I think that algorithms are already largely regulated...
In that they are embedded in products and services. If you sell a product or service with an algorithm that makes that product unsafe, then your company is liable. If you create an algorithm that misrepresents data, as in a financial scam or your average VW diesel, you are liable. If your algorithm unjustly impacts the economic opportunities of one or more racial/ethnic/gender groups, then you are liable.
Yes, you have to be careful when writing or incorporating algorithms, but the same can be said for code in general, or even many physical components of a tangible product. I worked at a medical device company where our materials people changed out the type of plastic used in a device, (stupidly) without testing the toxicity of the new plastic--oops. The Food and Drug Administration slapped us into next week over that one.
In terms of public services/government, you can in many cases also sue if an algorithm impacts your benefits/employability/economic or property rights. You can also vote to "kick the bums out" if a specific elected official or group of officials is involved.