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Non-convex Optimisation Using the Polyak-Łojasiewicz Inequality

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If you have a question about this talk, please contact Mateja Jamnik.

We consider the idea of solving a non-convex optimisation problem by adding a large enough strongly-convex function to make the objective function convex. This allows the use of simpler convex optimisers, yet, given the large strong-convexity constant required, yields a value closer to the minimum of the function added than that of the objective one. We try to fix this with the novel idea of instead adding a function that makes the objective satisfy the Polyak-Łojasiewicz (PL) inequality, a much weaker condition than strong-convexity. Building on previous work, we construct an optimisation algorithm relying on this method. We find that a much smaller multiplicative constant is needed for convergence to a minimum. We attempt to find and prove convergence rates and computational complexity and test which algorithm yields a more accurate minimum.

This talk is part of the Artificial Intelligence Research Group Talks (Computer Laboratory) series.

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