[ML] Avoid zero size steps in L-BFGS #2078
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tveasey
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Oct 28, 2021
Our implementation could generate zero size steps and fail to converge. There are a couple of different scenarios
in which this was possible:
1. The function gradient was smaller than double epsilon times the norm of argument vector in which case x - g(x)
= x to working precision,
2. The gradient function returned zero at the initial point.
We were also checking a strict inequality for convergence, which failed to identify we'd converged if we were
taking zero sized steps.
To handle both cases I've added a fallback to perform a more elaborate line search if we try to take a too small
step which ensures we test steps which are larger than epsilon * x. We also now try some random probes to see if
we can find a direction in which the function decreases if the gradient function returns zero (this can be useful if
the function is used for finding local minimum of non-convex functions).
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Our implementation could generate zero size steps and fail to converge. There are a couple of different scenarios in which this was possible:
x - g(x) = xto working precisionWe were also checking a strict inequality for convergence, which failed to identify we'd converged if we were taking zero sized steps.
To handle both cases I've added a fallback to perform a more elaborate line search if we try to take a too small step which ensures we test steps which are larger than
epsilon * x. We also now try some random probes to see if we can find a direction in which the function decreases if the gradient function returns zero.