Webb10 maj 2024 · The Polyak-Lojasiewicz (PL) inequality, and not what you have written, is not wrong, since it is a hypothesis. On the other hand, in general, the inequality is not true. For example, the functions f ( x) = x k for k even is convex, and it only satisfies 1 k f ′ ( x) ≥ … Webb25 juni 2024 · We introduce the notions of proxy convexity and proxy Polyak-Lojasiewicz (PL) inequalities, which are satisfied if the original objective function induces a proxy objective function that is implicitly minimized when using gradient methods.
Linear Convergence and Support Vector Identifiation of …
WebbPL inequality linear convergence rate of the proposed algorithm is achieved. Moreover, we propose a modified self-scaling symmetric rank one incorporated in the framework for SPQN method, ... Webbfunction satisfies the PL inequality if for any x2Rn, 1 2 kr f(x)2 )) holds for some >0. Verification of the PL condition requires access to both the objective function value and the norm of gradient, both of which are typically tractable and can be estimated from a sub-sample of the data. However, for verifying guaranteed bad credit student loans
OPT2024: 12th Annual Workshop on Optimization for Machine …
WebbDefinition 1. (Polyak-Łojasiewicz (PL) Inequality) A func-tion satisfies the PL inequality if, for some >0, 1 2 krf(z)k2 (f(z) f) for all z2Rm; where f = min x2Rm f(x). We say such an f is -PL or has the -PL property. 4 A -PL function has a unique global minimum value, denoted by f , and the PL condition implies that every stationary point ... Webb4 aug. 2024 · The Polyak-Lojasiewicz (PL) inequality is one of the most general sufficient conditions for discrete-time gradient descent to exhibit linear convergence rates without … Webb11 feb. 2024 · Relating to the theory of Lyapunov stability for nonlinear systems, the PL inequality essentially means that the function value itself is a valid Lyapunov function for exponential stability of the global minimum under the nonlinear gradient descent dynamics. guaranteed bad with charge offs