing capability as well as data availability and quality.
• Fundamentally, both are based on deep mathematics and are shining examples of how mathematics â€” along with data and computers â€” can be used to solve complex business problems.

Indeed, mathematical optimization and machine learning are two tools that, at first glance â€” like scissors and pliers â€” may seem to have a lot in common. When you look closely at their fundamental features and actual applications, however, you’ll see some important differences.

In this article, I’ll lay out the four main differences between mathematical optimization and machine learning so that, if you’re thinking of investing in one of these technologies, you can more easily determine which one is right for you.

1. Type Of Analytics

Generally speaking, there areÂ three different typesÂ of advanced analytics tools: descriptive (which provide insights on what has happened in the past or is happening currently in your business environment), predictive (which enable you to predict what will happen in the future) and prescriptive (which help you decide what you should do in order to reach your business goals).

Machine learning â€” the preeminent predictive analytics tool available today â€” is capable of processing massive amounts of historical “big data” to automatically identify patterns, learn from the past and make predictions about the future.

Mathematical optimization â€” theÂ leading prescriptive analytics toolÂ in the market â€” leverages the latest available data, a mathematical model of your business environment and an algorithm-based solver to generate solutions to your most challenging business problems and empower you to make the best possible business decisions.

The output of machine learning â€” predictions â€” can be used to guide certain decisions, but machine learning isn’t fundamentally equipped to handle business problems that involveÂ intricate, interconnected sets of decisionsÂ (some of which have more possible outcomes than there are atoms in the universe) like mathematical optimization can.

2. Applications

Another critical difference between mathematical optimization and machine learning is how these two technologies are used.

Machine learning is employed in a seemingly endless range of applications â€” many of which touch our everyday lives, including image and speech recognition, product recommendations, virtual personal assistants, fraud detection, and self-driving cars.

Enterprises use mathematical optimization across the business spectrum in a wide variety of applications to addressÂ large-scale, mission-critical business problems, including production planning, workforce scheduling, electric power distribution, and shipment routing.

As many machine learning applications are consumer-facing and have become part and parcel of our daily lives, this technology is more visible and well-known than mathematical optimization. However, the impact of both technologies can be felt across virtually every industry and in practically every aspect of our world today.

Businesses today, particularly since the onset of the Covid-19 pandemic, operate in an environment characterized by constant change and disruption.

Mathematical optimization applications â€” as they are based on aÂ detailed mathematical modelÂ (which functions as aÂ digital twinÂ of your operating environment) and run on the most up-to-date data â€” can easily adjust to changing conditions and give you the visibility and agility you need to efficientlyÂ respond to disruption.

In contrast, machine learning applications â€” which rely on historical data â€” often suffer from what’s called “model drift,” which refers to the fact that machine learning models lose their predictive power due to changes in the operating environment and data. Over time, and especially when encountering sudden changes, machine learning predictions become less accurate. When this happens, machine learning models need to be retrained on new data.

It should be noted that the robustness of mathematical optimization models comes at a cost, as these models typically require a greater investment ofÂ time and effort to buildÂ upfront than their machine learning counterparts.

4. Maturity

Both mathematical optimization and machine learning have long and illustrious histories. The initial incarnations of these technologies appeared in the middle of the 20th century, while many of the underlying techniques were first developed hundreds of years ago.

Although both technologies are well-established, they’re at different stages in their lifecycles.

Mathematical optimization went through what GartnerÂ would callÂ the “peak of inflated expectations” in the early 1970s when, buoyed by a streak of successes, practitioners believed that mathematical optimization could be used to address an enormous range of real-world problems. It then fell into the “trough of disillusionment” in the late 1970s when the technology failed to live up to the hype and eventually settled into a “plateau of productivity” in the 1990s and beyond, as mathematical optimization is now a proven technology that companies across industries have applied widely.

According to Gartner, machine learning â€” which is now essentially ubiquitous across the business world â€”Â has reachedÂ the “peak of inflated expectations.” In the coming years, we’ll likely see a sense of disillusionment set in when machine learning isn’t able to fulfill sky-high expectations. Ultimately, however, the technology will achieve broad market viability and value.

One thing is certain: Mathematical optimization and machine learning will have an enduring and expanding impact on the world we live in for years to come, and enterprises will continue to find innovative ways to use these AI tools to tackle their most important business challenges.

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