Digital Low-Pass Filter

A simple mechanism that can be used to learn parameter values over time is the digital low-pass filter. [The filter lets low frequencies pass through, while blocking high frequencies.] A simple digital low-pass filter is defined by:

out_i+1 = α * in_i + (1 - α) * out_i, where α << 1.

This filter reduces ``noise'' in the input, passing through the long-term trend, but with a time delay. There is memory of past data, but with exponential forgetting of old data. A filter like this was used to adjust weights of heuristic feature detectors in Samuel's checker-player program. Multiple parameter values can be learned simultaneously.