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We consider the problem of online learning with non-convex losses. In termsof feedback, we assume that the learner observes - or otherwise constructs - aninexact model for the loss function encountered at each stage, and we propose amixed-strategy learning policy based on dual averaging. In this generalcontext, we derive a series of tight regret minimization guarantees, both forthe learner's static (external) regret, as well as the regret incurred againstthe best dynamic policy in hindsight. Subsequently, we apply this generaltemplate to the case where the learner only has access to the actual lossincurred at each stage of the process. This is achieved by means of akernel-based estimator which generates an inexact model for each round's lossfunction using only the learner's realized losses as input.

Online non-convex optimization with imperfect feedback