Research map / Optimization / Nonconvex and smooth optimization
Continuous-time Analysis of Anchor Acceleration
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| set anchor coefficient exponent p = 1 instead of p < 1 in beta(t)=gamma/t^p (ablation) | anchor ODE · linear monotone operator A=[[0,1],[-1,0]] | convergence of ||A(X(t))||^2: O(1/t^2p) -> O(1/t^2) | Helped |
| set anchor coefficient exponent p = 1 instead of p > 1 (ablation) | anchor ODE · linear monotone operator A=[[0,1],[-1,0]] | convergence of ||A(X(t))||^2: O(1) -> O(1/t^2) | Helped |
| use gamma >= 1 instead of gamma < 1 with p = 1 (ablation) | anchor ODE beta(t)=gamma/t · monotone operators | rate of ||A(X(t))||^2: O(1/t^2gamma) -> O(1/t^2) | Helped |
| add the anchor term beta(t)(X-X0) to the plain flow X' = -A(X) (ablation) | continuous-time flow on a rotation operator · linear monotone operator | convergence to zero of A | Helped |
| use beta(t)=2mu/(e^{2 mu t}-1) instead of 1/t for strongly monotone operators | anchor ODE · mu-strongly monotone operators | rate of ||A(X(t))||^2: Theta(1/t^2) -> O(1/e^{2 mu t}) | Helped |
| use the exponentially decaying beta(t) when A is merely monotone | anchor ODE with beta(t)=2mu/(e^{2 mu t}-1) · monotone operators | convergence of A(X(t)) | Hurt |
| adaptive anchor coefficient beta_k instead of fixed 1/(k+1) schedule | anchored PG-EXTRA · decentralized compressed sensing | squared M-norm of residual vs iteration | Helped |
| anchor PG-EXTRA with Halpern coefficient gamma/(k^p+gamma), p=1.5, gamma=2.0 | PG-EXTRA · decentralized compressed sensing | squared M-norm of residual vs iteration | Helped |
| anchor PG-EXTRA with APPM coefficient | PG-EXTRA · decentralized compressed sensing | squared M-norm of residual vs iteration | Helped |
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