Safeguarded Learned Convex Optimization

Applications abound in which optimization problems must be repeatedly solved, each time with new (but similar) data. Analytic algorithms can hand-designed to provably solve these an iterative fashion. On one hand, data-driven "learn optimize" (L2O) much fewer iterations and similar cost per iteration as general-purpose algorithms. the other unfortunately, many L2O lack converge guarantees. To fuse advantages of approaches, we present a Safe-L2O framework. updates incorporate safeguard guarantee convergence for convex proximal and/or gradient oracles. The is simple computationally cheap implement, it activated only when would perform poorly or appear diverge. This yields numerical benefits employing machine learning create rapid while still guaranteeing convergence. Our examples show algorithms, even provided data not from distribution training