Linesearch-Enhanced Inexact Forward-Backward Methods for Bilevel Optimization
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Bilevel optimization problems arise in various real-world applications, often being characterized by the impossibility of having the exact objective function and its gradient available. Developing mathematically sound optimization methods that effectively handle inexact information is crucial for ensuring reliable and efficient solutions. In this talk we propose a line-search based algorithm for solving a bilevel optimization problem, where the approximate gradient and function evaluation obeys an adaptive tolerance rule. Our method is based on implicit differentiation under some standard assumptions, and its main novelty with respect to similar approaches is the well posed, inexact line-search procedure using only approximate function values and adaptive accuracy control. This work is partially supported by the PRIN projects “Sustainable tomographic imaging with learning and regularization” (CUP E53D23005480006) and “Inverse Problems in the Imaging Sciences” (CUP E53D23005580006), under the National Recovery and Resilience Plan (NRRP) funded by the European Union - NextGenerationEU.