  We consider an online learning process to forecast a sequence of outcomes for
nonconvex models. A typical measure to evaluate online learning algorithms is
regret but such standard definition of regret is intractable for nonconvex
models even in offline settings. Hence, gradient based definition of regrets
are common for both offline and online nonconvex problems. Recently, a notion
of local gradient based regret was introduced. Inspired by the concept of
calibration and a local gradient based regret, we introduce another definition
of regret and we discuss why our definition is more interpretable for
forecasting problems. We also provide bound analysis for our regret under
certain assumptions.
