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Automatic differentiation of nonsmooth iterative algorithms
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use nonsmooth piggyback differentiation under a contraction assumption | Lipschitz path-differentiable iterative algorithms · Fixed-point maps | convergence to the fixed-point derivative | Helped |
| Use a Lipschitz gradient selection for the iteration mapping | Nonsmooth piggyback differentiation · Semialgebraic piecewise smooth selection functions | derivative convergence rate: C (√ρ + ε)^k | Helped |
| Apply nonsmooth piggyback differentiation to Heavy-Ball with α = 1 and β = 3/4 | Heavy-Ball · Strongly convex piecewise quadratic counterexample | stability of propagated derivatives: −9/8 | Hurt |
| Use Heavy-Ball rather than a non-inertial method for the nonsmooth example | Iterative solver differentiation · Piecewise quadratic objective at θ = 0 | derivative propagation stability: −9/8 | Hurt |
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