If you search with Google "Value Averaging", you're swamped with dozens of web pages which explain how it works, why lump-sum investing is better and why not, template Excel sheets and so forth.
So I will not waste space by explaining what VA is.
From a broader perspective, VA is just another mean-reverting strategy, like following the Delta of a short Put can be in the sense that it's a scheme which tells you when and how much of your total wealth you should invest to have some payoff.
From a closer perspective, everything about VA revolves around a so-called "value path", that is, a time series which tells you what the value of your portfolio should be at every time.
As this is a time series entirely made up by the investor, it might have every possible shape: whilst educational material often suggests flat annual growth rate (and possible enhancement by making this growth rate time-dependent), this seems too simplistic in a quantitative world where we could use every possible machinery taken from stochastic processes, econometrics, machine learning and so forth.
So my question is: do you know what are the most advanced developments on this theme produced so far by researchers and/or practitioners?