Preposition at start

Try not to start a sentence with a lone preposition unless absolutely necessary or unless the preposition indicates place or time (i.e. the prepositions in, on and at).

Look at this sentence:

With a decrease in drug-related crimes by eighty-one percent from 2012, the government can focus on more serious crimes.

That sentence seems to suggest  that the government is using "a decrease" instrumentally, which is to say as if it were some sort of tool that helps the government focus, which might work in a sentence such as: "With a drink in my hand, I can focus on serious conversation."  But that is not the effect we want here. 

Better to get rid of the preposition and see how it goes from there. The result, achieved simply by getting rid of the preposition and putting the subject first, is clearer than the original:   

A decrease in drug-related crimes by eighty-one percent from 2012 means that the government can now focus on serious crimes.

or

The decrease in drug-related crimes by eighty-one percent from 2012 has enabled the government to focus on serious crimes instead.

So, start with a subject not a preposition if you can. 

If you love your prepositions at the start, then get good at picking the right one.

Thanks to the decrease in drug-related crimes by eighty-one percent from 2012, the government can now focus on serious crimes.

Consider this: 

Through name-calling , insults, and hate speech, the president shows little empathy towards specific groups and citizens of his country.

Better because simpler  would be:

The president's lack of empathy for certain groups of citizens is evident in his name-calling, insults and hate-speech.

Here is another: 

With marijuana being one of the fastest growing industries in the United States, it stands to reap many monetary benefits.

Which would be better thus:

As marijuana is one of the fastest growing industries in the United States, its legalization  promises  many financial benefits.

Another example, in which the opening preposition robs the sentence of direction is this: 

With the exponential growth of AI, countries will inevitably invest in it and harness its capabilities for their own political ends. 

The sentence becomes more direct and effective through the removal of "with", which forces the writer to make several other clarifying adjustments, as follows: 

The exponential growth of AI means countries that have invested in it can harness its political (and social and commercial) capabilities, and reap its benefits (earlier than those that have not). 

Still, even after the addition of a few clarifying words,  it's not great, and the reason is too many  potential subjects/topics: AI, countries, investment, capabilities, benefits,  political ends. 

A preposition at the start refuses to tell the reader what the main subject of the sentence is. When there are many potential subjects, this lack of immediate focus at the top of the sentence becomes  problem.  

Was the writer really intending to talk about the growth of AI or just about AI, or something else? 

I call this the "x of y problem" and write about it here. If, even after the removal of an initial preposition, you still have an "x of y" construction  at the top of your sentence, make sure you know which one is the real subject: the x or the y.  

Here are some sentences generated from the original example that conveying different messages that point in different directions, depending on the choice of subject and the placement of any other x of y constructions.   

Countries that have had the foresight to invest in AI can now reap the political, social and commercial benefits of its exponential growth and development.

The exponential growth of AI will inevitably cause countries to invest in it for strategic and political reasons. 

The benefits of AI will be reaped by those countries that have invested heavily in it for strategic political purposes. [Note the passive construction].

Political strategy and "rasion d'état" have dictated governments' interest and investment in AI, which has now become strategically significant as  AI capabilities show signs of exponential growth.