论文标题
非指数加权聚合：无限损失功能的遗憾范围
Non-exponentially weighted aggregation: regret bounds for unbounded loss functions
论文作者
论文摘要
我们通过一般（可能是无限的损失功能）解决在线优化问题。众所周知，当损失界限时，指数加权的聚合策略（EWA）会导致$ \ sqrt {t} $在$ t $ steps之后感到遗憾。在本文中，我们研究了一种广义的聚合策略，在该策略中，权重不再取决于损失。我们的策略基于遵循正规领导者（FTRL）的基础：我们最大程度地减少了预期的损失以及正规机，这就是$ ϕ $ divergence。当常规器是kullback-leibler差异时，我们将EWA作为特殊情况。使用替代差异可以实现无限的损失，而在某些情况下以最坏的遗憾为代价。
We tackle the problem of online optimization with a general, possibly unbounded, loss function. It is well known that when the loss is bounded, the exponentially weighted aggregation strategy (EWA) leads to a regret in $\sqrt{T}$ after $T$ steps. In this paper, we study a generalized aggregation strategy, where the weights no longer depend exponentially on the losses. Our strategy is based on Follow The Regularized Leader (FTRL): we minimize the expected losses plus a regularizer, that is here a $ϕ$-divergence. When the regularizer is the Kullback-Leibler divergence, we obtain EWA as a special case. Using alternative divergences enables unbounded losses, at the cost of a worst regret bound in some cases.
